The amount of time it takes to drive somewhere is inversely proportional to the speed at which you drive.The time of a trip is 3 hours when you drive at 60 km/h.a)Determine the equation for the function t(v), which relating the time of the trip ("t", in hours) to thespeed (v, in km/h).b)Find the time it would take to complete the above trip if you drove at 90 km/h.c)What speed should you drive at to complete the trip in 75 minutes?2.

This is the application of calculus, mathematical physics, equation of motion.

Answered: The amount of time it takes to drive…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) = Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Submit Answer
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the weight (in pounds) w=f(d) of an object varies inversely as the square of its distance (in thousands of miles) d from the center of earth a. an astronaut weights 180 pounds at sea level (about 4 thousand miles from earth's center) find an equation of F b. how much would the astronaut weight at 2 thousand miles above earth's surface? c. at what distance fromthe center of earth would the astronaut weigh , pound? miles? ( round to the nearest miles as needed) d. estimate how much the astronaut would weight on the surface of the moon. the moon is a mean distance of about 239 thousand miles from earth pound? ( round to three decimal places as needed)
3. The height of a rocket, h, is increasing at a rate of 18 feet per second. If its height at five seconds is 118 feet, then write an equation for h as a function of time, t, in seconds since it was fired.
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The cost of driving a car includes both fixed costs and mileage costs. Assume that it costs $178.40 per month for insurance and car payments and $0.26 per mile for gasoline, oil, and routine maintenance. (a) Find values for m and b so that y = mx + b models the monthly cost of driving the car x miles. (b) What does the value of b represent?
The following equation represents the relationship between hours of TV watched per day (x) and the number of situps a person can do (ŷ).ŷ = -0.895xx + 32.409Use this model to predict the number of situps a person who watches 2.5 hours of TV can do. (to 2 decimal places)
Please box your answers.
When there is no wind, a runner is able to run 10 000 m at an average speed of x m/s. When he runs with a tailwind, his average speed increases by 0.05 m/s and it takes him 15 s less to run the 10 000 m. The equation shown below represents this relationship. 10 000 10 000 x+0.05 X = 15, x > 0 6. When there is no wind, find the runner's average speed, to the nearest hundredth of a metre per second.
Kara knows that the speed of the car before it brakes suddenly is a function of the length of the skid marks left by its tires on the road and that the equation of the function is given by s = 14vd, where d is the length of the skid mark (in meters) and s is, the speed of the car (in km/h), before the brake pedal is pushed. If she had to brake suddenly for a red light and left skid marks that were 25 m long, at what speed was she traveling before she had to brake? O 1.33 km/h O 3.189 km/h O 44.643 km/h O 70 km/h
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