Calculus Help!!. I keep getting it wrong please let me know... (on a page will be great but it is all good text wise). Thank you

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A large sphere of material is placed in a dissolving liquid. (a) When the radius is 1 m, it is observed to be changing at 7 cm/hour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time? cm3/hr (b) Suppose, instead, that the liquid is known to dissolve the material at a rate of 1 m3/hour, at what rate will its radius rchange with respect to time when r = 1 meter? when r = 1/2 meter? , = 1 m/hr r = 1/2 m/hr (c) What happens to the rate of change of the radius in part (b) as r a 0"? r a co? r>0+ A road running north to south crosses a road going east to west at the point P. Car A is driving north along the rst 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 50 km/hr, while car B is 15 kilometers to the east of P and traveling at 120 km/hr. How fast is the distance between the two cars changing? 127.6 km/hr X Recall that two quantities x and y are related if there exists a function fsuch that y = f(x). Ifx and y are also functions of time, t, then y(t) = f(x(t)). By the Chain Rule, the rates of change ofx and y are related as y'(t) = f'(x(t))x'(t). Sketch a picture that models the described situation. Use the given information to label the picture with variables reflecting distances from each car to point P and the distance between the cars. Identify the units associated with each variable and write the variable quantities as functions of time. Write a function that implicitly relates these distances and apply the Chain Rule to find how the relation between their rates of change. What are the units of the given quantities? What fact about the sides of a right triangle can be used to relate the distances? How can instantaneous distances and rates of change be found from the given information? Are these rates and distances positive or negative relative to P and the locations of the cars? 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 7 feet? ftz/min A volcanic cone spews ine particles of rock which land in the surrounding area and cause the size of the cone to increase. (a) Suppose that a volcanologist takes measurements that show that when the cone is 100 meters wide and 50 meters tall, its height is increasing at 0.5 meters/day. If the assumption is made that the cone will retain its heightwidth proportion, what is the rate at which the volume of rock is being released by the volcano? m3/day (b) Suppose that the volcanologist takes more measurements and realizes the original assumption was poorly made, because the width is increasing at 0.6 meters/day. What would be the new finding for the rate at which the volume of rock is being released by the volcano? m3/day \fConsider the curve ex2 ' y = y7" + 8. Using logarithmic differentiation find {33 Give the answer as a function of both x and y. 2xex2 y _y7x+81n(y7) 2 7x+7+ex y 7xy