The explicit formula for the arithmetic sequence 12, 5, -2, -9,..is a(n) = -7n + 19.
To find the explicit formula for this arithmetic sequence, we first need to determine the common difference, which is the amount by which each term differs from the previous term.
d = 5 - 12 = -7
d = -2 - 5 = -7
d = -9 - (-2) = -7
Since the common difference is -7, we can use the formula for an arithmetic sequence:
a(n) = a (1) + (n - 1) d
where a(n) is the nth term of the sequence, a (1) is the first term, n is the term number, and d is the common difference.
Plugging in the given values, we get:
a(n) = 12 + (n - 1) (-7)
Simplifying, we get:
a(n) = -7n + 19
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The explicit formula for the arithmetic sequence will be f(n) = 19 -7n.
f(n) = a + (n - 1) d,
where an is the first term and is the explicit formula for an arithmetic series.
d = Common Difference
n = number of terms
The provided arithmetic series is = 12, 5, -2, -9.
First term: a = 12.
Common variation: d= 5-12= 7
[Difference between any two words that follow one another.]
When a = 12 and d = -7 are entered into equation (1), we obtain
f(n) = 12 + (n - 1) ( - 7 )
Thus, the explicit formula for the above arithmetic sequence is
f(n) = 12 = (n - 1). ( - 7 )
If we continue to solve it, we obtain
f(n) = 12 - 7n + 7
f(n) = 19 - 7n
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What is the difference between the simple and compound interest if you borrow $3,000 at a 6% interest rate for 2 years?
$180.00
$10.00
$6.00
$80.00
Answer:
Correct option is C)
Simple interest =
100
3000×6×2
=360
Compound interest =3000(1+
100
6
)
2
−3000=18×20.6=370.8
∴ Difference is Rs.10.8.
you can convert this value to $$
or simply the answer will be 2. $10
(hob-evzw-zjw) come
Answer:
B is your answer.
10.80$ which you just round to 10. 10 is your answer.
Step-by-step explanation:
For simple interest, the formula is:
Simple Interest = Principal × Rate × Time
For compound interest, the formula is:
Compound Interest = Principal × (1 + Rate)^Time - Principal
Let's calculate the values:
Principal = $3,000
Rate = 6% or 0.06
Time = 2 years
Simple Interest = $3,000 × 0.06 × 2 = $360
To calculate compound interest, we need to use the formula:
Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000
= $3,000 × (1.06)^2 - $3,000
= $3,000 × 1.1236 - $3,000
= $3,370.80 - $3,000
= $370.80
The difference between simple and compound interest is:
$370.80 - $360 = $10.80
hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.
The steps for proof by mathematical induction that P(n) is true for all positive integers n, All options are true.
The steps for a proof by mathematical induction that P(n) is true for all positive integers n are as follows:
a. Verify that P(1) is true.
b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k.
c. Verify that P(1), P(2), P(3), ..., P(k) is all true, where k is a specific large, positive integer.
d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k.
e. Demonstrate that P(k+1) implies Plk) is true for all integers k.
Therefore, option (a), option (b), option (c), option (d), and option (e) are the steps for proof by mathematical induction that P(n) is true for all positive integers n.
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Find the length of the missing side
A. 21
B. 22
C. 23
D. 24
Answer:
D
Step-by-step explanation:
Pythag theorem for right triangles
c^2 = a ^2 + b^2
25 ^2 = 7^2 + ?^2
25^2 - 7^2 = ?^2
?^2 = 576
? = 24 units
QRT=(3x+5)
TRS=(10x-7)
Find the measure of each angle.
Answer:
I'm sorry, but the given expressions QRT and TRS do not seem to correspond to angles. They appear to be algebraic expressions involving variables x. Without further information or context, it is not possible to determine any angles or measures of angles.
Please provide additional information or clarify the question.
what is the area of ABC
The answer of the given question based on the finding the area of the triangle of ABC the answer is the area of triangle ABC is approximately 62.82 square cm.
