Abarrel 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)

As per the statement:

The sauce flow can be expressed with the function is given by:

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:

Part A.

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

then;

Substitute the function r(t) we have;

           .....[1]

therefore, the area of the circle of spilled sauce as a function of time, is:

.

Part B:

We have to find how large is the area of spilled sauce after 5 minute.

use  π = 3.14 and t = 5 minutes

Substitutes these in [1] we have;

⇒

Simplify:

square unit

therefore, 314 square unit large is the area of spilled sauce after 5 minute.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .