The area of an oil spill is increasing at a rate of 25t

$$\mathrm { ft } ^ { 2 } / \mathrm { s }$$

seconds after the spill. Between times t=2 and t=4 the area of the spill increases by ___

$$ft^2$$

.

What three variables influence the speed of stream flow?

Sketch the curves of the given functions by addition of ordinates. $y=3-2 \cos x$

Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.

$$\begin{gather*} (x + 3)y'' + xy' + (\ln |x|)y = 0, \,\,\, y(1) = 0, \,\,\, y'(1) = 1 \end{gather*}$$

Variations in members of a population help ____.

Find the inner surface area A of a cylindrical 250.0 cubic cm cup as a function of the radius r of the base. Then if A = 175.0 square cm, solve for r. Write one or two paragraphs explaining your method for setting up the function, and how you used a graphing calculator to solve for r with the given value of A.

The life span of the lightbulbs manufactured by a certain company is measured by a random variable X with probability density function

$$f(x)=\left\{\begin{matrix} 0.01e^{-0.01x}, &\text{ if }x\geq 0 \\ 0, &\text{ if }x<0 \end{matrix}\right.$$

where x denotes the life span (in hours) of a randomly selected bulb. a. What is the probability that the life span of a randomly selected bulb is between 50 and 60 hours? b. What is the probability that the life span of a randomly selected bulb is no greater than 60 hours? c. What is the probability that the life span of a randomly selected bulb is greater than 60 hours?

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x,$ and $p(x)=\frac{x}{2}.$ Find the value of each of the following: $(f-g)\left(60^{\circ}\right)$

The flow rate of water in a 6-m-wide rectangular channel is to be measured using a 1.1-m-high sharp-crested rectangular weir that spans across the channel. If the head above the weir crest is 0.60 m upstream from the weir, determine the flow rate of water.

Describe a real-world situation that can be modeled by the equation 15x = 135. Solve the equation and explain what the solution means in this situation.

Use your calculator to write the following in the form $10^{x}$ where x is correct to 4 decimal places: 6

Determine whether 97 divides $n^{2}-85$ for some choice of $n \geq 1$

What factors influence how quickly chyme leaves the stomach?

In each part, Determine whether the three vectors lie in a plane in R3. (a) v1 = (2, -2, 0) , v2 = (6, 1, 4), v3 = (2, 0 , -4) (b) v1= (-6, 7, 2), v2 = (3, 2, 4), v3 = (4, -1, 2)