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Regie is playing with a ball on top of a building but the ball fell and hits the ground after 5.7 seconds. Calculate the final velocity of the ball just before it hits the ground, and how high is the building?

What is the inverse of the given function?
f (x) = −6^x

If #f(x)=  x^2 + x # and #g(x) = sqrtx + x #, how do you differentiate #f(g(x)) # using the chain rule?

What is the vertex of #y= 8x^2 − 6x + 128#?

How do you verify #(2cos^2x1)^2/(cos^4xsin^4x)=12sin^2x#?

What are the points of inflection of #f(x)=8x^2 + sin(2xpi)
# on # x in [0, 2pi]#?

What is the equation of the tangent line of #f(x) =x^53x^4+x^2/2# at #x=2#?

How do you differentiate #f(x)= (1  sin^2x)/(1  sinx)^2 # using the quotient rule?

A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #6 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

What is the kinetic energy of an object with a mass of #2 kg# that has been in freefall for #5 s#?

How do you simplify #(x+3)/(x+5) + 6/(x^2+3x10)#?

What is the equation of the line with slope # m= 12/11 # that passes through # (2,11) #?

What are the asymptote(s) and hole(s), if any, of # f(x) =1/x^21/(1x)+x/(3x)#?

How do you find #(10 sqrt(2))/(sqrt(5))#?

How do you write a function notation for the situation: 10 more than twice the number x?

The straight line #y = mx# where #m > 0# forms an angle of #30^@# with the positive #x#axis. What does #m# equal?

What is the vertex of # y= x^2  8?

How do you write the phrase "fourfifths of the sum of 20 and 5" as a mathematical expression?

Is #f(x)=(x3)(x+3)(x2)# increasing or decreasing at #x=1#?

A driver in a car traveling at a speed of 21.8 m/s sees a car 101 m away on the road. How long will it take for the car to uniformly decelerate to a complete stop in exactly 99 m?

How to find (f) if f′(x)=16x^3+6x+7 and f(1)=−1 ?

If an object with uniform acceleration (or deceleration) has a speed of #2 m/s# at #t=0# and moves a total of 6 m by #t=5#, what was the object's rate of acceleration?

What is the kinetic energy of a 2,000 kg boat moving at 5.0 m/s?

What is the barbell’s mass?