Answer:
A
Step-by-step explanation:
Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
Find the area of the cicumfrance of a circle with diameter of 5ft use 3.14 for pi
Step-by-step explanation:
The formula to solve for the area of a circle is given by,
A
=
1
4
π
d
2
where
d
is the diameter.
Substituting the given, we have
A
=
1
4
×
3.14
×
(
3
ft
)
2
=
1
4
×
3.14
×
9
ft
2
A
=
7.065
ft
2
Next, solve for the circumference.
The formula for the circumference of a circle is written as,
C
=
π
d
where
d
is the diameter.
Substituting the given, we have
C
=
3.14
×
3
ft
C
=
9.42
ft
Hence, the
Area
=
7.065
ft
2
and the
Circumference
=
9.42
ft
.
Answer:
A = 19.625 ft²
C = 15.7 ft
Step-by-step explanation:
The equation for the area of a circle is πr², where r is the radius.
The radius is half of the diameter, so the radius here is 2.5.
Plug the radius into the equation and substitute 3.14 for π:
A = 3.14 x 2.5²
2.5² = 2.5 x 2.5 = 6.25
A = 3.14 x 6.25 = 19.625
Area = 19.625 ft²
The equation for the circumference of a circle is 2πr.
Plug the radius into the equation and substitute 3.14 for π:
C = 2 x 3.14 x 2.5
C = 15.7
Circumference = 15.7 feet.
which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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Write each polynomial in Standard form and name it based on its degree an number of terms.
9x²-213
Standard --
Degree
Terms
We would name this polynomial as a quadratic polynomial with two terms.
In standard mathematics, what is a polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
In the standard form of a polynomial, the terms are written in descending order of degree. The standard form for a polynomial of degree n is:
a1x + a0 + anxn + an-1xn-1 +...
We have the polynomial in this case:
9x² - 213
To write it in standard form, rearrange the terms in descending order of degree as follows:
213 + 9x²
As a result, the standard form of the polynomial is:
9x² - 213
This polynomial has degree 2 (because x's highest exponent is 2) and two terms (since there are two distinct parts to the expression, a constant and a term with an x squared coefficient).
As a result, we'd call this polynomial a quadratic polynomial with two terms.
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Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
The neck of a gifaffe is 4 1/2 feet in length. Its neck is 30 perocent of it height whats the higet of the giffae
The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.
Firstly convert the mixed fraction to fraction.
Length of neck of giraffe = (4×2)+1/2
Length of neck = 9/2 feet
Now, let us assume the height of giraffe be x. So, equation will be -
30% × x = 9/2
Rewriting the equation
30/100 × x = 9/2
Cancelling zero
3x/10 = 9/2
Again rewriting the equation
x = 90/6
Performing division on Right Hand Side of the equation
x = 15 feet
Thus, height of giraffe is 15 feet.
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Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
Select the correct answer. Solve for x. x2 - 2x - 24 = 0
A.
-4, -6
B.
-4, 6
C.
2, -6
D.
4, 6
Answer:
B. -4, 6
Step-by-step explanation:
What is the solution to -1/2 [x-1] =0?
x=1
x=-1 or x=1
x=1 or x=2
No solutions exists
Answer:
x=1
Step-by-step explanation:
What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
Can someone please help me with this?
The measure of the side MR is given as 20
How to solve for the side MRWe have to first find the value of the angle
∠TQR = 180 - (35 + 25)
= 180 - 60
= 120 degrees
180 - 120 = 60 degrees
angle TPR = 90 degrees
next we have to find ∠PTQ
= 180 - (90 + 60)
= 180 - 150
= 30 degrees
given that TMN = TQR
TNP = PTQ
So if TMN = 35 degrees since TQR = 35 degrees
PTQ = 30, so TNP = 30 degrees
The measure of QR = 4 since MN = 4
NP = pq
np = 6
Hence the measure of MR
= 4 + 6 + 6 + 4
= 20
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A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
Write a method removeAll that removes all occurrences of a particular value. For example, if a variable list contains the following values:[3, 9, 4, 2, 3, 8, 17, 4, 3, 18]The call of list.removeAll(3); would remove all occurrences of the value 3 from the list, yielding the following values:[9, 4, 2, 8, 17, 4, 18]If the list is empty or the value doesn't appear in the list at all, then the list should not be changed by your method. You must preserve the original order of the elements of the list.
