Find the mass and center of mass of a wire in the shape of the helix x = t, y = 2 cos t, z = 2 sin t, 0 ≤ t ≤ 2π, if the density at any point is equal to the square of the distance from the origin.

The equation of the tangent plane is given by:
20736(x - 3) + 12288(y - 4) + 1(z - (-62188)) = 0

To find the equation of the tangent plane to the surface x⁴y⁴ + z - 20 = 0 at the point (3, 4, z), we first need to find the partial derivatives with respect to x, y, and z.

∂f/∂x = 4x³y⁴
∂f/∂y = 4x⁴y³
∂f/∂z = 1

Now, we evaluate the partial derivatives at the given point (3, 4, z):

∂f/∂x(3, 4, z) = 4(3³)(4⁴) = 20736
∂f/∂y(3, 4, z) = 4(3⁴)(4³) = 12288
∂f/∂z(3, 4, z) = 1

Next, we find the value of z by substituting x = 3 and y = 4 in the equation:

(3⁴)(4⁴) + z - 20 = 0
z = 20 - (3⁴)(4⁴) = 20 - 62208 = -62188

The point on the surface is (3, 4, -62188). The equation of the tangent plane is given by:

20736(x - 3) + 12288(y - 4) + 1(z - (-62188)) = 0

This simplifies to:

20736x + 12288y + z = 1885580

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The observed relationship can be described as a negative correlation.

The basketball coach observes a decrease in points scored by his team over the first ten weeks of the season.

This indicates a negative correlation between time (progressing through the season) and points scored. Without seeing the data, we cannot determine if the coach's observation is correct or incorrect. However, the observed relationship can be described as a negative correlation.

However, it is important to note that without actually seeing the data and analyzing it, we cannot conclusively determine if the coach's observation is correct or incorrect.

The observed relationship, as described by the coach, suggests a negative correlation, but the strength and significance of this correlation would need to be evaluated through statistical analysis of the data.

In addition, it is also possible that other factors may be influencing the decrease in points scored, such as changes in team strategy, player injuries, or tougher opponents.

Without considering these other factors and analyzing the data, it would be premature to draw definitive conclusions about the relationship between time and points scored.

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The first and fourth sequences show a geometric series.

Consequently, the sequences 2, 3, 4.5, 6.75, … and 4, 8, 16, 32, … are the geometric series.

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Complete Question:-

Which of the following show a geometric series? select all that apply.

1) 2 3 4.5 6.75 …

2) 2 2.5 3 3.5 …

3) 6 7 9 12 …

4) 4 8 16 20 …

5) 8 4 2 1 …

Answer:

Step-by-step explanation:

A) The point estimate for the proportion of all homeowners in the city who would support a ban on nonnatural lawn fertilizers is 0.297.

B) The 95% confidence interval for the proportion of all homeowners in the city who would support a ban on nonnatural lawn fertilizers is (0.266, 0.328).

A) The point estimate is the best estimate for the proportion of all homeowners in the city who would support a ban on nonnatural lawn fertilizers to protect fish in the local waterways. We can find this by taking the proportion of homeowners in the sample who said they would support a ban:

point estimate = x/n = 22/74 = 0.297

Therefore, the point estimate for the proportion of all homeowners in the city who would support a ban on nonnatural lawn fertilizers is 0.297.

B) The margin of error is ±3.1%. To find the lower and upper limits of the confidence interval, we can use the following formula:

lower limit = point estimate - margin of error

upper limit = point estimate + margin of error

Substituting the values we know, we get:

lower limit = 0.297 - 0.031 = 0.266

upper limit = 0.297 + 0.031 = 0.328

Therefore, the 95% confidence interval for the proportion of all homeowners in the city who would support a ban on nonnatural lawn fertilizers is (0.266, 0.328).

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Using the properties of exponents:

5. The value of x is 9

6. The value of b is -4

7. The value of n is 0

From the question, we are to calculate the value of the exponent in each question

5.

8² · 8ˣ = 8¹¹

Applying the multiplication law of indices, this can be written as

8² ⁺ ˣ = 8¹¹

Equate the powers

2 + x = 11

Solve for x by subtracting 2 from both sides

2 - 2 + x = 11 - 2

x = 9

6.

