please help i will answer the brainlyist 3.99 x 10^-2 - 1.5 x 10^-3

The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.

When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.

from equation of motion

H= ut-1/2gt^2( the object is moving upward)

where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity

(g=10ms^-2).

therefore h= 8.14×2.41-(1/2×10×2.41)

= 19.62-12.05

h= 7.57m

when the object is thrown Down,

V = u + gt

u will be 0 at top before coming down

V = gt

t= 8.14/10

= 0.814s

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The conversion of -16°C to Kelvin is 257.15°K

It is given that in order to convert a Celsius temperature to Kelvin Temperature we have to add 273.15 to the Celsius temperature

The Celsius scale, commonly known as centigrade, uses a base of 0° for water's freezing point and 100° for water's boiling point.

The difference between a kelvin (K), which is a division of the kelvin scale, and a degree on the Celsius scale is where zero is. The zero point on the Kelvin scale is at absolute zero, whereas the zero point on the Celsius scale is the freezing point of water. As a result, 0°K is equivalent to -273.15°C and 0°C to 273.15 kelvins.

We need to convert -16°C into degrees Kelvin

-16 + 273.15

257.15°K

Therefore, the conversion of -16°C to Kelvin is 257.15°K

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Answer:

here are 117,600 ways the runners can finish first, second, and third in the race.

Step-by-step explanation:

The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.

The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.

For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.

Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.

To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.

Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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We will assume that we can solve this question using technology. We can use a graphing calculator to check the scatter plot to see the possible relationship between these two variables.

We can graph the following scatter plot with these two variables:

If we observe the graph, we can see that both variables have a linear relationship. The phenomenon y is related to phenomenon x in a possible linear relationship.

To find the line that best represents this relationship, we can use technology using a graphing calculator. If we do that, we can obtain the following graph:

We can see that the line has a negative slope, and the equation for this line is:

The graphing calculator used the formulas for the regression line available on the internet, and in books. The process to obtain it manually is time-consuming.

The correlation coefficient for this case is equal to r = -0.9527, which means that the negative correlation is very strong between these two variables (as was mentioned in the question).

In summary, the equation of the regression line that predicts the value of the phenomenon y knowing that of the phenomenon x is:

[This is the slope-intercept form of the line. The slope, m = -0.948276, and the y-intercept, i. e., the point where the line passes through the y-axis, is equal to b = 18.1345.]

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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The average price of the stock over the first eight years is 50.69 units / year .

Given :

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function :

S ( t ) = 37 + 16 e^0.04t.

We find the average value of the stock ,

\(f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx\)

\(f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx\)

\(f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt\)

= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( \(e^{-0.04 * 8 }\) - \(e^{-0.04 * 0\))

= 50.69 units / year.

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Answer:

The y intercept is at (0, 4)

Step-by-step explanation:

The y-intercept happens when the curve reaches an x-coordinate of zero.  Because this is a quadratic expression, we know that it is a proper parabolic function, and will have a single y-intercept:

\(y = 6x^2 - 10x + 4\\y = 6(0)^2 - 10(0) + 4\\y = 4\)

So the y intercept for this function is at (0, 4)

i am going to answer question 1, so q1 is a number line

The integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y = x₂ - 3x and y = x about the horizontal line y = 6 is  2πx(6 - x² + 3x)dx, which is integrated from x=0 to x=3, which gives us   81π/2.

To find the integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y=x² - 3x and y=x about the horizontal line y=6, we can use the method of cylindrical shells.

First, we need to find the limits of integration, The graphs of y = x² - 3x  and y=x intersect at x=0 and x=3. Therefore, we integrate from x=0 to x=3.

Next, we consider a vertical strip of width dx at a distance x from the y- boxes. the height of the strip is the difference between the height of the curve y=  x² - 3x and the line y=6, which is   6 - (x² - 3x) = 6 - x² + 3x. the circumference of the shell is 2π times the distance x from the y-axis, and the thickness of the shell is dx. the volume of the shell is the product of the height, circumference, and thickness which is

dV = 2πx(6 - x² + 3x)dx

To find the total volume, we integrate this expression from x=0 to x=3.

V = ∫₀³ 2πx(6 - x² + 3x)dx, after simplifying the integrand we get :

V = 2π ∫₀³ (6x - x³ + 3x²)dx, integrating term by term we get :

V = 2π [(3x²/2) - (x⁴/4) + (x^3)] from 0 to 3, now  evaluation at the limits of integration we get:

V = 2π [(3(3)²/2) - ((3)⁴/4) + (3)³] - 2π [(0)^2/2 - ((0)⁴/4) + (0)^3]=  2π [(27/2) - (27/4) + 27] - 0 = 81π/2

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Answer: 11

Step-by-step explanation:

F(1) = 3(1) + 8

F(1) = 3 + 8

F(1) = 11

You just substitute the x in for 1 and solve from there.