It should be noted that this approach follows the need to maintain the list's original order of elements.
what is function ?A function is a relationship between a set of possible outcomes (referred to as the range) and a set of inputs (referred to as the domain), with the property that each input is associated to exactly one output. A function, then, is a mathematical rule that designates a specific output value for each input value. Equations, graphs, and tables are frequently used to represent functions. They are employed to mimic real-world occurrences and to address issues in numerous branches of mathematics, science, engineering, and other disciplines.
given
The value to be deleted from the list is represented by an integer value that the method accepts as an argument.
The method iterates through the list's components using a while loop.
The method determines if the current element equals the requested value while it is in the loop. If so, the procedure uses the ArrayList class's remove method to remove the element from the list. If not, the method increases the index variable and moves on to the next element.
The procedure keeps going over the list until all instances of the given value have been eliminated.
It should be noted that this approach follows the need to maintain the list's original order of elements.
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what is the sum of all integer values of $x$ such that $\frac{31}{90} < \frac{x}{100} < \frac{41}{110}$ is true?
Construct a residual plot of the amount of money in a person’s bank account and their age that would indicate a linear model
To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:
bank account = β0 + β1 * age + ε
where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.
Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:
residual = bank account - (β0 + β1 * age)
We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.
In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.
Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.
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If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59 F and a
standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean
temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all
possible random samples of size 10 from this population?
The standard deviation of the sampling distribution of the sample mean for the given sample size is equal to 3.1623°F.
For the normally distributed data,
Mean of the population distribution 'μ' = 59F
Population standard deviation 'σ' = 10°F
Sample size 'n' = 10
Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,
= σ / √(n)
Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,
= 10°F / √(10)
= 3.1623°F
Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.
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suppose 46.37% of all voters in the last election supported the current governor. a telephone survey contacts 328 voters from the last election and asks if they voted for the current governor. what is the probability that at least half of the voters contacted supported the current governor in the last election?
The probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
What is the probability?To calculate the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election, we can use the binomial probability formula.
The formula is: P(x) = (ⁿCₓ) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾
In this case, n = 328, p = 46.37%, and x = 164 (since half of 328 is 164).
Plugging in the numbers we get:
P(x) = ³²⁸C₁₆₄ × (0.4637)¹⁶⁴ × (0.5363)⁽³²⁸⁻¹⁶⁴⁾ = 0.0532
Therefore, the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
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a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
a manager recorded the number of gallons of ice cream sold for the past six periods. he asked you to choose a forecasting model to predict the demand for gallons of ice cream in period 7. you consider applying a two-period moving average model and a two-period weighted moving average model with weights of 0.6 and 0.4. a) which model is better for this data set (hint: show all your work including forecasts for each period and calculations using measures of forecast accuracy)? (9 points)
The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.
To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:
Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2
For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:
Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)
We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:
MAD = |Actual demand – Forecasted demand|
To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:
MSE = (Actual demand – Forecasted demand)^2
After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.
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a) Work out the value that completes the equation for the line on the graph. b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300- 250 200 150 100 50 0 2 4 6 8 10 12 14 16 Distance cycled (miles)
The value that completes the equation for the line on the graph is -200. Keira has cycled 44.8 miles if she has burned 640 calories.
What is slope?It describes how much the dependent variable (y) changes for a given change in the independent variable (x).
According to question:a) To work out the value that completes the equation for the line on the graph, we need to find the equation of the line that passes through two points on the graph. Let's choose two points on the line, for example, (8, 250) and (16, 400).
