a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3

$\frac{dV(t)}{dT} = A*V(t)^{2} \\$ and V(0) = 900 $cm^{3}$

where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to $V(t)^{2}$ . Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.

(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.

$\frac{dr(t)}{dt} = B*\sqrt{r(t)}$

Here again appears a constant B for the "proportional" part. And i wrote the velocity as $\frac{dr(t)}{dt}$ "the rate of change of the position with respect to te time".

7 0

3 years ago

Suppose it is known that for a given differentiable function y=f(x), its tangent line (local linearization) at the point where a

AleksandrR [38]

Answer:

y(-4) = 5

y'(-4) = -7

Step-by-step explanation:

Hi!

Since the tangent line T and the curve y must coincide at x=-4

y(-4) = T(-4) = 5

On the other hand, the derivative of the curve evaluated at -4 y'(x=-4) must be the slope of the tangent line. Which inspecting the tangent line T(x) is -7

That is:

y'(-4) = -7

6 0

3 years ago

If a formula had addition, division, exponents, and brackets which would the spreadsheet calculate first?

kondaur [170]

It would calculate brackets first.

6 0

3 years ago

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