Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.

the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = πp2.

part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work.

part b: how large is the area of spilled paint after 2 minutes? you may use 3.14 to approximate π in this problem.

Given the paint flow can be expressed with the function as:

where, t represents time in minutes and p represents  how far the paint is spreading.

It is also given that: The flowing paint is creating a circular pattern on the tile

The area of the pattern can be expressed as:

A

To find the area of the circle of spilled paint as a function of time.

⇒

therefore,  the area of the circle of spilled paint as a function of time .         ......[1]

B

To find how large is the area of spilled paint after 2 minutes.

Substitute t = 2 minutes and in [1] we have;

square units.

Therefore, 314 square units large is  the area of spilled paint after 2 minutes.

mk./km: lm

step-by-step explanation:

,mlmlm

; mk

lk

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!