Help ASAP - Find the area of the composite figure made up of a square and a semicircle. Use 3.14 as an approximation for and give your
answer to the nearest square inch. Enter only the number.

The area of the surface above the region R is 4096π square units.

Given that:

The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]

The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].

To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.

The integral for the area is given by:

[tex]Area = \int\int_R f(x, y) dA[/tex]

To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.

Using polar coordinates, we can parameterize the region R as follows:

x = rcos(θ)

y = rsin(θ)

where r goes from 0 to 8, and θ goes from 0 to 2π.

Now, rewrite the integral in polar coordinates:

[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]

Now, we can integrate with respect to r first and then with respect to θ:

[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]

Integrate with respect to r:

[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]

Now, we can integrate with respect to θ:

[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]

Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))

Area = 4096π + 128(0) - 0

Area = 4096π square units

So, the area of the surface above the region R is 4096π square units.

Learn more about Integration here:

https://brainly.com/question/31744185

#SPJ4

Answer:

Step-by-step explanation:

Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.

  Linda has $15

  Reuben has $25 . . . . . . $10 more than Linda

  Manuel has $30 . . . . . . twice what Linda has

Answer:

77

Step-by-step explanation:

At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.

Answer:

e

Step-by-step explanation:

e

Answer:

a[tex]\geq[/tex]-3

Step-by-step explanation:

Answer:

-3  ≤  a

Step-by-step explanation:

6≥ -6(a+2)

Divide each side by -6, remembering to flip the inequality

6/-6 ≤ -6/-6(a+2)

-1 ≤ (a+2)

Subtract 2 from each side

-1 -2  ≤  a+2-2

-3  ≤  a

Answer:

a. uses a related sample - repeated measures

c. uses a related sample (matched subjects)

Step-by-step explanation:

A) You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.  

The design described uses a related sample - repeated measures because the scores were compared on the Hoarding Severity scale before and after the treatment.

B) John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people.

The design described uses a related sample (matched subjects)

Answer:

increase of 30

Step-by-step explanation:

1255- 1075 = 180

This is an increase of 180

Divide by the number of numbers which is 6

180 /6 = 30

The mean will increase by 30

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

The correct answer is the first one.

Step-by-step explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.

Answer:

option 1

Step-by-step explanation:

Answer:

6x + y = -18

Step-by-step explanation:

The given equation is,

y - 6 = -6(x + 4)

We have to rewrite this equation in the form of Ax + By = C

Where A, B and C are the integers.

By solving the given equation,

y - 6 = -6x - 24 [Distributive property]

y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]

y = -6x - 18

y + 6x = -6x + 6x - 18

6x + y = -18

Here A = 6, B = 1 and C = -18.

Therefore, 6x + y = -18 will be the equation.

Answer:

f(x) = (x + 6)² - 29

Step-by-step explanation:

Given

f(x) = x² + 12x + 7

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

x² + 2(6)x + 36 - 36 + 7

= (x + 6)² - 29, thus

f(x) = (x + 6)² - 29

answers are 6, and -29

Answer:

To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||

(1,1,1) is not equal to (-10,5)

Step-by-step explanation:

a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)

Any algebra raised to the power of zero is equal to 1.

a°b° = 1 × 1 = 1

1 + ab + a^2b^2 < -10x^3 + 5x

The vectors:

(1,1,1) < (-10,5)

This verifies the Cauchy-Schwarz Inequality

Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.

Answer:

115 miles

Step-by-step explanation:

First find the distance at 50 mph

d = 50 mph * .5 hours

   = 25 miles

Then find the distance at 60 mph

d = 60 mph * 1.5 hours

   = 90 miles

Add the distances together

25+90

115 miles

Answer:

he drives a 115 miles

Step-by-step explanation:

if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90

90+25=115 so he drove 115 miles.

The correct graph will be the first one (A)

Answer:

answer is

B) 36,72,80

Step-by-step explanation:

because is the right angle it is exactly 90°

Answer:

y = -3.5x² + 2.7x -8.2

Step-by-step explanation:

the quadratic equation is set up as a² + bx + c, so just plug in the values

Answer:

[tex]-3.5x^2 + 2.7x -8.2[/tex]

Step-by-step explanation:

Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].

So, we can use your values of a, b, and c, and plug them into the equation.

A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].

B is 2.7, so the second term is [tex]2.7x[/tex]

And -8.2 is the C, so the third term is [tex]-8.2[/tex]

So we have [tex]-3.5x^2+2.7x-8.2[/tex]

Hope this helped!

I hope this will help uh.....

Answer:

Hey there!

The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.

Let me know if this helps :)

Answer: Rectangle

Step-by-step explanation:

In a rectangular prism, every cross-section parallel to a side is a rectangle.

Hope it helps <3

Answer:

Range { 2,6,8}

Step-by-step explanation:

The domain is the input and the range is the output

Range { 2,6,8}

Answer:

2, 6, 8

Step-by-step explanation:

The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.

Answer:

The spread of the data in Set B is greater than the spread of the data in Set A.