5⁷ · 5ᵇ = 5³

Applying the multiplication law of indices, this can be written as

5⁷ ⁺ ᵇ = 5³

Equate the powers

7 + b = 3

Solve for b by subtracting 7 from both sides

7 - 7 + b = 3 - 7

b = -4

7.

x¹² · xⁿ = x¹²

Applying the multiplication law of indices, this can be written as

x¹² ⁺ ⁿ = x¹²

Equate the powers

12 + n = 12

Solve for n by subtracting 12 from both sides

12 - 12 + n = 12 - 12

n = 0

Hence, the value of n is 0

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The maximum diameter of the spheres Selim can purchase is approximately 1.78 feet, The correct answer is option (C).

To find the maximum diameter of the concrete spheres Selim can purchase, we need to consider the cost and surface area of the spheres. Given that the spheres cost $2 per square foot and Selim can spend $20 per sphere, we can start by finding the maximum surface area he can afford for each sphere.
1. Calculate the maximum surface area:
$20 ÷ $2 per square foot = 10 square feet
Now that we know the maximum surface area is 10 square feet, we can use the formula for the surface area of a sphere to find the maximum diameter.
2. Use the sphere surface area formula:
Surface area = 4πr², where r is the radius of the sphere.

Since the maximum surface area is 10 square feet, we can plug this value into the formula and solve for the radius.
10 = 4πr²
3. Divide both sides by 4π:
10 ÷ 4π = 0.796
4. Take the square root to find the radius:
r = 0.893 ft
5. Finally, multiply the radius by 2 to get the diameter:
D = 2 * 0.893 = 1.786 ft
Therefore, the maximum diameter of the spheres Selim can purchase is approximately 1.78 feet, which corresponds to option C.

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If measure of two "vertically-opposite-angles" are 115° and (2x + 5)°, then the equation to find value of "x" is 115° = (2x + 5)°,and value of "x" is 55.

The Vertically opposite angles are defined as a pair of non-adjacent angles formed by the intersection of two lines. and if the two angles are vertically opposite then their measures are equal, so, to find the value of "x", we equate the measure of both the angles,

The measure of the two angles are 115° and (2x + 5)°,

So, on equating,

We get,

⇒ 115° = (2x + 5)°,

⇒ 110° = 2x,

⇒ x = 55,

Therefore, the value of x is 55.

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The given question is incomplete, the complete question is

The measure of the two vertically opposite angles are 115° and (2x + 5)°, Write an equation that can be used to find the value of x. What is the value of x?

Answer:

  C. R+S+T = 201°

Step-by-step explanation:

You want to know which of the offered angle relations is true regarding quadrilateral RSTU.

The sum of angles in a quadrilateral is 360°. You use this fact to find angle T. Then you can compute the various differences to see which one matches the answer choices.

  T = 360° -R -S -U = 55°

In the attached calculator display, we have done exactly that. We find ...

  T -R = 38° . . . . A is false

  S -T = 74° . . . . B is false

  R +S +T = 201° . . . . C is TRUE

  R +T +U = 231° . . . . D is false

Answer:

To answer your question, we need to use some properties of rectangles and triangles.

A rectangle has four right angles, so angle R = angle S = angle T = angle U = 90 degrees.

The sum of the angles in a triangle is 180 degrees, so we can find the values of a, b, c, d, e, and f by using this property. For example, a + b + angle S = 180, so a + b = 90. Similarly, c + d = 90, e + f = 90, and f + g + angle U = 180, so f + g = 30.

Now we can evaluate each statement and see which one is true.

A) The difference between the measures of LT and LR is 4°. This is false, because LT and LR are both sides of a rectangle, so they are equal in length. The difference between them is zero, not four.

B) The difference between the measures of 2S and LT is 95°. This is false, because 2S is an angle and LT is a length. They have different units and cannot be compared or subtracted.

C) The sum of the measures of LR, 2S, and LT is 201°. This is false, because LR and LT are lengths and 2S is an angle. They have different units and cannot be added together.

D) The sum of the measures of LR, LT, and ZU is 193°. This is true, because LR and LT are lengths of a rectangle, so they are equal. ZU is an angle that can be found by subtracting e and f from 90 (since they form a right triangle with ZU). So ZU = 90 - e - f = 90 - (90 - c - d) - (90 - a - b) = a + b + c + d - 90. We know that a + b = c + d = 90, so ZU = 90 - 90 = 0.