What is Triangle?A triangle is three-sided polygon with three angles. It is two-dimensional geometric shape, and one of basic shapes in geometry. A triangle can be classified based on length of its sides and measure of its angles. The sum of the interior angles of triangle are 180 degrees. Triangles are used in many fields, like mathematics, engineering, architecture, and art.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
where the base is one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
In this case, we know that AB = 11 cm and AC = 17 cm, and angle A is 45 degrees. To find the height of the triangle, we need to use trigonometry.
First, we can find the length of BC using the Law of Cosines:
BC² = AB² + AC² - 2 * AB * AC * cos(A)
BC² = 11² + 17² - 2 * 11 * 17 * cos(45)
BC² = 156 - 265.42
BC² = 109.42
BC = 10.46 cm (rounded to two decimal places)
Now we can use the sine function to find the height of the triangle:
sin(A) = height / BC
height = BC * sin(A)
height = 10.46 * sin(45)
height = 7.39 cm (rounded to two decimal places)
Finally, we can use the area formula to find the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 * 7.39
Area = 62.82 square cm (rounded to two decimal places)
Therefore, the area of triangle ABC is approximately 62.82 square cm.
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5.4 ADDING A MULTIPLE OF THE ith ROW TO THE jth row. Example 6: Create a 5 by 5 matrix, E by typing: Type: Ε=[11 2-134:10-1-2-1; 8 3 2 11:10-2-3-2:1112-1]. Find det(E) by typing: Type DE =det(E)
The `det(E2) of the given matrix is equal to 366`.
Given a 5 by 5 matrix E= `[11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;2 -1 -2 1 1]`.
To find `det(E)`, we can use the following steps.
Step 1: Create a 5 by 5 matrix E1 by adding a multiple of the ith row to the jth row, given i = 3 and j = 5.
We need to add -1/3 times the 3rd row to the 5th row. It can be done by the following operation.`E1 = E` (start with the original matrix) `=> E1(5,:) = E(5,:) - E(3,:) / 3` (subtract the 3rd row of E divided by 3 from the 5th row of E)
This results in the matrix `E1 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;1/3 -7/3 -7/3 7/3 4/3]
`Step 2: Create a 5 by 5 matrix E2 by adding a multiple of the ith row to the jth row, given i = 2 and j = 5.We need to add -20 times the 2nd row to the 5th row.
It can be done by the following operation.`E2 = E1` (start with the matrix from Step 1) `=> E2(5,:) = E1(5,:) - 20 * E1(2,:)` (subtract 20 times the 2nd row of E1 from the 5th row of E1)
This results in the matrix `E2 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;0 -13 33 -13 44]
`Step 3: Find det(E2) by using the cofactor expansion along the 5th column.`det(E2) = 0 - (-13) * A1 + 33 * A2 - (-13) * A3 + 44 * A4 - 0 * A5`where A1, A2, A3, A4, and A5 are the 2 by 2 determinants of the submatrices obtained by deleting the 5th row and the ith column, for i = 1, 2, 3, 4, and 5. We can use the following notation.
A1 = det([11 -1 -3 4;10 -2 -1 -2;-1 3 2 1;]) = 324A2 = det([11 2 -3 4;10 -1 -1 -2;-1 2 2 1;]) = -54A3 = det([11 2 -1 4;10 -1 -2 -2;-1 2 3 1;]) = -142A4 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 50A5 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 366.
Therefore `det(E2) = 0 - (-13) * 324 + 33 * (-54) - (-13) * (-142) + 44 * 50 - 0 * 50 = 366`.
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Write the reciprical of 2/3
Answer:
the answer is 3/2
Step-by-step explanation:
Answer:
the answer si 3/2
Whats 21 square root of 98 divided by 7 square root of 21
The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407
A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.
Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.
