Gus has a fish tank that holds 47104710 inches^3 3 of water. he is using a cylinder shaped bucket with a radius of 55 inches and a height of 2020 inches to fill the tank. how many times will gus need to fill the bucket to completely fill the fish tank if he doesn't spill a drop? use 3.143.14 for \piπ.

3 times.

Step-by-step explanation:

We are told that Gus has a fish tank that holds of water. He is using a cylinder shaped bucket with a radius of 5 inches and a height of 20 inches to fill the tank.

To find the number of times Gus needs to fill the bucket we will divide volume of fish tank by volume of the bucket.

We will use the cylinder volume formula to find the volume of bucket.

, where,

V= Volume of cylinder.

r= Radius of cylinder.

h= Height of cylinder.

Upon substituting our given values in volume formula we will get,

Therefore, the volume of bucket is 1570 cubic inches.

Now let us divide 4710 by 1570.

Therefore, Gus will need to fill the bucket 3 times to completely fill the fish tank.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240