Therefore, the sum of LR, LT, and ZU is LR + LT + 0 = 2LR = 2(17) = 34 degrees.

The correct answer is D.

Step-by-step explanation:

I hope that would help!!

Can I have Brainliest please?

Have a nice day

Given that quadrilateral PQRS is a parallelogram, you can prove that it is also a rectangle by A: Use the distance formula to find the length of both diagonals to see if they are congruent and B: Find the slopes of all sides to determine if the angles are right angles. Therefore, the correct option is C: C. Both A and B are valid.

To prove that PQRS is a rectangle, we need to show that all angles are right angles.

Option A: Using the distance formula, we can find the lengths of both diagonals, PR and QS. If PR and QS are congruent, then we know that opposite sides of the parallelogram are congruent and parallel (since PQRS is a parallelogram). If we can also show that PR and QS intersect at a 90-degree angle, then we have proven that PQRS is a rectangle.

Option B: Finding the slopes of all sides can help us determine if the angles are right angles. If the product of the slopes of adjacent sides is -1, then we know that the sides are perpendicular (since the slope of a line perpendicular to another line is the negative reciprocal of its slope). If we can show that all adjacent sides have slopes that multiply to -1, then we have proven that PQRS is a rectangle.

Both options A and B can be used to prove that PQRS is a rectangle, so the correct answer is C.

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a. True, more than 5% of the children selected "other".

b. True, 15% of kids say that Lucky Charms is their favourite cereal.

c. As the cereal that the most students chose, Frosted Flakes, it is true that this is the most popular cereal.

d. Fruit Loops were picked half as frequently as Frosted Flakes.

Using Percentage calcuate number of children:

Total number of children = 15 + 10 + 2 + 20 + 3 = 50

a). 3 children chose other.

Percentage = 3/50 × 100

= 6%

So it's accurate to say that more than 5% of the kids selected "other".

b). 15 children chose "lucky charm".

Percentage = 15/50 × 100

= 30%.

So it is true that 15% of kids prefer Lucky Charms cereal.

c). Frosted Flakes are the cereal that the majority of pupils choose, so it is true that this is the case.

d). Ten kids all chose Fruit Loops.

Twenty kids chose Frosted Flakes.

As a result, Frosted Flakes were picked twice as often as Fruit Loops.

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Answer:

g(x) = -2f(x)

Step-by-step explanation:

From the graph, we can see that g(x) is a reflection of f(x) about the x-axis, followed by a vertical stretch by a factor of 2. This is equivalent to multiplying f(x) by -2, which gives us the transformation:

g(x) = -2f(x)

it's important to carefully consider the assumptions and limitations of any statistical test or interval, and to ensure that they are appropriate for the data and research question at hand.

There are a few potential reasons why the procedure the student used may not be appropriate in this context:

1.Sample size: The accuracy of the t-distribution depends on the sample size and the assumption that the population follows a normal distribution. If the sample size is too small, the t-distribution may not provide an accurate estimate of the population parameters. In particular, a sample size of less than 30 is often considered too small for the t-distribution to be reliable.

2.Independence assumption: In order to use a t-test or t-interval, the samples should be independent. It's possible that some of the Italian and Spanish scientists may be related or have worked together, which could violate the independence assumption.

3.Population distributions: The validity of a t-test or t-interval also depends on the assumption that the populations have similar variances. If the variances are significantly different, this can affect the accuracy of the results.

4.Random sampling: In order for the results to be valid, the samples should be selected randomly from the populations of Italian and Spanish scientists. If the samples are not random, this could introduce bias into the results.

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This relationship between slopes can be explained by the fact that the curves y = x^2 and x = y are perpendicular to each other.

To calculate the slope of the curve y = x^2 at the point (3,9), we need to take the derivative of the equation with respect to x. This gives us y' = 2x. At the point (3,9), the slope would be y'(3) = 2(3) = 6.

To calculate the slope of the curve x = y at the point (9,3), we need to rewrite the equation in terms of y. This gives us y = x, and taking the derivative of y with respect to x gives us y' = 1. So the slope at the point (9,3) would be y'(9) = 1.

The simple relationship between these answers is that they are reciprocals of each other. The slope of the curve y = x^2 at a certain point is the inverse of the slope of the curve x = y at the same point.