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find the number equivalant to the ratio 25:6
Answer:
A ratio of 25 to 6 can be written as 25 to 6, 25:6, or 25/6. Furthermore, 25 and 6 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on. A ratio of 25 to 6 simply means that for every 25 of something, there are 6 of something else, with a total of 31
Step-by-step explanation:
done hope u like it !!
Jack's school is selling tickets to a spring Musical on the first day of ticket sales for school so 46 senior citizen tickets and 44 a child tickets for total of 362 the school took in 85 on the second day by selling two senior citizen tickets and 25 child tickets Bonnie price of a senior citizen ticket and the price of a child ticket.
On the first day of ticket sales for the school’s spring musical, 46 senior citizen tickets and 44 child tickets were sold, bringing the total number of tickets sold to 362.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.
The second day saw a slightly lower number of tickets sold, with two senior citizen tickets and 25 child tickets purchased, for a total of 85. The price of a senior citizen ticket and a child ticket was likely the same on both days, and likely the same price as it is for the rest of the ticket sales.
The school likely has a set price for tickets, which would not change as the number goes up or down. It is common for schools to give discounts for senior citizens, so the price of their tickets is usually lower than the price of a child ticket. The school set the prices of the tickets in a way that would bring in the most money, while still being affordable for the community to attend.
The school likely had a plan in place for how many tickets they wanted to sell and what prices they wanted to set. They also likely had a goal of how much money they wanted to bring in from the ticket sales. After the two days of ticket sales, the school was able to see how many tickets were sold and how much money was collected. This can help the school to adjust their plan, if necessary, to reach their goal.
The money brought in from the ticket sales will likely help the school to cover the costs of putting on the musical. It may also help to pay for any other expenses associated with the production of the show. The school may also use the money to purchase new materials or supplies for the performing arts department.
Overall, the school was able to bring in a total of 447 from the two days of ticket sales. This money will help to ensure that the school’s spring musical is a success. The school was also able to offer discounted tickets to senior citizens, which allowed more people to attend the show.
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The price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.
Jack's school is selling tickets to a spring Musical. On the first day of ticket sales, the school sold a total of 362 tickets, 46 of which were senior citizen tickets and 44 of which were child tickets. On the second day of ticket sales, the school sold two senior citizen tickets and 25 child tickets, for a total of 85 tickets.
To calculate the price of each ticket, we can divide the total amount taken in by the number of tickets sold. For senior citizen tickets, the total amount taken in was 85, and two were sold, so the price of a senior citizen ticket is 85/2 = 42.50. For child tickets, the total amount taken in was 85, and 25 were sold, so the price of a child ticket is 85/25 = 3.40.
In conclusion, the price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.
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A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
h(t) = −16t2 + ? t + ?
maximum height:
The ball reaches a maximum height of approximately 146 feet, to the nearest foot.
What exactly does the term Maximus height mean?Maximum Height refers to the highest point of the structure or sign as measured from the average natural ground level at the base of the supporting structure.
The ball is thrown upward with an initial velocity of 75 feet per second, implying that v0 = 75. We are also told that the ball is thrown from a height of 4 feet, implying that h0 = 4.
The function: can be used to model the ball's vertical motion.
16t2 + v0t + h0 = h(t).
Substituting v0 and h0 values yields:
h(t) = -16t^2 + 75t + 4
To determine the maximum height of the ball, we must first locate the vertex of the parabolic function h. (t). The vertex of the parabola is given by the equation y = ax2 + bx + c:
x = -b / 2a
y = c - b^2 / 4a
a = -16, b = 75, and c = 4 in this case. Substituting these values into the above formulas yields:
t = -75 / 2(-16) = 2.34 sec
h(t) = 4 - (752) / (4(-16)) 146 ft.
As a result, the ball reaches a maximum height of about 146 feet to the nearest foot.
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The exponential probability distribution is used with: A. A discrete random variable B. A continuous random variable C. Any probability distribution with an exponential term D. An approximation of the binomial probability distribution
The exponential probability distribution is employed with a random variable that is continuous in nature.
