Answer:
12b (1-2) -n (u-8) this is the answer
MAthematics pls help
Answer:
x = 4
Step-by-step explanation:
6x + 21 = 5x + 25
Then, subtract 5x from both sides:
x + 21 = 25
Then, subtract 21 from both sides.
x = 4
Therefore, x is equal to 4 degrees
Below is a list of all possible outcomes in the experiment of rolling two die. 1.2 1,3 14 15 1,6 21 22 23 24 25 2,6 34B2 33 3,4 3 5 3.6 41 4 2 43 4,4 4 5 4,6 5 52 33 5 4 5,5 56 6,1 6,2 6.3 6 4 6,5 6.6 Determine the following probabilities. Write your answers as reduced fractions_ P(sum is odd) P(sum is 5) P(sum is 7) = P(sum is 7 and at least one of the die is a 1) = 18 P(sum is 7 or at least one of the die is 1) = 36
Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12
Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.
In the given experiment of rolling two dice, the following probabilities are to be determined:
P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:
1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15
Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.
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Write a numerical expression for the verbal expression. The quotient of thirty-two and four divided by the sum of one and three
The numerical expression for the verbal expression "The quotient of thirty-two and four divided by the sum of one and three" is 2.
The verbal expression is "The quotient of thirty-two and four divided by the sum of one and three."
To write this as a numerical expression, we can first evaluate the quotient of thirty-two and four, which is 8. Then we can divide 8 by the sum of one and three, which is 4.
Therefore, the numerical expression for the verbal expression is:
= 8 ÷ (1 + 3)
Add the number
= 8 ÷ 4
Divide the numbers
= 2
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Find the interest refund on a 35-month loan with interest of $2,802 if the loan is paid in full with 13 months remaining.
Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
Find k so that and will be orthogonal (form a 90 degree angle).
The [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex] are orthogonal.So, the value of k is 8/3.
What is Vector?A quantity or phenomenon with separate characteristics for both magnitude and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, energy, electromagnetic fields, and weight are a few examples of vectors in nature.
Two vectors are orthogonal if and only if their dot product is zero. Therefore, we need to find the value of k such that the dot product of [tex]$\vec{a}$[/tex] and[tex]$\vec{b}$[/tex] [tex]$\vec{b}$[/tex][tex]\vec{b}[/tex] is zero.
The dot product of [tex]$\vec{a}$[/tex] and [tex]$\vec{b}$[/tex] is given by:
[tex]$$\vec{a} \cdot \vec{b} = (2)(-4) + (3)(k) = -8 + 3k$$[/tex]
For the vectors to be orthogonal, their dot product must be zero, so we set -8 + 3k = 0 and solve for k:
-8 + 3k = 0
3k = 8
[tex]$k = \frac{8}{3}$$[/tex]
Therefore, [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex] are orthogonal.So, the value of k is 8/3.
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What is the decimal of 2 75/100
2.75 is the decimal of fraction .
In math, what is a fraction?
The amount is represented mathematically as a quotient, where the numerator and denominator are split. In a simple fraction, both are integers. A complicated fraction includes a fraction, either in the denominator or the numerator.
The numerator and denominator must be smaller in a proper fraction. A fraction is a number that is a component of a whole. A whole is appraised by dissecting it into many sections. Half of a whole number or item, for instance, is represented by the number 12.
= [tex]2\frac{75}{100}[/tex]
= [tex]2\frac{3}{4}[/tex]
= 11/4
= 2.75
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Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours, when the average speed is 90 km/h. Find the distance of between the two towns
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours when the average speed is 90 km/h. the distance between the two towns is 60 km.
Considering the distance between the Winston and carver be "d", since here we got that during off-peak hours, the average speed is 90 km/h. so by using the formula of distance which is distance =speed x time=> d = 90t.