To illustrate this principle with two more points on these curves, let's choose a second-quadrant point on y = x^2, such as (-2,4), and a corresponding point on x = y, which would be (4,-2).

At the point (-2,4) on y = x^2, the slope would be y'(-2) = 2(-2) = -4. At the corresponding point (4,-2) on x = y, the slope would be y'(4) = 1. Again, we can see that these slopes are reciprocals of each other.

This means that the slopes of the tangent lines at any two intersecting points will always be reciprocals of each other.

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Ana will take 100 ml on the first day and 5 ml less each day for 20 days, requiring a total of 1050 ml; the prescribed amount of 960 ml is not enough, resulting in a shortage of 90 ml, which will last for 18 days.

Ana will take the syrup for 20 days, and on each day, she will take 5 ml less than the previous day. To calculate the total amount of syrup Ana will need for the 20 days, we can use the formula for the sum of an arithmetic series,

S = (n/2) x (a₁ + aₙ), In this case, n = 20, a1 = 100 ml, and an = 100 ml - (19 x 5 ml) = 5 ml. Plugging in the values, we get,

S = (20/2) x (100 ml + 5 ml) = 1050 ml

So Ana will need a total of 1050 ml of syrup for the 20 days. The doctor prescribed 3 bottles of 320 ml each, which is a total of 960 ml. This is not enough to cover the full 20 days of treatment, as Ana will need 1050 ml. Therefore, there is a shortage of 90 ml of syrup. To calculate how many days Ana will lack syrup for, we need to divide the shortage by the daily reduction in dose,

90 ml/5 ml per day = 18 days

So Ana will have enough syrup for the first 2 days, but she will lack syrup for the next 18 days.

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Complete question - Ana has to take a syrup for 20 days, the doctor has prescribed 3 bottles of 320 ml each, she has to take the syrup in such a way that each day that passes she takes 5 ml less than the day before. If you start taking a 100 ml dose, how many ml will you take on the last day? Was the amount of syrup prescribed by the doctor enough? How much syrup is left over or lacking? if he lacked syrup, for how many days would he lack?

Using the tail-to-tip method, the sum of the two vectors is 76.32 m.

Using the tail-to-tip method, the sum of the two vectors will be the resultant of the vectors.

The magnitude of the resultant of the vectors is calculated as follows;

r = √(x² + y² )

where;

r = √ (40² + 65²)

r = 76.32 m

Thus, the sum of the two vectors using tail-to-tip method is determined by finding the resultant of the two vectors using Pythagoras theorem as shown above.

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The missing parts of the triangle are:

To find the missing parts of the triangle, we can use the Law of Sines and Law of Cosines.

First, we can use the Law of Cosines to find angle A:

cos(A) = (b² + c² - a²) / (2bc)

cos(A) = (13.7² + 16.7² - 8²) / (2 * 13.7 * 16.7)

cos(A) = 0.773

A = [tex]cos^-^1^(^0^.^7^7^3^)[/tex]

A ≈ 28.4°

Next, we can use the fact that the sum of the angles in a triangle is 180° to find angles B and C:

B = 180° - A - C

B = 180° - 28.4° - 99.1°

B ≈ 52.5°

C = 180° - A - B

C = 180° - 28.4° - 52.5°

C ≈ 99.1°

Therefore, the missing parts of the triangle are:

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Answer:

2[tex]\sqrt{17}[/tex]

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Distance = [tex]\sqrt{(7-(-1))^{2} + (4-2)^{2} }[/tex]

Simplify, and you will get the answer

2[tex]\sqrt{17}[/tex]

The amount of paper required to cover each memory box is 5220 square inches.

Considering the edge of the cube = L units.

Thus the area of one side of the cube will be equal to L² unit².

Now, there will be 6 such sides for a closed cube then the total surface area will be 6*(L)² unit²

The given length breadth and height of the box is 35in, 24in, and 30in.

The formula for the surface area of a rectangular prism is:

SA = 2(lw + lh + wh)

Where:

SA = surface area l = length w = width h = height

For this memory box, the given length (35 in), width (24 in), and height (30 in).

Substituting  these values into the formula the SA obtained will be:

SA = 2(35 × 24 + 35 × 30 + 24 × 30) SA

= 2(840 + 1050 + 720) SA

= 2(2610) SA = 5220inches²

Therefore, the answer will be 5220 square inches.