Answer:

C y = 3/2x - 1/8

Step-by-step explanation:

We know that the line has a positive slope, because it goes up from the lower left to upper right

We can eliminate B and D

For y = 6x - 11/8

A slope of 6 is very steep

Putting in 6

y = 6*6 -approximately 1 = 35 so the value at 3 would be 35

This is too big

Checking C

y = 3/2(6) - 0 = 9 or 9  This would be about right

Answer: A is the answer

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Answer:

-4x+4y+3=0

Step-by-step explanation:

(4x-2y+9=0)+(-8x+6y-6=0)

Add like terms:

-4x+4y+3=0

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

number 8 is D) 78.7 in.

and number 9 is C) 63°

hope these are the answers you are looking for

Step-by-step explanation:

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The actual dimensions of the patio are 20 feet by 16 feet.

The scale factor is 1 inch to 4 feet,

This means that 1 inch on the scale drawing represents 4 feet in reality.

So the dimensions of the scale drawing are:

20 feet x (1/4) = 5 inches (length on scale drawing)

16 feet x (1/4) = 4 inches (width on scale drawing)

The area of the actual patio is:

= 20 feet x  16 feet

= 320 square feet

The area of the scale drawing is:

= 5 inches x 4 inches

= 20 square inches

The ratio of the area of the scaled drawing to the actual area of the patio is: 20 square inches : 320 square feet

To simplify this ratio, we need to convert both values to the same units.

Converting the area of the scale drawing to square feet:

= 20 square inches x  (1/144) square feet/square inch

= 0.1389 square feet

So the ratio of the area of the scaled drawing to the actual area of the patio is:

0.1389 square feet : 320 square feet

Or, in simplified form:

1 : 2306.56

Thus,

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

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A statement that must be added to the given to keep this proof valid include the following: D. KN || LM.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

Based on the basic proportionality theorem, we know that line segment KN is parallel to line segment LM.

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Answer:

the answer would be 34

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/2, 2/17

For the denominators (2, 17) the least common multiple (LCM) is 34.

LCM(2, 17)

Therefore, the least common denominator (LCD) is 34.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/2 = 1/2 × 17/17 = 17/34

2/17 = 2/17 × 2/2 = 4/34

Answer:

-x - 8y + 5

Step-by-step explanation:

Add the numbers

4x - 4 - 8y + 8 - 5x + 1 =

4x + 5 - 8y - 5y

Combine like terms

4x + 5 - 8y - 5y

-x + 5 - 8y

Rearrange terms

-x + 5 - 8y

-x - 8y + 5

The solution of expression is,

⇒ - x - 8y + 5

We have to given that,

An expression is,

⇒ 4x - 4 - 8y + 8 - 5x + 1

Now, We can simplify by combining like terms as,

⇒ 4x - 4 - 8y + 8 - 5x + 1

⇒ 4x - 5x - 8y - 4 + 8 + 1

⇒ - x - 8y + 5

Therefore, The solution of expression is,

⇒ - x - 8y + 5

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Answer:

(x - 2)² + (y + 3)² = 32

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre of the circle is at the midpoint of the diameter

Calculate the centre (x, y ) using the midpoint formula

(x, y ) = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (6, - 7)

(x , y ) = ( \(\frac{-2+6}{2}\) , \(\frac{1-7}{2}\) ) = ( \(\frac{4}{2}\) , \(\frac{-6}{2}\) ) = (2, - 3)

The radius is the distance from the centre to either of the endpoints

Calculate the radius using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+( y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 2, 1)

r = \(\sqrt{(-2-2)^2+(1-(-3))^2}\)

  = \(\sqrt{(-4)^2+(1+3)^2\)

   = \(\sqrt{16+4^2}\)

   = \(\sqrt{16+16}\)

   = \(\sqrt{32}\)

Then equation of circle is

(x - 2)² + (y - (- 3) )² = (\(\sqrt{32}\) )² , that is

(x - 2)² + (y + 3)² = 32

Answer:

Step-by-step explanation:

Answer:

\(\frac{2}{11} *\frac{33}{10}\\\frac{66}{110} \\ \frac{3}{5}\)

Step-by-step explanation:

Hope it will help you.

\(\\ \tt\hookrightarrow \dfrac{2}{11}\:of 3\dfrac{3}{10}\)

\(\\ \tt\hookrightarrow \dfrac{2}{11}\times 3\dfrac{3}{10}\)

\(\\ \tt\hookrightarrow \dfrac{2}{11}\times \dfrac{33}{10}\)

\(\\ \tt\hookrightarrow \dfrac{66}{110}\)

\(\\ \tt\hookrightarrow \dfrac{6}{10}\)

\(\\ \tt\hookrightarrow \dfrac{3}{5}\)

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

The average rate of change from year 1 to year 10 is 8.3 pounds per acre per year based on given function.