Whereas in rush hour, the average speed is 75 km/h, we also know that the trip takes 8 minutes longer during rush hour. calling the time it takes to travel during rush hour "t+8/60"( since 8 minutes is 8/60 of an hour). Now using the same formula as before:
d = 75(t + 8/60), since here we have two equations for d we can equal them to each other then we get :
90t = 75(t + 8/60)
=>90t = 75t + 10
=>90t-75t=10
=>t = 2/3
Since during the off-peak hours, it takes 2/3 hours or 40 minutes to travel the distance between Winston and carver. now using either equation to find the distance we get
d = 90t = 90(2/3) = 60 km or d = 75(t + 8/60) = 75(2/3 + 8/60) = 60 km
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Sarun is thrice as old as his sister Anita. If five years is subtracted from Anita’s age and seven years added to Sarun’s age , then
Sarun will be five times Anita’s age. How old were they three years ago?
Answer:
Anita is 11 years old and sarun 55 years old( not so sure about this answer... what do you think)
Step-by-step explanation:
let Anita's age be x
and sarun's age be 3x
if, x-5 = 3x+7
3x+7 = 5(x-5)
3x+7=5x-25
32=2x
x=16
their ages 3 years ago,
Anita= 16-5=11yrs
sarun= 3*16+7 = 55yrs
if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
the height of the akashi kaikyo bridge from the bride deck to the top of the center support is 297 meters and the distance from the center of the bridge to the connection of the suspension cable is 995 meters. (see picture below.) i would like you to find the angle of depression from the top of the center support to the end of the support cable.
The angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.
The angle of depression from the top of the center support to the end of the support cable can be found using trigonometry. Let's call this angle "x". Using the given information, we can form a right triangle with the center support, the end of the support cable, and a point directly below the center support on the ground.
The height of the center support, 297 meters, is the opposite side of the right triangle, while the distance from the center of the bridge to the connection of the suspension cable, 995 meters, is the adjacent side. Using the tangent function, we can calculate the angle of depression as follows:
tan(x) = opposite/adjacent
tan(x) = 297/995
x = tan^-1(297/995)
Using a calculator, we can find that x is approximately 16.59 degrees. Therefore, the angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.
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A car is purchased for £8500
In its first year, the value of the car will depreciate
by 10%.
Each year after that, the value of the car will
depreciate by 5%.
What is the value of the car at the end of 3 years?
Answer:
£ 6904.13
Step-by-step explanation:
the final value is given by
[tex]8500 (0.90)[/tex] at the final of the first year
then you need to add (0.95) twice (one from second and one from third year)
Notice if the depreciation is 5% the final value is 0.95 of the initial value at the beginning of the year
finally:
[tex]8500 (0.90) (0.95)^2 = 6904.13[/tex] (rounded to nearest cent!)
22 The regular selling price is a 22" tube television is $389. The markdown rate is 33%. Use the
percent paid to determine the sale price.
A. $245.34
C. $260.63
B. $267.89
D. $287.56
The Sale price is C. $260.63.
What is selling price?Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.
What is sale price?Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.
In the given question,
To find the sale price, we need to first calculate the amount of the markdown:
Markdown = Regular Price x Markdown Rate
Markdown = $389 x 0.33
Markdown = $128.37
The sale price is then the regular price minus the markdown:
Sale Price = Regular Price - Markdown
Sale Price = $389 - $128.37
Sale Price = $260.63
Therefore, the answer is C. $260.63.
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Using the given variable, write an inequality to model the scenario.
Bowlers that score at least 228 points will make it to the next round.
Let p = the number of points
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: 25:68
Step-by-step explanation:
If 68 is the total number of students, and 25 is the number of students who have vanilla, the ratio of the number of students who have vanilla to the total number of students is 25:68.