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An interest rate of approximately 2.40% per annum, compounded annually, is required to double an investment in 29 years.

Let "r" be the annual interest rate, then the investment will double after 29 years if (1 + r)^29 = 2. Solving this equation, we get r ≈ 0.0240 or 2.40% (rounded to two decimal places) as the required annual interest rate. This means that if the investment is compounded annually at this rate, it will double after 29 years.

Alternatively, we can use the formula for compound interest, A = P(1 + r/n)^(nt), where A is the future value, P is the present value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

We want to find the interest rate, r, that will double the investment, so we can set A = 2P, t = 29, n = 1 (compounded annually), and solve for r. This gives us r ≈ 0.0240 or 2.40%.

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The equations that would be correct with fraction 2/9 are:

81*x=18

45*x=100

900*c=200

Based on the given equation from the question, it can be seen that the fraction that is needed to complete the X is required, that will give the correct answer to each of the equation.

From the question, we can see that if we put X= 2/9 into the space above, we will have the correct solution. which is been performed below.

81*2/9=18

45*2/9=100

900*2/9=200

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The exact value of secθ secθ in simplest radical form is 106/81.

The length of the hypotenuse is the distance from the origin to the point (-9, 5):

√((-9)^2 + 5^2) = √(81 + 25) = √106

cosθ = adjacent/hypotenuse = -9/√106

Therefore, secθ = 1/cosθ = -√106/9.

In order to find the value of secθ secθ, we simply multiply secθ by itself:

secθ secθ = (-√106/9) * (-√106/9) = 106/81

The exact value of secθ secθ is 106/81.

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To approximate the values for Mₙ and S for n = 6 and 12, we'll use the trapezoidal rule (T), midpoint rule (M), and Simpson's rule (S). After calculating these approximations, we'll compute the errors Eₜ, Eₘ, and Eₛ.

For n = 6:
T₆ = (Approximation using trapezoidal rule)
M₆ = (Approximation using midpoint rule)
S₆ = (Approximation using Simpson's rule)

For n = 12:
T₁₂ = (Approximation using trapezoidal rule)
M₁₂ = (Approximation using midpoint rule)
S₁₂ = (Approximation using Simpson's rule)

Errors for n = 6:
Eₜ₆ = |Actual value - T₆|
Eₘ₆ = |Actual value - M₆|
Eₛ₆ = |Actual value - S₆|

Errors for n = 12:
Eₜ₁₂ = |Actual value - T₁₂|
Eₘ₁₂ = |Actual value - M₁₂|
Eₛ₁₂ = |Actual value - S₁₂|

As n is doubled (from 6 to 12), observe the changes in the errors:
- Eₜ and Eₘ typically decrease by a factor of about 4 (since error is proportional to 1/n² for these methods)
- Eₛ typically decreases by a factor of about 16 (since error is proportional to 1/n⁴ for Simpson's rule)

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Hose will take about 63.7 minutes to fill the pool and the the depth of the water is increasing at a rate of about 0.0079 feet per minute.

First, let's find the volume of the pool. The pool is in the shape of a cylinder with a height of 4 feet and a diameter of 16 feet, so its radius is half of the diameter, or 8 feet. The volume of a cylinder is given by

V = πr^2h

Plugging in the values, we get

V = π(8 ft)^2(4 ft)

V = 256π cubic feet

Next, let's convert the flow rate to cubic feet per minute. One gallon is equal to 0.1337 cubic feet, so the flow rate is

30 gallons/min x 0.1337 ft^3/gallon = 4.011 ft^3/min

Finally, we can use the formula

time = volume/flow rate

Plugging in the values, we get

time = 256π ft^3 / 4.011 ft^3/min

time ≈ 63.7 minutes

So it will take about 63.7 minutes to fill the pool.

Let's use the formula for the volume of a cylinder again to relate the volume of the water in the pool to its depth

V = πr^2h

We can solve this formula for h

h = V/πr^2

Taking the derivative of both sides with respect to time, we get

dh/dt = d/dt (V/πr^2)

The radius of the pool does not change, so we can treat it as a constant and take it out of the derivative

dh/dt = (1/πr^2) dV/dt

We know the flow rate is constant at 4.011 cubic feet per minute, so the rate of change of the volume of water in the pool is

dV/dt = 4.011

Plugging in the values, we get

dh/dt = (1/π(8 ft)^2) (4.011 ft^3/min)

dh/dt ≈ 0.0079 ft/min

So the depth of the water is increasing at a rate of about 0.0079 feet per minute.

