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1. A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and car B is driving east along the second road. At a particular time car A is 10 kilometers to the north of P and traveling at 60 km/hr, while car B is 15 kilometers to the east of P and traveling at 95 km/hr. How fast is the distance between the two cars changing?
2. Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 4 feet?
3. Use differentiation to approximate the maximum error in using 5 cm as the radius of a sphere to calculate its volume if the measurement is off by at most 8 mm. Find the approximation of both the relative and percentage error for the volume.
Find all maximum points, minimum points and points of inflexion, using differentiation techniques, for the function f(x) = x3 - 9x2 - 48x + 52.
What is the shape of the cable that supports the roadway of a suspension bridge? Our model is based on the following simplifying instructions
Write an expression for the position function, x(t), of the particle at any time t, 0
How many friend samples Sara should have in order to draw the conclusion with 95% confidence interval? Why?How would you explain your conclusion to Sara without using any statistical jargon? Why
The first car has consumed 35 gallons during that week, and the second has consumed 40 gallons, for a total of 2050 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week?
Prove that the function f(x) = C (a constant function) is Reimann integrable over [a,b] and calculate its Reimann integral over [a,b]
gold has a mass of 452 gram and a density of 19.3 gram per cm cube. what is the volume of the gold?
For a class of 43 students, for a certain exam, the mean grade is 67 and the standard deviation is 7, how many students should receive a C?
a baseball diamond had the shape of a square with sides of 90 feet long. A player hits the ball and runs tower first base with a speed of 24 feet per second. At what rate is the player distance from the third base changing when the player is halfw..
Determine if the following conforms to the intermediate value theorem. Clearly give the conditions and, if appropriate, find an appropriate value for c.
In the World Series, one National League team and one American League team compete for the title, which is awarded to the first team to win four games. In how many different ways can can the series be completed?
The number of days they spent in New York was the same as the total number of days they spent in Boston and Washington, and the couple spent 3 times as many days in New York as they did in Philadelphia. How many days did Joan and Dick stay in each..
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