The ratio of the number of students who have chocolate to the total number of students is [tex]\frac{43}{68}[/tex]
In the above question it is given that,
There are students some of them have gotten the vanilla ice-cream and some have chocolate ice-cream
The total number of students are = 68
The number of students who had vanilla ice-cream are = 25
The number of students who had chocolate ice-cream are = 68 - 25 = 43
We need to find the ratio of the number of students who have chocolate to the total number of students
Therefore, the ratio of the number of students who have chocolate to the total number of students = [tex]\frac{43}{68}[/tex]
Hence, the ratio of the number of students who have chocolate to the total number of students is [tex]\frac{43}{68}[/tex]
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what is the z-score for the 75th percentile of the standard normal distribution is: 0.67 1.645 1.28 -0.67 -1.28
The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.
The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.
I found one that shows the following:
Z value Table entry
0.67 0.7486
0.68 0.7517
As a result, the Z value for 0.75 is between 0.67 and 0.68.
Interpolation yields the z value of 0.6745.
If you have a TI-84 calculator, you may calculate the z value as follows:
VARS - 2nd (this will show the DISTR menu)
To select invNorm, press 3.
Enter the value for the area/table (0.75)
If you press enter, it will return the z value.
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Complete question:
what is the z-score for the 75th percentile of the standard normal distribution is:
0.67 1.645 1.28 -0.67 -1.28what is the solution to the equality shown?
3m+5>2(m-7)
Hello,
3m + 5 > 2(m - 7) =
3m + 5 > 2m - 14
3m - 2m > - 14 - 15
x > - 29
Step-by-step explanation:
3m±2m>-14-5
5m>-19
m>-19/5
m>3.8
if two sides of a square field were increased by five feet, as seen in the diagram, the area of the field would increase by 245 ft2 . find the area of the original square
If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².
To find the area of the original square, we can use the following formula:
Area of the original square = x²
where x is the original length of the square field.
Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².
Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:
(x + 5)² = 245 + x²
Expanding the left-hand side of the equation and simplifying, we get:
x² + 10x + 25 = 245 + x²
Solving for x, we get:
10x + 25 = 245
x = 22
Plugging x = 22 into the formula, we can find the area of the original square:
Area of the original square = x² = 22² = 484 ft²
Therefore, the area of the original square is 484 ft².
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5. Line 1 passes through the point D(2, 4) and has the same slope as the line segment joining
M(4, 5) and N(6, -19). Determine the equation of Line 1 in the form y = mx + b.
The equation of Line 1 in the form y=-12x+28
What is a Line Segment?A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.
Coordinates of Line 2 M(4,5) and N(6,-19)
Slope of Line 2 is =(-19-5)/(6-4)
=-24/2=-12
Slope of line 1 and line 2 are same
Cordinate of Line 1 is D(2,4)
D(2,4) must pass through line 1, so it must satisfy the equation
y=mx+b
4=2(-12)+b
4+24=b
b=28
the equation of Line 1 in the form y=-12x+28
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Tickets for the school play cost $5 for students and $8 for adults. For one performance, 128 tickets were sold for $751. How many tickets were for adults and how many were for students?
91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.
What is elimination method?The elimination method is a technique for solving a system of linear equations, which involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable.
According to question:Let x be the number of student tickets sold, and y be the number of adult tickets sold. Then we can set up a system of two equations to represent the information given:
x + y = 128 (1) (the total number of tickets sold is 128)
5x + 8y = 751 (2) (the total revenue from ticket sales is $751)
We can solve for one of the variables in terms of the other in the first equation:
x = 128 - y
Substituting this expression into the second equation to eliminate x, we get:
5(128 - y) + 8y = 751
Expanding and simplifying:
640 - 5y + 8y = 751
3y = 111
y = 37
Therefore, 37 adult tickets were sold. Substituting this value back into equation (1) to solve for x, we get:
x + 37 = 128
x = 91
Therefore, 91 student tickets were sold.
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Peter buys 30 apples at R5. 00 each. He sell each apple for R7. 0. How much profit does he makes?
Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.
To calculate his earnings, we subtract his price from his revenue.
profit = revenue - cost
In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.
Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.
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Please simplify the following expression while performing the given operation.
(-3+1)+(-4-i)
Answer:
To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:
(-3+1)+(-4-i) = -2 + (-4-i)
Next, we can simplify the addition of -2 and -4 by adding their numerical values:
-2 + (-4-i) = -6 - i
Therefore, (-3+1)+(-4-i) simplifies to -6-i.
Step-by-step explanation:
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
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Which exspression is equivalent to 9(4/3m-5-2/3m+2)
By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]
Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
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A line passes through the point (-4,4) and has a slope of -3
Answer:
y=-3x -8
Step-by-step explanation:
4= -3(-4) = b
b=4-12 = -8
y=-3x -8
Use the daily data for IBM below: RIBM is the log return of IBM adjusted closing prices. Is there evidence of volatility clustering using 15 lags? ret_ibm= diff(log(price_ibm)) nobs 714.000000 Mean 0.000187 Stdev 0.011466 Skewness -0.418588 Kurtosis 5.958068 Jarque - Bera Normalality Test X-squared: 1085.9541 P VALUE < 2.2e-16 Box-Ljung test data: ret_ibm X-squared = 16.355, df = 15, p-value = 0.3588 Box-Ljung test data: ret ibm 12 X-squared 39.655, df - 15, p-value -0.0005112 BOX-Ljung test data: relibm 2 X-squared - 39.655, df - 15, p-value = 0.0005112 Since the p-value>5% for the Box-Ljung Q test of returns we do not reject the null hypothesis and find no evidence of volatility clustering. Since the p-value>5% for the Box-Ljung Q test of returns we do not reject the null hypothesis and find evidence of volatility clustering. Since the p-value<5% for the Box-Ljung Q test of squared returns we reject the null hypothesis and find no evidence of volatility clustering. Since the p-value< 5% for the Box-Ljung Q test of squared returns we reject the null hypothesis and find evidence of volatility clustering.
The p-value for the Box-Ljung Q test of returns is greater than 5%, which means that we do not reject the null hypothesis and find no evidence of volatility clustering in the raw returns.
What is p value?In statistics, p-value is a measure of the strength of evidence against the null hypothesis. It is defined as the probability of obtaining the observed results, or results more extreme, assuming that the null hypothesis is true.
The null hypothesis is a statement that assumes there is no significant difference or relationship between two groups or variables being compared. The alternative hypothesis is the statement that there is a significant difference or relationship.
Given by the question.
Based on the information provided, we can conclude that there is evidence of volatility clustering in the IBM data using 15 lags. This is indicated by the p-value being less than 5% for the Box-Ljung Q test of squared returns. Therefore, we reject the null hypothesis and find evidence of volatility clustering.
However, since the test is conducted on squared returns, it is the p-value for this test that is more relevant in assessing volatility clustering.
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A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.
The maximum area of the surfboard correct to 2 places is 0.67 m².
Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.
Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)
Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)
We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)
Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.
To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),
we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.
Area of surfboard =
[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]
[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]
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Given the following key, what polynomial is modeled by the diagram below?
The polynomial function modeled by the given diagram is given as follows:
p(x) = 3x² - 7x - 6.
How to obtain the polynomial function?The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.
The polynomial is constructed as follows:
3 large non-shaded squares: 3x².Two non-shaded rectangles: 2x.Nine shaded rectangles: -9x.Six shaded small squares: -6.Then the expression used to construct the polynomial is given as follows:
p(x) = 3x² + 2x - 9x - 6.
Combining the like terms, the polynomial function is defined as follows:
p(x) = 3x² - 7x - 6.
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Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 +h). s(6 + h) = Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h. 8(6+h) - s(6) h = Rationalize the numerator in the average velocity. (If it applies, simplify again.) $(6 + h) - $(6) h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero. s(6 + h) – $(6) v(6) lim h -0
The instantaneous velocity of the object at t = 6 is 2.
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56
Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2
Therefore, the instantaneous velocity of the object at t = 6 is 2.
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