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The area of the union of two disks with radius 1 and centers one unit apart is (5/3)π + (√(3))/4.

To find the area of the union of the two disks, we can use calculus to integrate over the area of overlap. The area of the union of the two disks is equal to the sum of the areas of C₁ and C₂ minus the area of their overlap. Each disk has a surface area of π(1)² = π, and a distance of 1 between their centers. We can use the law of cosines here,

The law of cosines states that c² = a² + b² - 2ab cos(θ), where c is the distance between the centers of the disks (1), a and b are the radii of C₁ and C₂ (1), respectively. Simplifying, we have,

cos(θ) = (1 - 1² - 1²)/(-211)

= -1/2,  so,

θ = 120 degrees.

The area of the overlap is equal to the area of a sector of C₁ with angle 120 degrees minus the area of the triangle formed by the centers of the disks and the point of intersection of the disks. The area of the sector is (120/360)π(1)² = (1/3)π, and the area of the triangle is,

(1/2)(1)(1)(sin(120)) = (√(3))/4.

Therefore, the area of the overlap is (1/3)π - (√(3))/4. The area of the union of the two disks is,

π + π - [(1/3)π - (√(3))/4]

= (5/3)π + (√(3))/4.

Thus, the area of the union of the two disks is (5/3)π + (√(3))/4.

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Answer:

Step-by-step explanation:

They each juggled for 3/4 of a minute

There were 3 people in total

3 people times 3/4 of a minute equals 2 1/4 minutes

The simplified standard form of (3.05 x 10⁻⁷) (8.67 x 10⁴) is 2.642 x 10⁻¹.

To simplify (3.05 x 10⁻⁷) (8.67 x 10⁴) and leave the answer in standard form to 3 decimal places:

1: Multiply the decimal numbers:
3.05 * 8.67 = 26.4245

2: Add the exponents:
-7 + 4 = -3

3: Combine the result and exponent in standard form:
26.4245 x 10⁻³

4: Adjust the decimal to have only one non-zero digit to the left of the decimal point and adjust the exponent accordingly:
2.64245 x 10² x 10⁻³

5: Simplify by combining exponents:
2.64245 x 10⁻¹

6: Round to 3 decimal places:
2.642 x 10⁻¹

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The length of GC is 22.5

Here we know that the triangles GHC and JKC are similar, we know that the corresponding angles are congruent.

That is, angle GHC is equal to angle JKC, angle HGC is equal to angle KJC, and angle CHG is equal to angle CKJ.

∠GHC = ∠JKC

∠HGC = ∠KJC

∠CHG = ∠CKJ

We can denote this as:

ΔGHC ~ Δ JKC

Using the concept of similarity, we can write the following proportion:

GC/ JK = HC/ KC

Here, GC represents the length of the corresponding side of triangle GHC, and JK represents the length of the corresponding side of triangle JKC. HC and KC represent the lengths of the other sides that are also proportional.

We can cross-multiply to get:

GC × KC = HC × JK

Now, we can substitute the values we know.

=> x * 20 = 18 x 25

=> x = 22.5

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Answer:

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The total cost of repair is expressed by the function:

As we see,

Therefore the answer is option A.

Answer:

Martha started at 189 feet below sea level. She went up 790 feet to the top of the mountain, so her elevation was 790-189 = 601 feet above sea level. She then went down 254 feet, so her elevation is now 601-254 = 347 feet above sea level.

Here is the calculation in equation form:

```

Elevation = (Starting elevation) + (Ascent) - (Descent)

```

```

Elevation = 189 feet + 790 feet - 254 feet

```

```

Elevation = 347 feet

```

Answer: Martha is 347 ft above sea level.

Step-by-step explanation:

At first, she is -189 feet below sea level. She went up by 790 feet, bringing her to 690 feet above sea level. She descended by 254 feet and ended up at 347 feet above sea level.

Answer:

A = 4(16) + (1/2)π(8^2) = 64 + 32π cm^2

= 164.5 cm^2