What do you mean by exponential probability distribution ?
In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.
Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.
The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].
The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.
In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.
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Find the measures of one exterior angle of a regular polygon if the sum of the interior angles is 3960 degrees.
The exteriοr angle οf the pοlygοn is 15°.
What is pοlygοn?A pοlygοn has as many pairs οf interiοr and exteriοr as number οf its sides. Further each pair οf exteriοr and interiοr add up tο 180°.
Sum οf all the exteriοr angles οf any pοlygοn is 360°.
As sum οf all the interiοr angles οf the pοlygοn is 3960°.
Sum οf all pairs οf exteriοr and interiοr angles is
=> 3960°+360°=4320°
As each pair is 180° , Number οf sides οf pοlygοn = 4320/180 = 24
Sum οf exteriοr angles is always 360° and if pοlygοn is regular (i.e. all sides and angles are equal), size οf each exteriοr angle is
=> 360°/24 = 15°
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Solve for x in the triangle.
Answer:
D. 87
Step-by-step explanation:
You want to know the measure of the angle opposite the longest side in a triangle with side lengths 13, 16, and 20 inches.
Angle relationsThe angle x is opposite the side of length 20 inches in this triangle, which is the longest side. That tells you x is the largest angle.
The largest angle in any triangle is never less than 60°. This eliminates all answer choices except the last one:
x = 87
Law of CosinesIf you want to go to the trouble to solve the triangle, the law of cosines is helpful. For sides a, b, c and angle C, it tells you ...
c² = a² +b² -2ab·cos(C)
Solving for the angle, we have ...
C = arccos((a² +b² -c²)/(2ab))
C = arccos((13² +16² -20²)/(2·13·16)) = arccos(25/416) ≈ 86.55°
x ≈ 87
When Beth returns from holiday she changes €120 back into pounds. The exchange rate is now £1 = €1.16 (b) Work out how many pounds (£) Beth receives.
Beth receives £103.45 when she changes €120 back into pounds.
What is exchange rate?An exchange rate is the value of one currency expressed in terms of another currency. In other words, it is the rate at which one currency can be exchanged for another currency.
What is pound?Pound is a unit of currency that is used in several countries, including the United Kingdom, Egypt, Lebanon, and Sudan, among others. The pound symbol is "£".
In the given question,
If the exchange rate is £1 = €1.16, this means that for every euro, Beth will get £1/€1.16.
Therefore, the number of pounds Beth receives when she changes €120 back into pounds is:
120 euros * £1/€1.16 = £103.45 (rounded to two decimal places)
So Beth receives £103.45 when she changes €120 back into pounds.
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Winning the jackpot in a particular lottery requires that you selet the correct four numbers between 1 and 59 and, in a separate drawing, you must also select the correct single number between 1 and 41. Find the probability of winning the jackpot.
The probability of winning the jackpot is __ .
The probability of selecting the correct four numbers out of 59 is solved by the formula :
P(4 correct numbers) = (number of ways to choose 4 correct numbers) / (total number of possible 4-number combinations)
The total number of possible 4-number combinations out of 59 is:
C(4,59) = (59 choose 4) = 190,578
P(jackpot) = P(4 correct numbers) * P(1 correct number)
P(jackpot) = 1/41
thus, the probability of winning the jackpot in this particular lottery is 1/41.'
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The following financial data are for the dental practice of Dr. Ortiz when he began operations in July. Determine the amount that would appear in Dr. Ortiz’s balance sheet.
1. Owes $42,000 to the Sanderson Equipment Company.
2. Has cash balance of $31,000.
3. Has dental supplies $11,300.
4. Owes $13,360 to Galaxy Furniture Supply.
5. Has dental equipment of $57,100.
6. Had office furniture of $20,000.
By answering the presented question, we may conclude that Sanderson amount Equipment Company owes $42,000 Galaxy Furniture Supply owes $13,360. $55,360 in total liabilities
what is amount ?aggregate attempting to determine the time required, total number or amount. The quantity at sight or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, or a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity signifies how much there still is, how often you have, the amount you require, or the amount that you get. He needs that quantity of cash to get by.
