Write in Simplest Form pls (8a^3)^-4/3

     |-----|-----|-----|----|-----|-----|--│--|-----|----|-----|

    -5   -4   -3   -2   -1    0    1   │  2    3    4    5

                                            1 1/2

On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.

To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.

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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:

Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

Recall from the task content; the given functions are;

f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ

Therefore, for intersection; f (θ) and g(θ):

2 cos²θ = −1 − 4cos θ − 2cos²θ

4cos²θ + 4cosθ + 1 = 0

let cos θ = y;

4y² + 4y + 1 = 0

y = -1/2

Therefore; -1/2 = cos θ

θ = cos-¹ (-1/2)

θ = 2π/3, 4π/3.

Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

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Answer: Felipe has walked 25.1 meters.

Step-by-step explanation:

Felipe walks the length of his living room, which is 9.1 meters. He then turns and walks the width of his living room, which is 3.5 meters. Finally, he walks back to the corner he started from, which is another 9.1 meters.

The total distance that Felipe has walked is the sum of the distances he covered in each of these three parts of his walk. So, we need to add up 9.1 meters, 3.5 meters, and 9.1 meters to get the total distance.

9.1 m + 3.5 m + 9.1 m = 21.7 m

Therefore, Felipe has walked 21.7 meters so far. However, he still needs to walk back to the corner he started from. This distance is equal to the diagonal of the rectangle formed by his living room.

We can use the Pythagorean theorem to find the length of this diagonal. The length and width of the rectangle are 9.1 meters and 3.5 meters, respectively. Let d be the length of the diagonal, then:

d² = 9.1² + 3.5²

d² = 83.06

d ≈ 9.11 meters

Therefore, the total distance that Felipe has walked is approximately:

21.7 m + 9.11 m ≈ 25.1 m

So, Felipe has walked about 25.1 meters.

Answer:

Felipe has walked 25.2 meters in total.

Step-by-step explanation:

To find out how far Felipe has walked, we need to calculate the perimeter of his living room. The perimeter is the distance around the outside of a shape.

The formula for the perimeter of a rectangle is:

perimeter = 2(length + width)

Given that the length of Felipe's living room is 9.1 meters and the width is 3.5 meters, we can substitute these values into the formula and get:

perimeter = 2(9.1 + 3.5)

perimeter = 2(12.6)

perimeter = 25.2 meters

A ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, the total distance traveled by the ball is approximately 11.926 feet.

We have to calculate the distance traveled by the ball with the help of the given data, as shown below;The first height of the ball is 6 feet. Distance traveled by the ball at the first instance = 6 feet.The ball rebounds to one-third of its previous height, and the ball goes to a height of:6/3 = 2 feet.

Distance traveled by the ball after the first bounce = 6 + 2 + 2 = 10 feet.The ball rebounds again to one-third of its previous height, and the ball goes to a height of:2/3 = 0.6667 feet. Distance traveled by the ball after the second bounce = 10 + 0.6667 + 0.6667 = 11.3334 feet.

The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.6667/3 = 0.2222 feet. Distance traveled by the ball after the third bounce = 11.3334 + 0.2222 + 0.2222 = 11.7778 feet. The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.2222/3 = 0.0741 feet.

Distance traveled by the ball after the fourth bounce = 11.7778 + 0.0741 + 0.0741 = 11.926 feet. Therefore, the total distance traveled by the ball is approximately 11.926 feet.

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We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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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 answer to the problem that you need to is 1024

91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.

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.

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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The amount that would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the present value is $37,537.19.

The investment can be treated as a continuous stream with the interest paid at a rate of 4.2% compounded continuously.The present value of the investment can be calculated using the formula:P = C/e^(rt)Where,P = Present ValueC = Cash Flowsr = Interest Rate Per Periodt = Number of Periodse = Euler’s numberThe given values are as follows:C = $8,000 per yearr = 4.2% compounded continuously for 15 years.

C = $8,000e = 2.71828t = 15 yearsNow, we need to calculate the present value using the above formula.P = 8000/e^(0.042 x 15) = $82,273.24.The formula to calculate the amount that would have been invested 15 years ago is:A = P x e^(rt)Where,A = Future Value of the investmentP = Present Value of the investmentr = Rate of Interest Per Periodt = Number of Periodse = Euler’s numberThe present value of the investment is $82,273.24.