In this case, the change in y is 400 - 250 = 150, and the change in x is 16 - 8 = 8. Therefore, the slope is:
slope = 150 / 8 = 18.75
y - y1 = m(x - x1)
Let's use the point (16, 400):
y - 400 = 18.75(x - 16)
Simplifying this equation, we get:
y = 18.75x - 200
Therefore, the value that completes the equation for the line on the graph is -200.
b) To find the distance cycled if Keira has burned 640 calories, we need to use the equation of the line we found in part (a). We can set y (calories burned) equal to 640 and solve for x (distance cycled):
640 = 18.75x - 200
840 = 18.75x
x = 44.8 (rounded to 2 decimal places)
Therefore, Keira has cycled 44.8 miles (to 2 decimal places) if she has burned 640 calories.
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If point is slid(translated) 4 units to the right, what would the new coordinates be (3,-4)
Weight of a badminton racket is 0. 950 kg find the weight of 12 such rackets
The weight of 12 badminton rackets, each weighing 0.950 kg, is 11.4 kg.
The weight of an object refers to the force exerted by gravity on that object. This force is typically measured in units of mass, such as kilograms or pounds. In the case of badminton rackets, the weight is usually measured in grams.
Now, let's consider the weight of a single badminton racket. You've been given the information that the weight of one racket is 0.950 kg. This means that the force exerted by gravity on that racket is 0.950 kg.
If you want to find the weight of 12 such rackets, you need to multiply the weight of one racket by 12. This gives you:
0.950 kg x 12 = 11.4 kg
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Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.
What is Pythagorean theorem?The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To find the length of the side labeled x, we will first need to calculate the length of the other two sides.
For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:
x = √(35² + 42²) = 50.1
For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(60² + 50²) = 75.3
For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(28² + 34²) = 39.6
Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.
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The rounded value of x in the triangles is:
25) x ≈ 76
27) x ≈ 21
29) x ≈ 104
Give a brief account on trigonometric relations.All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.
25) Since, Sinθ = Opposite side/hypotenuse
Sin35° = 39/hypotenuse
hypotenuse = 39/Sin35°
Sin35° = 0.57
hypotenuse = 39/0.57
hypotenuse = 68.42
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
68.42² = 39² + perpendicular²
4681.29 - 1521 = perpendicular²
4681.29 - 1521 = perpendicular²
3160.29 = perpendicular²
√3160.29 = perpendicular
56.21 = perpendicular
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos42° = 56.21/x
0.74 = 56.21/x
x = 56.21/0.74
x = 75.95
x ≈ 76
27) Cosθ = Adjacent side/hypotenuse
Cos60° = 14/hypotenuse
0.5 = 14/hypotenuse
hypotenuse = 14/0.5
hypotenuse = 28
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
28² = 14² + perpendicular²
784 - 196 = perpendicular²
588 = perpendicular²
√588 = 24.24
perpendicular = 24.24
For the calculation of x:
Sinθ = Opposite side/hypotenuse
Sin50 = 24.24/hypotenuse
0.76 = 24.24/hypotenuse
hypotenuse = 24.24/0.76
hypotenuse = 31.89
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
31.89² = x² + 24.24²
1016.97 = x² + 587.57
x² = 1016.97 - 587.57
x² = 429.4
x = √429.4
x = 20.72
x ≈ 21
29) Sinθ = Opposite side/hypotenuse
Sin28° = 44/hypotenuse
0.46 = 44/hypotenuse
hypotenuse = 44/0.46
hypotenuse = 95.65
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
95.65² = 44² + perpendicular²
perpendicular² = 9148.92 - 1936
perpendicular² = 7212.92
perpendicular = √7212.92
perpendicular = 84.92
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos34 = 84.92/x
x = 84.92/0.82
x = 103.56
x ≈ 104
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y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
