The position of a particle moving along a line is given by s(t) = 2t3 - 24t2 + 90t + 7 for t ≥ 0. for what values of t is the speed of the particle increasing?

The speed of the particle increases for

Step-by-step explanation:

Given:

To find the speed of the particle, we need a second derivative of the equation

Differentiating, we get,

Again differentiating , we get,

Since, we need to find at what value the speed of the particle increasing, we need to equate to find the interval at which the speed of the particle increases. Thus,

Thus, the interval are and

Substituting any one value between the interval in the equation

The speed of the particle does not increase at the interval

Now, substituting any one value between the interval in the equation

Thus, the speed of the particle increases during the interval

Hence, the speed of the particle increases for

y=mx+b

step-by-step explanation:

m slope

b y-intercept

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "