evaluate f ( - 5 ) =

Answer:

[tex]A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524[/tex]

Step-by-step explanation:

Use the Washer Method [tex]A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx[/tex] where [tex]R(x)[/tex] is the outer radius and [tex]r(x)[/tex] is the inner radius.

If we sketch out the graph, we see that [tex]y=1[/tex] intersects points [tex](1,1)[/tex] and [tex](3,1)[/tex], which will be our bounds of integration.

Here, our outer radius will be [tex]R(x)=(-1-1)=-2[/tex] and our inner radius will be [tex]r(x)=-1-\frac{1}{x}[/tex].

Thus, we can compute the integral and find the volume:

[tex]A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2} \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\[/tex]

[tex]A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524[/tex]

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

Answer:

8 in

Step-by-step explanation:

A 45-45-90 triangle is a special triangle with side length ratio 1 : 1 : √2

The legs are equal in length.

The length of the hypotenuse is √2 times the length of a leg.

Therefore, if the hypotenuse of a 45-45-90 triangle is 8√2 inches, the leg lengths are 8 inches each in length.

Answer:

Graph A is the answer

Step-by-step explanation:

The width of the origin is equal to 3 and the slope is 1

Answer:

11/5mi or 2.2mi

Step-by-step explanation:

1/2 +3/5 +11/10 =11/5mi

Hey there!

0.5 + 0.6 + 1.1 = 2.2

Total miles = 2.2mi

Answer:

  CE ≈ 8.24 units

Step-by-step explanation:

The circumference of a circle is given by the formula ...

  C = 2πr

Your circle has a radius CD of 4 units, so its circumference is ...

  C = 2π(4 units) = 8π units

__

The arc of interest is 118°. The whole circle is 360°, so the length of the arc is 118/360 times the circumference of the circle:

  CE = (118/360)(8π units) ≈ 8.24 units

well it would be very helpful thank you

Answer:

y = - x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (9, 0) ← 2 points on the line

m = [tex]\frac{0-9}{9-0}[/tex] = [tex]\frac{-9}{9}[/tex] = - 1

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = - x + 9 ← equation of line

Answer:

1/7 and 1/2

Step-by-step explanation:

The probability of orange marble is 1/7

Probability of tails is 1/2

If you need to add this, then it'll be 1/14

7 x 2 = 14

1 x 1 = 1

Answer:

24x8+3+9=$44,839 a month

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Since l and r Parrell lines that means the measure of 4 is 80 since there vertical angles. And then  1 and 4 needs to be supplementary which means the two angles combined equals 180. so 180-80=100

so 1s angle measure is 100

Answer:

40

Step-by-step explanation:

A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.

To find the measure of angle DPE, we have to add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).

Let's add Angle FPD and Angle EPG.

105 + 35 = 140

Now, let's subtract that from 180.

180 - 140 = 40

So, the measure of Angle DPE is 40. I hope this helps! Have a lovely day! (i basically just copy-and-pasted my answer to problem 17 because it was the same answer as this lol)

Answer: 377.36cm^2

Step-by-step explanation:

1. find proper equation. to find the volume of any three dimensional cube or box, use: length * width * height

2. plug in given numbers into the equation: 8.9cm * 4cm * 10.6* which gives us our answer, 377.36cm^2

hoped this helped! ♡

Answer:

[tex]5 \frac{5}{14} [/tex]

Step-by-step explanation:

[tex]3 \frac{5}{7} + 1 \frac{9}{14} [/tex]

Turn them into improper fractions

[tex] \frac{26}{7} + \frac{23}{14} [/tex]

[tex] \frac{2}{2} \times \frac{26}{7} + \frac{23}{14} [/tex]

[tex] \frac{52 + 23}{14} [/tex]

[tex] \frac{75}{14} [/tex]

Turn it into a mixed fraction

[tex]5 \frac{5}{14} [/tex]

Answer:

Step-by-step explanation:

[tex]\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}[/tex]

where [tex]u = x + e^{x}[/tex]

So we can obtain: [tex]\frac{dy}{dx}=(1+e^{x})\cos(u)=(1+e^{x})\cos(x+e^{x})[/tex]

Answer:

Step-by-step explanation:

B(0, -14) ⇒ x₁ = 0 & y₁ = -14

F(4,6) ⇒  x₂ = 4 & y₂ = 6

[tex]Midpoint = \left(\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{1}+y_{2}}{2} \right)[/tex]

                [tex]=\left(\dfrac{0+4}{2},\dfrac{-14 + 6}{2}\right)\\\\\\= \left(\dfrac{4}{2}, \dfrac{-8}{2} \right)\\\\\\=\left(2, -4 \right)[/tex]

Answer:

A. Directions: Encircle the letter of the correct answers

Step-by-step explanation:

1.the I in resign sounds like the I in.

A. hit B. High

Answers:

jamal has 30 stickers in total.

chris has 7 stamps in each group.

