Applications of Differential Calculus — Quiz 5

Questions in this quiz (10)

1. In a plane a particle is given by the pair of equations $$x=3t$$ and $$y=5t-t^2$$. The particle moves along

   • an ellipse
   • a hyperbola
   • a line
   • a parabola

2. If a particle moves along a curve with constant speed, then

   • velocity magnitude equals zero
   • velocity and acceleration perpendicular
   • acceleration constant
   • straight line motion

3. A particle is moving on the curve $$y=x^2+\ln x$$ so that $$\frac{dx}{dt}=3$$ at all times $$t$$. At the point $$(1,1)$$, $$\frac{dy}{dt}$$ is

   • $$3$$
   • $$6$$
   • $$9$$
   • $$12$$

4. A particle moves along the path $$y=x^3-2x^2+1$$. If the particle's horizontal rate of change when $$x=3$$ is $$-2$$ ft/sec, what is its vertical rate of change?

   • $$-6$$
   • $$-10$$
   • $$-14$$
   • $$-30$$

5. If a spherical balloon is being deflated at a rate of $$8$$ in^3/sec, at what rate is the radius decreasing when $$r=4$$ in?

   • $$-\frac1{8\pi}$$
   • $$-\frac1{6\pi}$$
   • $$-\frac1{4\pi}$$
   • $$-\frac1{2\pi}$$

6. A cube is expanding so that each side increases at $$5$$ in/sec. At what rate is the surface area changing when one side is $$3$$ ft?

   • $$360$$
   • $$720$$
   • $$1080$$
   • $$180$$

7. A drone is flying horizontally 200 feet away from a tower. Its height is given by $$h(t)=-16t^2+1600$$. Find the rate of change of the angle of elevation when $$t=5$$.

   • $$0.85$$
   • $$1.12$$
   • $$1.38$$
   • $$1.75$$

8. Determine if each statement is true or false. If $$f(x)$$ is continuous on $$[a,b]$$ and differentiable on $$(a,b)$$.

   • both true
   • a true b false
   • a false b true
   • both false

9. Two speed cameras are placed 3 miles apart. Driver passes second camera in 2 minutes. Why guilty by MVT?

   • average speed exceeded
   • instantaneous exceeded
   • speed constant
   • acceleration positive

10. At what values of $$x$$ is Mean Value Theorem satisfied for $$f(x)=x^3-3x^2+2x+4$$ on $$[0,3]$$

    • $$1$$
    • $$2$$
    • $$1,2$$
    • $$0$$