Step-by-step explanation:

Just took the test :3

Answer: length = 1, width = 1, height = 3, volume = 5

Step-by-step explanation:

Degree is the biggest exponent for the variables in the expression

Length = 4x - 1. The exponent for x is 1 --> degree = 1

Width = x          The exponent for x is 1  --> degree = 1

Height = x³       The exponent for x³ is 3  --> degree = 3

Volume = 4x⁵ - x⁴.  The biggest exponent for x is 5  --> degree = 5

Answer:

- First answer: 1

- Second answer: 1

- Third answer: 3

- Last answer: 5

Step-by-step explanation:

Correct on E2020

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

__

The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

[tex]csc (\theta)=\frac{33}{55}[/tex]

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:

[tex]sin(\theta)=\frac{55}{33}[/tex]

3) So, remembering operations with fractions then the cosecant is:

[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]

[tex]csc (\theta)=\frac{33}{55}[/tex]

Answer:

The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .

Step-by-step explanation:

We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

So, the area of an equilateral triangle =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

where, s = side of an equilateral triangle

A  =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

Cross multiplying the fractions we get;

[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]

[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]

Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;

[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]

Taking square root both sides we get;

[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]

[tex]P(First\ White) = \dfrac{3}{10}[/tex]

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Answer:

[tex]\boxed{x = 9}[/tex]

Step-by-step explanation:

m = -1/3

b = 7

And y = 4 (Given)

Putting all of the givens in [tex]y = mx+b[/tex] to solve for x

=> 4 = (-1/3) x + 7

Subtracting 7 to both sides

=> 4-7 = (-1/3) x

=> -3 = (-1/3) x

Multiplying both sides by -3

=> -3 * -3 = x

=> 9 = x

OR

=> x = 9

Answer:

x = 9

Step-by-step explanation:

m = -1/3

b = 7

Using slope-intercept form:

y = mx + b

m is slope, b is y-intercept.

y = -1/3x + 7

Solve for x:

Plug y as 4

4 = 1/3x + 7

Subtract 7 on both sides.

-3 = -1/3x

Multiply both sides by -3.

9 = x

Answer:

Vertical angles are congruent.

Step-by-step explanation:

Vertical angles are opposite angles formed by intersecting lines, and are always congruent.

Answer:

j < 2

Step-by-step explanation:

Simplify both sides of the inequality and isolating the variable would get you the answer

Answer:  A, B, and D

Step-by-step explanation:

Input the coordinates into the inequality to see which makes a true statement:

                             5x - 2y < 8

A) x = -1, y = 1       5(-1) - 2(1) < 8

                              -5  -  2   < 8

                                    -7     < 8       TRUE!

B) x = -3, y = 4       5(-3) - 2(4) < 8

                              -15  -  8   < 8

                                    -23    < 8     TRUE!

C) x = 4, y = 0       5(4) - 2(0) < 8

                              20  -  0   < 8

                                    20     < 8    False

D) x = -2, y = 3       5(-2) - 2(3) < 8

                              -10  -  6   < 8

                                    -16     < 8   TRUE!

Answer:

Step-by-step explanation:

Given,

Hypotenuse ( h ) = 158 cm

Perpendicular ( p ) = 83

Base ( b ) = ?

Now, Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

Plug the values

[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]

Evaluate the power

[tex] {b}^{2} = 24964 - 6889[/tex]

Calculate the difference

[tex] {b}^{2} = 18075[/tex]

[tex]b = \sqrt{18075} [/tex]

Calculate

[tex]b = 134.4 \: cm[/tex]

Hope this helps..

Best regards!!

Answer: 168

Step-by-step explanation:

First, let's count the types of selection:

We can select:

Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)

Pack: standard, custom, or sport styling, (3 options)

type of transmission: Manual or automatic (2 options)

Color: (7 options)

The total number of combinations is equal to the product of the number of options in each selection:

C = 4*3*2*7 = 168

Answer:

The required probability = 0.144

Step-by-step explanation:

Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%

Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.

That would be;

P(making money) * P(making money) * P(losing money)

Kindly recollect;

P(making money) = 60% = 60/100 = 0.6

P(losing money) = 40% = 40/100 = 0.4

The probability we want to calculate is thus;

0.6 * 0.6 * 0.4 = 0.144

Answer:

Step-by-step explanation:

From the summary of the given data;

After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.

Let consider [tex]p_1[/tex] to be the probability of those that experience the drowsiness in group 1

[tex]p_1[/tex] = [tex]\dfrac{137}{452}[/tex]

[tex]p_1[/tex] = 0.3031

After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.

Let consider [tex]p_2[/tex] to be the probability of those that experience the drowsiness in group 1

[tex]p_2[/tex] = [tex]\dfrac{31}{99}[/tex]

[tex]p_2[/tex] = 0.3131

The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.

In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.

So; the null and the  alternative hypothesis can be computed as:

[tex]H_o :p_1 =p_2[/tex]

[tex]H_a= p_1<p_2[/tex]

The test statistics is computed as follows:

[tex]Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }[/tex]

[tex]Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }[/tex]

[tex]Z = \dfrac{-0.01}{0.051378 }[/tex]

Z = - 0.1946

At the level of significance ∝ = 0.05

From the standard normal table;

the critical value for Z(0.05) = -1.645

Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.

Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2