Step-by-step explanation:

1. use multiplication, 6*5=30

2. use division, 56/8=7

hope this helped! ♡

Answer:

jamal has 30 stickers in total.

chris has 7 stamps in each group.

Step-by-step explanation:

a) The determination of the standard quota for the Dagonal district is 40.57%.

b) 1. The standard divisor is 267.19 (4,275/16).

2. The standard, lower, and upper quotas for the four districts are as follow:

                               North         South           East         West      

Standard quota     18.36%       26.32%     45.61%       9.71%

Lower quota             18%          26%            45%            9%

Upper quota             18%          26%            46%           10%

The quota method of apportionment is the use of the standard divisor to round off standard quotas, according to some agreed ground norms.

When the standard quota is rounded down to an integer, it gives the lower quota, and rounding up gives the upper quota.

The standard divisor is calculated as the total population divided by the total number of seats.

The standard divisor gives the average number of people represented by a Board or seat member.

Hamilton, NY Population:

Residents of Hamilton, NY = 73,465

Board Trustee Members = 12

                             Basel         Heights       Dagonal      Total

Population            13,244        30, 415        29,806    73,465

Proportion            18.03%        41.40%         40.57%      100%

Allocation of Board

Seats                         2                  5                 5               12

Gotham City Population:

Number of seats = 16 seats

                             North         South         East         West      Total

Population               785          1,125         1,950        415       4,275

Proportion            18.36%      26.32%     45.61%       9.71%    100%

Allocation of Board

Seats                        3                 4                7              2          16

Learn more about the quota system at brainly.com/question/12105335

Answer:

y = x - 1

Step-by-step explanation:

First find the slope. Subtract the y's and put that on top of a fraction. Then subtract x's and put that on the bottom. Simplify if possible.

7-1 is 6 goes on top.

8-2 is 6 goes below.

6/6 is 1 when simplified.

Slope is 1.

Slope-intercept form is y = mx + b.

m is slope, so fill that in.

y = (1)x + b

Now we need to find b.

Use either one of the given points; they will give you the same answer no matter which one you choose. Let's use (2,1) because smaller numbers.

y is 1 and x is 2.

y= (1)x + b

1 = (1)2 + b

1 = 2 + b

-1 = b

Now fill in both m and b. Leave x and y as letters (variables)

y = (1)x + -1

Final answer:

y = x - 1

Answer:

Answer:

B. 4

Step-by-step explanation:

To undo multiplication (which is what is being asked of us) you must divide. 28 divided by 7 is 4

so

4 x 7 is 28

If Brianna is taking care of 7 chickens, Tamara is taking care of 4 times the number of chickens because she is taking care of 28

Answer:

Pill 1 costs 25e, and pill 2 costs 75e. Complete parts a and below. An a. How many of each pill should he buy in order to minimize his cost? What is the minimum?

Step-by-step explanation:

Answer:

26,620

Step-by-step explanation:

1 year: 20,000 x 0.10 = 2000

2 years: 22,000 x 0.10 = 2200

3 years: 24200 x 0.10 = 2420

2420 + 24200 = 26620

Have an amazing day!!

Please rate and mark brainliest!!!!

Theres a button on the question taht you are wanting to answer. Sometimes it will allow one other times it is 2

Using it's concept, it is found that there is a [tex]\frac{11}{17}[/tex] probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, a total of 1 + 4 + 2 + 0 + 1 + 2 + 2 + 0 + 2 + 3 = 17 students were sampled.

Of those, 1 + 2 + 1 + 2 + 2 = 8 live in on campus housing, and 3 live off campus but are graduate students, hence there are 11 desired outcomes and the probability is given by:

[tex]\frac{11}{17}[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

Step-by-step explanation:

Measure of inner angle of the n-sided polygon is

[tex]\frac{180(n-2)}{n}[/tex]

~~~~~~~~~~~~~~

m∠PQR = [tex]\frac{180(10-2)}{10}[/tex] = 144°

PQ = QR ⇒ m∠QPR = m∠QRP

m∠PRQ = ( 180° - 144° ) ÷ 2 = 18 °

Answer:

∠PRQ = 18°

Step-by-step explanation:

Sum of interior angles of a polygon = (n - 2) × 180°
(where n is the number of sides)

Interior angle of a regular polygon = sum of interior angles ÷ n
(where n is the number of sides)

Given:

⇒ Sum of interior angles of a polygon = (10 - 2) × 180° = 1440°

⇒ Interior angle of a regular polygon = 1440° ÷ 10 = 144°

Therefore, as PQ and QR are the sides of the polygon, ∠PQR = 144°

Sum of interior angles of a triangle = 180°

⇒ ∠PQR + ∠RPQ + ∠PRQ = 180°

⇒ 144° + ∠RPQ + ∠PRQ = 180°

⇒ ∠RPQ + ∠PRQ = 36°

As the polygon is regular, PQ = QR which means that ΔPQR is isosceles.

Therefore, ∠RPQ = ∠PRQ

⇒ ∠PRQ = 36° ÷ 2 = 18°