The following figures would appear on Dr. Ortiz's balance sheet:
Assets:
Cash: $31,000
$11,300 for dental supplies
$57,100 for dental equipment
$20,000 for office furnishings
The total value of the assets is $119,400.
Liabilities:
Sanderson Equipment Company owes $42,000
Galaxy Furniture Supply owes $13,360.
$55,360 in total liabilities
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1. Use the data in hprice1.dta to estimate an OLS model that relates house price in thousands of dollars to the house size measured in square feet (i.e., the variable sqrft) and the number of bedrooms in the house (bdrms). Write it the result in equation form.
2. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
3. What is the estimated increase in price for a house additional bedroom that is 140 square feet in size? Compare this to your answer in question two above.
4. What percentage of the variation in price is explained by square footage and number of bedrooms?
5. The first house in the sample has sqrft=2,438 and bdrms=4. Find the predicted price for this house using the model you estimated above.
6. The actual selling price of the first house in the sample was $300,000 (i.e. price= 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
In the following question, among the various parts to solve on houses - 1. price = β0 + β1sqrft + β2bdrms, 2. β2, 3. β2 + 140β1, 4. R-squared value is provided in the regression output, 5. 276.878 thousand dollars, 6. 23.122.
1. The regression equation of house price in thousands of dollars to the house size measured in square feet (sqft) and the number of bedrooms in the house (bdrms) can be written as follows: price = β0 + β1sqrft + β2bdrms Here, price refers to the house price in thousands of dollars, sqft refers to the house size measured in square feet and bdrms refers to the number of bedrooms in the house.
2. The estimated increase in price for a house with one more bedroom, holding square footage constant is equal to the coefficient of bdrms in the regression equation, which is β2.
3. The estimated increase in price for a house with an additional bedroom that is 140 square feet in size can be calculated as follows: β2 + 140β1. Comparing this to the answer in question two above, we can see that the price increase is greater when an additional 140 square feet are added to the house rather than an additional bedroom.
4. The percentage of the variation in price explained by square footage and the number of bedrooms can be found using the R-squared value. The R-squared value is a measure of how much of the variation in the dependent variable (house price) is explained by the independent variables (sqft and bdrms). In this case, the R-squared value is provided in the regression output.
5. To find the predicted price for the first house in the sample using the model estimated above, we need to plug in the values of sqft and bdrms for the first house into the regression equation. Here, sqrft = 2,438 and bdrms = 4. Thus, the predicted price for the first house is given by: price = β0 + β1sqrft + β2bdrms = -14.973 + 0.128sqrft + 15.204bdrms = -14.973 + 0.128(2,438) + 15.204(4) = 276.878 thousand dollars.
6. The residual for the first house in the sample can be calculated as follows: Residual = Actual price - Predicted price = 300 - 276.878 = 23.122. The fact that the residual is positive suggests that the buyer overpaid for the house.
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what is the squar root of 2,100
Answer:
The square root of 2,100 is approximately 45.8257569495584 when rounded to 15 decimal places.
Find the tangential and normal components of the acceleration vector for the curve → r ( t ) = 〈 − 3 t , − 5 t ^ 2 , − 2 t ^ 4 〉 at the point t = 1
The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459
How do we calculate the tangential component?The acceleration vector can be found from the following formula:
[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]
To find the tangential component of the acceleration vector, we first need the velocity vector v(t).
[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]
Next, we need to normalize the velocity vector using the following formula:
[tex]T(t) = v(t) / ||v(t)||,[/tex]
Where ||v(t)|| is the magnitude of the velocity vector.
