1 - Find a formula for the rate of change dv/dt ofthe volume of a balloon being inflated such thatit radius R increases at a rate equal to dR/dt.2 - Find a formula for the rate of change da/dt ofthe area A of a square whose side x centimeterschanges at a rate equal to 2 cm/sec.3- Two cars start moving from the same point intwo directions that makes 90 degrees at theconstant speeds of s1 and s2. Find a formula forthe rate of change of the distance D between thetwo cars.

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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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The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit -10 000 of radius 10 000 km can be modelled by the function E = 2×100 where E is the energy, in %3| Joules, and r is the new radius, in kilometers. a) Determine the average rate of change between r = b) Determine the instantaneous rate of change at r = c) What is the difference between an average rate of change and an instantaneous rate of change? 10 000 km and r= 15 000 km. 15 000 km.
A rectangular sheet of metal has a length of 12 cm decreasing at a rate of 0.2 cm/s, and a width of 9 cm and an increase of at a rate of 0.1 cm/s. Find the rate of change of its area at the moment it becomes a square 11:24 AM
A trough has ends shaped like isosceles triangles, and has a length of 10m, width 4m, and height 7m, as shown in the image below. Water is being pumped into the trough at a rate of 4m3/min. At what rate does the height of the water change when the water is 1m deep? dh/dt + = ? m/min
Empirical evidence suggests that the volume V (measured in liters) of a kangaroo's pouch depends on its body weight W (measured in kilograms) according to the formula dV 0.2 dW A'reasonable model for the weight of a kangaroo depending on its height H (measured in m) is W 20 H? Suppose that over the course of 4 years, a kangaroo has grown at a constant rate from 1 m to 2 m. Determine the rate of change of the volume of its pouch with respect to time (measured in liters per year) when its height was 1.3 m. Note: You may round your answer. Please specify at least 3 digits behind the decimal place. So your solution should be accurate up to ±0.001. Answer: liters/year
Assume that the radius r of a sphere is expanding at a rate of 20 cm/min. The volume of a sphere is V Tr'and its surface area is 4är. Determine the rate at which the surface area is changing with respect to time at t = 2 min, assuming that r = 10 at t = 0. (Use symbolic notation and fractions where needed.) dA cm?/min dt
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Sand is dumped in such a way that the shape of the sand pile is always a cone with its height, h equal to three times its radius, r. Given that the sand is dumped at a constant rate of 10 m3 /s, calculate the rate at which the radius is increasing when its height is 3 m.
An ant colony explores an area enclosed by a circle centered at its nest. This area (and the circle containing it) expands as they have time to explore. Due to the need for ants to return to the colony periodically, as the radius expands, the change in the radius of the area explored with respect to time slows down. Specifically, if r is the radius of the area the ants have explored in meters, then = 3 m/day. Find the rate of change of the area explored by the ants 4 in m2/day when the radius of the area explored is 3m. dt
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1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that it radius R increases at a rate equal to dR/dt.