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Calculus
Show that the curve (y^2 -1) = 1/(x^2 -4) has no asymptote parallel to axes.
Calculus
If sinA=5/8 and cosB=4/7. And 90 is less than or equal to A which is less than 180 and -90 is less than B which is less than 0. What is the value of sin (A+B)?
Calculus
Given.
int_0^1 15 x sqrt(x^2+9)dx = 50 sqrt(10)-135
Evaluate.
int_1^0 15 u sqrt(u^2+9)du
int_0^1 15 x sqrt(x^2+9)dx = 50 sqrt(10)-135
Evaluate.
int_1^0 15 u sqrt(u^2+9)du
Calculus
A high-speed bullet train accelerates and decelerates at the rate of 5 ft/s2. Its maximum cruising speed is 90 mi/h. (Give your answers correct to one decimal place.)
(a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?
_____________________ mi
(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?
______________________ mi
(c) Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart.
_________________________ min
(d) The trip from one station to the next takes 37.5 minutes. How far apart are the stations?
_________________________ mi
(a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?
_____________________ mi
(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?
______________________ mi
(c) Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart.
_________________________ min
(d) The trip from one station to the next takes 37.5 minutes. How far apart are the stations?
_________________________ mi
Calculus
Find f.
f '' (x) = 3 - 7x - 38x3
f(0) = 1
f '(0) = 4
f(x) = ___________________
f '' (x) = 3 - 7x - 38x3
f(0) = 1
f '(0) = 4
f(x) = ___________________
Calculus
Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m/s and its downward acceleration is given by the function below. If the raindrop is initially 500 m above the ground, how long does it take to fall? (Give your answer correct to two decimal places.)
a={(9-0.9t ( if ) 0<=t<=10,
0 ( if ) t > 10)
____ s
a={(9-0.9t ( if ) 0<=t<=10,
0 ( if ) t > 10)
____ s
Calculus
The linear density of a rod of length 9 m is given by ρ(x) = 1 / √x, in grams per centimeter, where x is measured in centimeters from one end of the rod. Find the mass of the rod.
__________ g
__________ g
Calculus
A particle is moving with the given data. Find the position of the particle.
a(t) = t - 2
s(0) = 1
v(0) = 1
s(t) =_________
a(t) = t - 2
s(0) = 1
v(0) = 1
s(t) =_________
Calculus
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 60t at which time the fuel is exhausted and it becomes a freely "falling" body. Fourteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -18 ft/s in 5 s. The rocket then "floats" to the ground at that rate.
(b) At what time does the rocket reach its maximum height? (Give your answer correct to one decimal place.)
___________________ s
What is that height? (Give your answer correct to the nearest whole number.)
____________________ ft
(c) At what time does the rocket land? (Give your answer correct to one decimal place.)
_______________________ s
(b) At what time does the rocket reach its maximum height? (Give your answer correct to one decimal place.)
___________________ s
What is that height? (Give your answer correct to the nearest whole number.)
____________________ ft
(c) At what time does the rocket land? (Give your answer correct to one decimal place.)
_______________________ s
Calculus
A particle is moving with the given data. Find the position of the particle.
v(t) = 1.5√t
s(4) = 12
s(t) =
v(t) = 1.5√t
s(4) = 12
s(t) =