[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]
Then, the tangential component of a(1) is:
[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]
How do we calculate the normal component?To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.
[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)} = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]
Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:
[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]
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What will be the exponent of the product of 8.9 x 1012 and 4.7 x 10-2 in Scientific Notation?
the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.
define exponentialExponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.
First, we multiply the two numbers:
(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰
41.83 x 10¹⁰ = 4.183 x 10¹¹
Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.
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The dwarf lantern shark is the smallest shark in the world. At birth, it is about 55 millimeters long. As an adult, it is only 3 times as long. How many centimeters long is an adult dwarf lantern shark? centimeters
Answer: 165
Step-by-step explanation:
55 x 3 = 165
Consider a hash table, a hash function of key % 10. Which of the following programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation? O c1 = 1 and 2 = 0 O c1 = 5 and c2 = 1 O c1 = 1 and c2 - 5 O c1 = 10 and 2
D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.
The quadratic probing equation is defined as:
h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,
where h′(k) is the hash value of key
k and m is the size of the hash table.
The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.
The given hash function is h(k) = k % 10.
Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:
Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.
Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.
Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.
Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.
Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.
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without calculation, find one eigenvalue and two linearly independent eigenvectors of a d 2 4 5 5 5 5 5 5 5 5 5 3 5 . justify your answer.
The eigenvalues of A are λ = 0 (with multiplicity 1) and λ = 5 (with multiplicity 2), and the corresponding eigenvectors are [1, 0, -1], [0, 1, -1], and [1, -1, 1].
The matrix A = [5 5 5; 5 5 5; 5 5 5] is a 3x3 matrix with all entries equal to 5.
First, we can calculate the determinant of A - λI, where I is the identity matrix and λ is an unknown eigenvalue:
A - λI = [5-λ 5 5; 5 5-λ 5; 5 5 5-λ]
det(A - λI) = (5-λ)[(5-λ)(5-λ)-25] - 5[5(5-λ)-25] + 5[5-25]
= (5-λ)(λ^2 - 15λ) = -λ(λ-5)^2
From this equation, we can see that the eigenvalues are λ = 0 and λ = 5 (with multiplicity 2).
To find the eigenvectors, we can substitute each eigenvalue into the equation (A - λI)x = 0 and solve for x.
For λ = 0, we have:
A - 0I = A = [5 5 5; 5 5 5; 5 5 5]
(A - 0I)x = 0x = [0 0 0]
This implies that any vector of the form [a, b, -a-b] is an eigenvector for λ = 0. For example, we can choose [1, 0, -1] and [0, 1, -1] as linearly independent eigenvectors corresponding to λ = 0.
For λ = 5, we have:
A - 5I = [0 5 5; 5 0 5; 5 5 0]
(A - 5I)x = 0
⇒ 5x2 + 5x3 = 0
⇒ 5x1 + 5x3 = 0
⇒ 5x1 + 5x2 = 0
This implies that any vector of the form [1, -1, 1] is an eigenvector for λ = 5. Therefore, we can choose [1, -1, 1] as another linearly independent eigenvector corresponding to λ = 5.
Eigenvectors are a fundamental concept in linear algebra. They are essentially special vectors that remain in the same direction when a linear transformation is applied to them, only changing in magnitude. In other words, an eigenvector of a linear transformation is a vector that when multiplied by the transformation matrix, results in a scalar multiple of itself.
Eigenvectors play a crucial role in diagonalizing matrices, which can simplify calculations involving matrix operations. They are also useful for solving differential equations and understanding the behavior of dynamic systems. In addition, eigenvectors are often used for data analysis, such as in principal component analysis (PCA), which is a technique for reducing the dimensionality of data.
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a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is
The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
The probability that there are no repeated digits in a 3-digit pin number is 0.72.
Formula used:
[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]
There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.
Therefore, the total number of possible 3-digit pin numbers with no repeated digits is
[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]
The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].
Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.
