Due to a lightning strike, a forest fire begins to burn and is spreading outward in a shape that is roughly circular. the radius of the circle is modeled by the function r(t) = 2t + 1, where t is the time in minutes and r is measured in meters.

1). write a function for the area burned by the fire directly as a function of t by computing (a ◦ r)(t).

2) find the area of the circular burn after 20 minutes.

1 - meter²

2 - 5,281 meter²

Step-by-step explanation:

We are given that,

Radius of the circle is modeled by the function, , where 't' is the time in minutes.

Part 1: It is required to compute the area of the forest burned.

Since, Area of the circle =

So,

i.e.

i.e.

Thus, the area of the forest burned by the fire is meter²

Part 2: It is required to find the area after 20 minutes of burn.

That is, t = 20 mins.

So substituting, we get,

i.e.

i.e.

i.e.

i.e. meter²

Thus, the area burned after 20 mins of fire is 5,281 meter².

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.