AI Physics Trainer | Edtech Consultant
If $ f(x) = \frac{x^2-x}{x-1} $ and $ g(x) = x $ is it true that $ f = g $?
Evaluate the integral.
$ \displaystyle \int^1_0 \cosh t \,dt $
In Exercises 23-32, find the $ x $- and $ y $-intercepts of the graph of the equation.
$ y = 2x^3-4x^2 $
In Exercises 71 - 74, evaluate $ g(x) = \ln x $ at the indicated value of $ x $ without using a calculator.
$ x = e^{-4} $
Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.
(II) A rocket rises vertically, from rest, with an acceleration of 3.2 m/s$^2$ until it runs out of fuel at an altitude of 775 m. After this point, its acceleration is that of gravity, downward. ($a$) What is the velocity of the rocket when it runs out of fuel? ($b$) How long does it take to reach this point? ($c$) What maximum altitude does the rocket reach? ($d$) How much time (total) does it take to reach maximum altitude? ($e$) With what velocity does it strike the Earth? ($f$) How long (total) is it in the air?
A car accelerates at a rate of $6t - 4t$ m/s² where $t$ is the time in seconds after the car moves from rest.Simplify the expression.
Evaluate: z ÷ 6 + x + x ? 5; use x = 1, and z = 6
Janice is traveling to Canada and will change 250 US dollars into Canadian dollars. At the current exchange rate, 1 US dollars is equal to 1.28 Canadian dollars. How many Canadian dollars will she get for her trip?
As a ball rolls down an inclined plane, its velocity v(t) (in cm/sec) at time t (in seconds) is given by v(t) = v0 + at for initial velocity v0 and acceleration a (in cm/sec2). If v(3) = 41 and v(5) = 45, find v0 and a.
The mean of the grades for a class of 100 students is 80. If themean grade of the 60boys in the class is 75, what is the mean grade of the girls inthe class?(a) 80(b) 85(c) 87.5(d) 90(e) 78.5(f) 92.5
A rope moving at 30 m/s is in contact with a pulley of radius 0.5 m. What is the magnitude of the angular velocity of the pulley?