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The population of Toledo, Ohio, in 2000 was approximately 500,000. Assume the population is increasing at a rate of 5% per year. a. Write the exponential function that relates the total population as a function of t. b. Use a. to determine the rate at which the population is increasing in t years. c. Use b. to determine the rate at which the population is increasing in 10 years.
The population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.
What is exponential function?An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a positive constant called the base, and "x" is a variable that can take on any real value. The base "a" is typically greater than 1, which means the function grows at an increasing rate as "x" increases.
According to question:a. The exponential function that relates the total population as a function of t is given by:
P(t) = P₀ × (1 + r)ᵗ
where P₀ is the initial population, r is the annual growth rate (as a decimal), and t is the time in years.
Using the given values, we have:
P₀ = 500,000 (given)
r = 0.05 (5% expressed as a decimal)
Thus, the exponential function is:
P(t) = 500,000 × (1 + 0.05)ᵗ
b. The rate at which the population is increasing in t years is given by the derivative of the population function with respect to time:
dP/dt = P₀ × r × (1 + r)ᵗ
Substituting the given values, we get:
dP/dt = 500,000 × 0.05 × (1 + 0.05)ᵗ
c. To determine the rate at which the population is increasing in 10 years, we simply substitute t = 10 into the expression we derived in part b:
dP/dt = 500,000 × 0.05 × (1 + 0.05)¹⁰
Using a calculator, we get:
dP/dt ≈ 32,263
Therefore, the population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.
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Consider the function f left parenthesis x right parenthesis equals cube root of x near x equals 8. Find the linear approximation error when using the linear approximation to estimate cube root of 8.25 end root.
The linear approximation error when using the linear approximation to estimate the cube root of 8.25 is 0.0593.
When we want to find the linear approximation error, we can use the formula
Error = f(x) - L(x),
Where `f(x)` is the actual value of the function at `x`, and `L(x)` is the linear approximation of the function at `x`.
The linear approximation of a function f(x) near x=a is given by:
L(x) = f(a) + f'(a)(x-a)
In this case, we want to find the linear approximation of the function f(x) = cube root of x near x=8. To do so, we first need to find the value of f(8) and f'(8).
f(8) = cube root of 8 ⇒ 2
To find f'(8), we take the derivative of f(x) with respect to x:
f(x) = x^(1/3)
f'(x) = (1/3)x^(-2/3)
So, f'(8) = (1/3)(8)^(-2/3) ⇒ 1/12
Therefore, the linear approximation of f(x) near x=8 is:
L(x) = 2 + (1/12)(x-8)
Now, we want to use this linear approximation to estimate the value of the cube root of 8.25. To do so, we substitute x=8.25 into the linear approximation:
L(8.25) = 2 + (1/12)(8.25-8) ⇒ 2.0208
The actual value of the cube root of 8.25 is:
∛8.25 ⇒ 2.0801
So, the error in the linear approximation is:
2.0801 - 2.0208 ⇒ 0.0593
Therefore, the linear approximation error when using the linear approximation to estimate a cube root of 8.25 is approximately 0.0593.
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Write as a single power of 3:
27divided by 9a
Answer:
Step-by-step explanation:
27/9a
= 3^3/3^2 a
= 3/a
I need help with answer this question
Answer:
y = 2x/15 + 6
Step-by-step explanation:
3y/2 = x/5 + 9
3y = (x/5 + 9) (2) The 2 that was dividing goes on to multiply on the other side.
3y= 2x/5 + 18
y = (2x/5 + 18) / 3 The 3 that was multiplying goes on to divide on the other side.
y = 2x/15 + 6
I need help please i will give you stars and 12 points
Answer:
5:3 = 5/3
Step-by-step explanation:
Given Sin∅ = 3/5
We know sin∅ = Perpendicular/Hypotenuse
And, By inverse relationship, we get
cosec∅ = Hypotenuse/Perpendicular = 1/sin∅
So, csc∅ = 5/3, 5:3
