PLEASE HELP!!

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

4 0

M(meters) = 0.9144*y(yards)

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A ball rolls down an inclined plane such that the distance (in centimeters) that it rolls in t seconds is given by s(t) = 2t^3 +

IRISSAK [1]

The ball's velocity will be represented by the derivative of its distance function:

$s'(t)=6t^2+6t$

Now find the times $t$ for which this is equal to 30, i.e. solve

$6t^2+6t=30\implies t^2+t-5=0$

This has two solutions, $t=-\dfrac{1\pm\sqrt{21}}2$ , but only one is positive and falls in the interval $[0,3]$ . So the velocity reaches 30 cm/s when $t=-\dfrac{1-\sqrt{21}}2\approx1.79$ .

3 0

3 years ago

Suppose total benefits and total costs are given by b(y) = 100y − 8y2 and c(y) = 10y2. what is the maximum level of net benefits

olga nikolaevna [1]

Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).

B(y)=b-c
B(y)=100y-18y²

Now that we have a net benefits function we need find it's derivate with respect to y.

$\frac{dB(y)}{dy} =100-36y$

Now we must find at which point this function is equal to zero.

0=100-36y
36y=100
y=2.8

Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.

B(2.8)=100(2.8)-18(2.8)²=138.88≈139.

One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.

3 0

3 years ago

If you deposit $5000 at the end of each year for 30 years using an annual interest rate of 9% compounded annually, how much mone

hichkok12 [17]

$163,500

5000(0.09) x 30 = 13,500
5000 x 30 = 150,000
Altogether 163,500

6 0

3 years ago

Please help me on this

emmainna [20.7K]

I got 1/81

hope this helps.

8 0

3 years ago