For an object whose velocity in ft/sec is given by v(t) = -3t2 + 5, what is its displacement, in feet, on the interval t = 0 to t = 2 secs?

Step-by-step explanation:

To find the displacement I'll give you two ways since I don't know if you had experience with calculus. So here's both ways.

Way 1: Graph 1: Geometric Apporoach.

I'll a graph where t is x axis and v is y axis. So we have a velocity versus time graph.

Then, we graph the function

Look Above this what graph I get

Now, to find displacement,

Remeber displacement is the product of velocity and time. So here displacement is area under the curve.

We want displacement from 0 to 2. so let form the shape under the curve.

Look at the second graph, we form a triangle and we get this

Area of Triangle is 1/2 bh.

The base is 2 and the height is -6 so we get

Our height is -12 because velocity is a vector so it can be negative and down is negative.

So the displacement is -12

Way 2: Calculus Way.

We can use integration to find the answer.

So now we have

Now we do,

So the area under the curve is -12. Thus displacement is -12

2500

step-by-step explanation:

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.