We must compute the change in crop yield (in pounds per acre) during that time period and divide by the number of years to determine the average rate of change from year 1 to year 10:

Average change rate is equal to (f(10) - f(1)) / (10 - 1)

where f(x): function that represents the crop yield over an x-year period in pounds per acre.

When we enter the numbers 10 and 1 as substitutes in the function, we obtain:

f(10) = \(-10^2\) + 20(10) + 50 = 150

f(1) =\(-1^2\) + 20(1) + 50 = 69

Thus, from year one to year ten, the average rate of change is:

(150 - 69) / (10 - 1), or 8.3 pounds per acre per year, is the average rate of change.

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Answer:

π/6 [(29)^³/₂ − 1]

81.247

Step-by-step explanation:

Surface area is:

S = ∫∫ √(fₓ² + fᵧ² + 1) dA

The partial derivatives are:

fₓ = -2x

fᵧ = -2y

Substituting:

S = ∫∫ √(4x² + 4y² + 1) dA

To make this easier, we can convert to polar coordinates.

S = ∫∫ √(4r² + 1) dA

S = ∫∫ √(4r² + 1) r dr dθ

S = ⅛ ∫∫ 8r √(4r² + 1) dr dθ

The limits for θ are 0 to 2π.  The minimum of r is 0.  The maximum of r is:

-6 = 1 − x² − y²

-6 = 1 − r²

r² = 7

r = √7

Integrating the first integral:

S = ⅛ ∫ ⅔ (4r² + 1)^³/₂ |₀ᴿ dθ

S = ⅛ ∫ [⅔ (4(7) + 1)^³/₂ − ⅔ (4(0) + 1)^³/₂] dθ

S = ⅛ ∫ [⅔ (29)^³/₂ − ⅔] dθ

S = ¹/₁₂ [(29)^³/₂ − 1] ∫ dθ

Integrating the second integral:

S = ¹/₁₂ [(29)^³/₂ − 1] θ |₀²ᵖⁱ

S = ¹/₁₂ [(29)^³/₂ − 1] (2π − 0)

S = π/6 [(29)^³/₂ − 1]

S ≈ 81.247

The area of a shape is the amount of space it covers.

The surface area is approximately 81.3 unit squares

The given parameters are:

\(\mathbf{z = 1 - x^2 - y^2}\)

\(\mathbf{z = -6}\)

Calculate the partial derivatives of \(\mathbf{z = 1 - x^2 - y^2}\)

\(\mathbf{f_x = -2x}\)

\(\mathbf{f_y = -2y}\)

So, the surface area is:

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(f_x^2 + f_y^2 +1 )}} \, dA }\)

So, we have:

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{((-2x)^2 + (-2y)^2 +1 )}} \, dA }\)

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4x^2 + 4y^2 +1 )}} \, dA }\)

Factor out 4

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4(x^2 + y^2) +1 )}} \, dA }\)

Substitute

\(\mathbf{r^2 = x^2 + y^2}\\\mathbf{dA = rdr d\theta}\)

So, we have:

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r\ dr\ d\theta }\)

Multiply by 1

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times 1\ dr\ d\theta }\)

Express 1 as 8/8

\(\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times \frac{8}{8}\ dr\ d\theta }\)

Rewrite as:

\(\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }\)

From the question,

\(\mathbf{z = -6}\)

So, we have:

\(\mathbf{1 - r^2 = -6}\)

Add 6 to both sides

\(\mathbf{7 - r^2 = 0}\)

So, we have:

\(\mathbf{r^2 = 7}\)

Integrate \(\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }\)

\(\mathbf{A =\frac{1}{8} \int\limits^a_b {\frac{8}{12} (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }\)

\(\mathbf{A =\frac{1}{8} \times \frac{8}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }\)

\(\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }\)

\(\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32} -(4 \times 0^2 +1 )^{\frac 32} }, d\theta }\)

Substitute \(\mathbf{r^2 = 7}\)

\(\mathbf{A =\frac{1}{12} \int\limits^a_b { (4\times 7 +1 )^{\frac 32} - 1^{\frac 32}}, d\theta }\)

\(\mathbf{A =\frac{1}{12} \int\limits^a_b {29^{\frac 32} - 1}, d\theta }\)

Rewrite as:

\(\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \int\limits^a_b d\theta }\)

Integrate

\(\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times \theta |\limits^{2\pi}_0}\)

So, we have:

\(\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times (2\pi - 0) }\)

\(\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times 2\pi}\)

Rewrite as:

\(\mathbf{A =\frac{2\pi}{12} (29^{\frac 32} - 1)}\)

\(\mathbf{A =\frac{\pi}{6} (29^{\frac 32} - 1)}\)

\(\mathbf{A =81.3}\)

Hence, the surface area is approximately 81.3 unit squares

Read more about surface areas at:

https://brainly.com/question/3621496

Answer:

Sorry i would help you but i dont speak spanish

Step-by-step explanation:

SORRY!!