Question

FAN AND MEDAL
A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.

Part A: Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

for part A, we want to rewrite r in terms of t

Answer 2

r = 2t

then we substitute that into the area equation

A = pi * r^2 = pi * (2t)^2

Answer 3

for part B, you just let t = 5 and solve for A

Answer 4

let me know if you have additional questions

Answer 5

I still don't get part B @vocaloid

Answer 6

t = 5

A = pi * (2t)^2 = ?

Answer 7

so do i put 4t? @vocaloid

Answer 8

no

Answer 9

if t = 5

what does pi * (2t)^2 equal?

Answer 10

seven @vocaloid

Answer 11

no

Answer 12

what is (2t)^2?

Answer 13

9 i think

Answer 14

where are you getting these numbers??

Answer 15

if t = 5

what is 2t?

Answer 16

5 times 2

Answer 17

which equals...?

Answer 18

oh i multiplied wrong it's 10

Answer 19

good

now, what is 10^2?

Answer 20

the ^ sign means to divide right

Answer 21

no, it's an exponent

Answer 22

10^2 = 10 * 10 = ?

Answer 23

oh so it's 20

Answer 24

nope

Answer 25

what is 10 * 10?

Answer 26

100

Answer 27

good

now what is 100 * 3.14?

Answer 28

314

Answer 29

good, that's your final answer

Answer 30

thank you so much