George wanted to measure the angle of a water slide at the lake. He used a sheet of folded paper that formed a 20° angle. He measured and found that three of the folded paper angles would fit in the angle made by the slide and the ground.

Which of the following was the angle of the water slide?

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: 200 seconds

Okay - so then Oliver would take 3 minutes and 20 seconds. There are 60 seconds in a minute so it would be 30 times 60 = 180 + 20 = 200

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:

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°

Answer:

[tex]===============================[/tex]

In order to find the vertex of a parabola, we use the following formula:

[tex]\bold{\displaystyle\frac{-b}{2a} }}[/tex]

Remember, a parabola looks like so:

[tex]\tt{y=ax^2+bx+c}[/tex]

Now we know what a and b stand for.

In this case, b is -4, and a is -1:

[tex]\hookrightarrow\sf{\displaystyle\frac{-(-4)}{2(-1)}[/tex]

Simplify:

[tex]\hookrightarrow\sf{\displaystyle\frac{4}{-2} }}[/tex]

Divide:

[tex]\hookrightarrow\sf{-2}[/tex]

[tex]===================================[/tex]

[tex]\mathbb{DiAmOnD}\\{\boxed{An~Emotional~And~Creative~Helper}}}}[/tex]

Answer:

x = -3.5

y = 1.5

so W = (-3.5, 1.5)

Step-by-step explanation:

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:

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

Step-by-step explanation:

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:

3 > x

Step-by-step explanation:

3 is larger than all of the values on the line, of which the arrow is pointing. The circle is open, so it means that it is not greater than or equal to.

I hope this helps!

-No one

For a monthly sales figures at 5600 and expected to fall for the following 9 months at a rate of 2% each month, the  total sales for the next two years  is mathematically given as

A=11968.04

Generally,  the  total sales  is mathematically given as

A=5600(1-2/100)^9(1+4/100)^24

A=5600(.98)^9(1.04)^24

A=11968.04

In conclusion, total sales for the next two years

A=11968.04

Read more about Arithmetic

https://brainly.com/question/22568180

Answer:

Sample 1

Step-by-step explanation:

Let's solve this step by step:

  *the first digit cannot have '0' as its first digit since it would make the

  number one-digit

Total Choice: 9 choices * 10 choices = 90 choices

Hope that helps!

Answer:

(x+2)^2 + (y-4)^2 = 65

Step-by-step explanation:

r^2 = (4-(-4))^2 + (-1-(-2))^2 = 65

center = (-2, 4) so you add 2 to x and subtract 4 from y

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: 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:

16.

Step-by-step explanation:

Multiply 20 and 4/5 to get the result of who is going.

20 * (4/5)

(20*4)/5

80/5

16

16 friends will be going to the party.

Answer:

16 friends

Step-by-step explanation:

Out of 20 friends, 4/5 are going to the party. How many friends are going to the party?

4/5 * 20 or 20 * 4/5

[tex]\frac{4}{5}*20\\\\ \frac{4}{5} *\frac{20}{1} < ==reduce\\\\\frac{4}{1}* \frac{4}{1}\\\\\frac{16}{1} \\\\16[/tex]

Therefore, 16 friends are going to the party.

Hope this helps!

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:

well it would be very helpful thank you

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

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:

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)

in 20 days 4 half life will be completed

so n = 4

formula :-

[tex] \frac{ A\degree}{ {2}^{n} } = \frac{9056}{ {2}^{4} } = \frac{9056}{16} = 566grams[/tex]

The radioactive kind of promethium will have 566 grams left after 20 days.

Half-life is the time required for a quantity to reduce to half of its initial value.

Given, A radioactive kind of promethium with 9,056 grams and a half-life is 5 days.

∴ In the next 5 days, it'll have (9056/2) = 4528 grams.

Next 5 days it'll have (4528/2) = 2269 grams.

As it has a half-life in 5 days and 20 is multiple (4×5).

After 20 days the radioactive material will have (9056/2⁴) grams.

= 566 grams left.

learn more about half-life here :

https://brainly.com/question/16387602

#SPJ2

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

Answer:

(0,5)

Step-by-step explanation:

I'm really not sure but I'm pretty positive that this is the answer if not than my bad

The outputs are addition of 4 to their inputs therefore,if the input is n then the output will also be an addition of 4 hence n+4