The rate of interest is 4.2% compounded continuously.t = 15 yearsNow, we need to calculate the amount that would have been invested 15 years ago.A = 82,273.24 x e^(0.042 x 15) = $37,537.19

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Answer:

If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:

(x + 3)(x + 4) = 0

To convert this to standard form, we can multiply out the factors:

x^2 + 7x + 12 = 0

Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:

x^2 + 7x + 12 = 0

The confidence interval is calculated by adding and subtracting the product of a constant (usually 1.96), the margin of error, and the mean.

The constant times the margin of error is added and subtracted from the sample mean to obtain the confidence interval range.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
The constant is determined by the confidence level of your analysis (typically 95%) and the margin of error is determined by the standard deviation and the size of your sample.

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In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:

2/5 = 16/40

3/8 = 15/40

We can now sum the two fractions:

16/40 + 15/40 = 31/40

As a result, the proper answer is:

B. 16/40 + 15/40 = 31/40

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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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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:

Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.

So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~

Answer: your credit utilization ratio on that card would be 50% but the answer is 450

Step-by-step explanation:

900-450 = 450

The population increase according to the given years will be 27500, 23750 and 20833.

Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the number.

In this question,

p = 200,000 3/4t

When t=0

p=0

When t=1

p= 20000 3/4= 27500

when t=2

p= 20000 3/8 = 23750

When t=3

p= 20000 3/12 = 20833

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the  correct area of the symmetrical object is option (B). 78 square inches.

If two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.

In the first part of the object

Area of the object=½×H×Z

=½×13×6

=39 square inches

Given that object above is symmetrical through Z.

So, the area of 2nd part of object will also be 39 square inches

Hence total area is 78 square inches.

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Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

Why it is and how to form a graph?

To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.

Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:

y' = -0.08176x + 0.4485

0 = -0.08176x + 0.4485

x = 5.484

This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).

To verify this, we can plug in x = 2 into the quadratic equation:

y = –0.04088(2)²2 + 0.4485(2) + 1.862

y = 2.31752

Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:

Month (x) Precipitation

January 1 2.27 inches

February 2 2.32 inches

March 3 2.57 inches

April 4 2.94 inches

May 5 3.43 inches

June 6 3.94 inches

July 7 2.72 inches

August 8 2.86 inches

September 9 2.59 inches

October 10 2.03 inches

November 11 1.46 inches

December 12 1.03 inches

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Answer:

D: December

The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:

| Month (x) | Precipitation |

|-----------|---------------|

| January   | 2.27 inches   |

| February  | 2.27 inches   |

| March     | 2.24 inches   |

| April     | 2.18 inches   |

| May       | 2.09 inches   |

| June      | 1.98 inches   |

| July      | 1.84 inches   |

| August    | 1.68 inches   |

| September | 2.59 inches   |

| October   | 1.50 inches   |

| November  | 1.30 inches   |

| December  | 1.08 inches   |

According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.

Answer:

a = -9

Step-by-step explanation:

2(a+3) = -12

2a + 6 = -12

2a = -18

a = -9

Let's Check

2(-9 + 3) = -12

2(-6) = -12

-12 = -12

So, a = -9 is the correct answer.

Answer:

$109.99

Step-by-step explanation:

The original price of each tire is [tex]\[/tex][tex]109.99[/tex]

Take the amount saved and divide by 4 to find the amount saved on each tire

[tex]96.16\div4 =24.04[/tex]

Add that to the sale price of each tire to find the original price

[tex]85.95+24.04 =109.99[/tex]

Therefore, The original price is $109.99.

Answer:

8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

When n = 1:

n² + 7 = 1² + 7 = 8

When n = 2:

n² + 7 = 2² + 7 = 11

When n = 3:

n² + 7 = 3² + 7 = 16

When n = 4:

n² + 7 = 4² + 7 = 23

When n = 5:

n² + 7 = 5² + 7 = 32

When n = 6:

n² + 7 = 6² + 7 = 43

Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Answer:

When n = 1, n² + 7 = 1² + 7 = 8

When n = 2, n² + 7 = 2² + 7 = 11

When n = 3, n² + 7 = 3² + 7 = 16

When n = 4, n² + 7 = 4² + 7 = 23

When n = 5, n² + 7 = 5² + 7 = 32

When n = 6, n² + 7 = 6² + 7 = 43

The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

ᓚᘏᗢ

hope u have a good day man

Answer:

Let's use the formula for the volume of a right circular cone to solve this problem:

V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.

Using the chain rule of differentiation, we can express the rate of change of the volume as follows:

dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)

To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:

dV/dr = (2/3)πrh

dV/dh = (1/3)πr^2

Substituting the given values and their rates of change, we have:

dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)

dV/dt = 55,742.4 - 1,994,598.4

dV/dt = -1,938,856 in^3/s

Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.

Step-by-step explanation:

The number of students that are in the sixth grade is given as follows:

250 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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Cracking the code: 8 2One number is correct and well placed One number is correct but in the wrong placeTwo numbers are correct but in the wrong place38Nothing is correctCODE8One number is correct but in the wrong placeCracking the code of this sequence of numbers can be a bit tricky, but let's do it step by step. We are given the following clues about the sequence of numbers:

One number is correct and well placed: Since the sequence of numbers is 8 2, we know that the number 8 is in the first position. So the code is either 8 _ _ _ or _ _ _ 8.One number is correct but in the wrong place: This clue tells us that the number 2 is not in the second position of the code, but it is somewhere else.

Therefore, we know that the code is not 8 2 _ _ or _ _ 2 8.Two numbers are correct but in the wrong places: This clue tells us that the code contains the numbers 3 and 8, but they are in the wrong position. Since the code cannot be 8 2 _ _ or _ _ 2 8, we know that the two correct numbers are not in the last two positions. Therefore, the code must be _ 3 8 _ or _ 8 3 _.Nothing is correct: This clue tells us that the code cannot be 3 8 _, 8 3 _, or _ 3 8 because they all contain at least one correct number. Therefore, the code must be _ _ 3 8 or 3 8 _ _.One number is correct but in the wrong place: This clue tells us that the code cannot be 3 8 _, so it must be 8 3 _. Therefore, the code is 8 3 _ _.I hope this helps you crack the code!

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a)  When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

Using implicit differentiation, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dy/dt, we get:

dy/dt = -(x/y)(dx/dt)

Substituting x = 6, y = 8, and dx/dt = 4, we get:

dy/dt = -(6/8)(4) = -3

Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

b) Using implicit differentiation again, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dx/dt, we get:

dx/dt = -(y/x)(dy/dt)

Substituting x = 8, y = 6, and dy/dt = -2, we get:

dx/dt = -(6/8)(-2) = 1.5

Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.

To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).

In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.

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The derivative of the given function [tex]y = 5x^2 sec^{(-1)(2x-3)^2}[/tex] is [tex]dy/dx=-20x\sqrt{((2x-3)^2-1)}[/tex]

It can be derived as:

We can use the chain rule and the derivative of [tex]sec^{(-1)x}[/tex] which is [tex]-1/(x*\sqrt{(x^2-1)})[/tex]

First, we apply the chain rule to the function.

Let  [tex]u = (2x-3)^2[/tex], then:

[tex]y = 5x^2 sec^{(-1)u}[/tex]

[tex]dy/dx = d/dx [5x^2 sec^{(-1)u}][/tex]

[tex]dy/dx = d/dx [5x^2 sec^{(-1)[(2x-3)^2]}][/tex]

[tex]dy/dx= 5x^2 d/dx[sec^{(-1)u}][/tex]     (Using the chain rule)

Now, let [tex]v = u^{(1/2)} = (2x-3)[/tex].

Then:

[tex]dy/dx = 5x^2 d/dv [sec^{(-1)v}] dv/dx[/tex]          (Using the chain rule again)

We have:

[tex]d/dv [sec^{(-1)v}] = -1/(v*\sqrt{(v^2-1)}) = -1/[(2x-3)*\sqrt{((2x-3)^2-1)}][/tex]

Also, [tex]dv/dx = 2[/tex]

Substituting these back into the equation:

[tex]dy/dx = 5x^2 d/dv [sec^{(-1)v}] dv/dx[/tex]

[tex]dy/dx= 5x^2 (-1/[(2x-3)*\sqrt{((2x-3)^2-1)}] (2)[/tex]

Simplifying this expression gives:

[tex]dy/dx = -20x (2x-3)/[(2x-3)*\sqrt{((2x-3)^2-1)}][/tex]

[tex]dy/dx = -20x\sqrt{((2x-3)^2-1)}[/tex]

Therefore, the derivative of y with respect to x is:

[tex]dy/dx = -20x\sqrt{((2x-3)^2-1)}[/tex]

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#SPJ11

Answer:

Step-by-step explanation:

see diagram