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Free_Kalibri [48]

3 years ago

9

crater Lake in Oregon in shaped like a circle with a diameter of about 5.5 miles. What is the area of the surface of crater lake

?

1 answer:

N76 [4]3 years ago

3 0

Answer:

Given the statement: Crater Lake in Oregon in shaped like a circle with a diameter of about 5.5 miles.

Area of circle is given by:

$A = \pi \frac{d^2}{4}$

where

A represents the area of a circle

d represents the diameter of a circle.

then;

It is given that Surface of Crater lake is shaped like a circle.

Substitute the given values, we have;

Area of a circle = $\pi \frac{(5.5)^2}{4}$

= $3.14 \times \frac{30.25}{4} =3.14 \times 7.5625 = 23.74625$ square miles

therefore, the area of a surface of a crater lake is, 23.74625 square miles.

You might be interested in

The value of y varies jointly with the values of x and z When x = 4 and z = 10, the value of y is 360.

Igoryamba

Answer:

A

Step-by-step explanation:

Joint variation is given by:

$y=kxz$

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

$360=k(4)(10)$

Solving for k:

$40k=360\Rightarrow k=9$

Therefore, our equation is:

$y=9xz$

Then when x = 5 and z = 12:

$y=9(5)(12)=540$

The answer is A.

3 0

3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

Eight friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. They

posledela

Answer:The system of equations to describe the situation are

c + y = 8

6c + 3y = 36

Step-by-step explanation:

Let c represent the number of shirts.

Let y represent the number of caps.

Eight friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. This means that

c + y = 8 - - - - - - - - - - -1

They want to spend exactly $36 on the shirts and caps. Shirts cost $6 each and caps cost $3 each. This means that

6c + 3y = 36 - - - - - - - - - - 2

4 0

3 years ago

The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent t

Galina-37 [17]

Answer:

x = 1, y = 60

Step-by-step explanation:

Value of new-releases (x) = $20 each

Value of classic (y) = $8 each

Total budget = $500

Equation : 20x + 8y = 500

The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.

Lets assume the librarian buys at least one new-release DVD.

x=1

20x + 8y = 500

8y + 20(1) = 500

y = 60

<em>Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.</em>

!!

8 0

3 years ago

Ganezh [65]

Answer:

168 meters squared

Step-by-step explanation:

So we know that Jake walked from b to c and d meaning he didn't go from a to b, but we also know that scarlet walked a to b so to find the length we can subtract scarlet's walk by jake's walk or 38-31 which is 7.

So we know the length of one side is 7 so this means we have side a to b and c to d, but we still need to know b to c. So what we can do is get the length of a b c and d and isolate it so that we only have b to c. To do this we get the length of 7 and double it which is 14 and take it away from the 38m

38-14=24

so now we know that the side is 24 and we can solve for the area

24*7=168

so the answer is 168 meters squared

6 0

3 years ago