Calculus Answers

if sec(x+y/x-y)=a,prove that dy/dx=y/x

FIND dy/dx when ysecx +tanx+x^2y=0

According to Hook's Law, the force F (in pounds) require to stretch a certain spring x inches beyond its natural length is given by F = (4.5)x. If 10 <= F <= 18, what is the corresponding range for x?

If a baseball is thrown straight upward from level ground with an initial velocity of 72 ft/sec, its altitude s (in feet) after t seconds is given by s = -16t square + 72t. For what values of t will the ball be at least 32 feet above the ground?

The relationship between the Fahrenheit and Celsius temperature scales is given by C=(5/9) (F-32). if 60<=F<=80, express the corresponding range for C in trems of an inequality.

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.)
f(t) = 5 cos t, −3π/2 ≤ t ≤ 3π/2

absolute maximum

absolute minimum

local maximum

local minimum

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 69°C, it is cooling at a rate of 1°C per minute. When does this occur? (Round your answer to two decimal places.)

min

The trajectory of a missile is described by the by the function d=-0.15t^2+3.0t. Where d is the number of meters above the ground and t is the number of seconds after being lunched. Produce a graph of this function using an appropriate domain and range and use it and the above equation to answer the questions.
a) what is the maximum height of the missile
b) at what time does the missile reach this maximum height
c)how long is the missile in the air
d)is the missile launched from a point on the ground
e)what is the height of the missile at t=2 seconds and t=16 seconds
f)at what time would the height of the missile be 10 metres

Alfador produces gear for a racquetball league. It costs him $0.005 per square centimeter to produce racquetballs for the league. In the past, the league used racquetballs with diameter 4 cm, and he produced 30, 000 racquetballs. However, league regulations now require racquetballs to have diameter 4.05 cm.
Use differentials to estimate the increase in cost that Alfador must suffer in order to produce 30, 000 racquetballs under its new regulations. Should this be an overestimate or an underestimate?
You may use the fact that the surface area of a ball satisfies S = πX2, were X is the diameter of the ball.

the relationship between the Fahrenheit and Celsius temperature scales is given by c=(5/9)(F-32). if 60 is greater and equal F and F is greater and equal 80, express the corresponding rang for C in terms of an inequality?