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Solve the given problems by finding the appropriate derivative.
The speed of signaling by use of a certain communications cable is directly proportional to x2 to x-1 where x is the ratio of the radius of the core of the cable to the thickness of the surrounding insulation. For what value of x is s a maximum?
in the second quarter, sales increased by 15% for region b, and region a had 1.5 times as many sales as region b. what region a sales in the second quarter?
(a) Write an equation for the number s of supporters Trump claims to have in this city, in terms of the number d of days from today. (b) According to Trump, after how many days will he have 81,000 supporters in this city?
The difference between the ages of two friends is 2 years. The sum of their ages is 74 years. Find the age of the older friend.
Determine whether each statement below is always true, sometimes true, or never true. Explain why you chose each answer. A rectangle is a rhombus. Two angles of a scalene triangle are congruent.
The Rourke family traveled 20 kilometers farther than the Clarke family. How many hours did each family spend on their boat trip?
A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the instant the radius is 30 cm?
Does this sample indicate that songs classified as dance music have lower beats per minute than the songs ranked on a Top 200 list?
Find a definite integral that represents the arc length of the curve over the indicated interval and observe that the length cannot be evaluated with the techniques studied so far
Find the average cost function C associated with the following total cost function C. a) C(x) = 0.000008x3 - 0.1x2 + 110x + 59000. What is the marginal average cost function C'?
Is the following system consistent or inconsistent?
How much work is required to empty the full trough by pumping the water out the top? Simply set-up the integral, do not evaluate.
Find the midpoint and length of the line segment PQ where P=(2,-7) and Q=(5,1). We will also use vectors to find the length of the segment.
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