Applications of Differential Calculus — Quiz 5
Practice Applications of Differential Calculus — Quiz 5 on The School of Mathematics (Applications of Differential Calculus) with 10 scored questions in about 10 min. This set covers problems such as: “In a plane a particle is given by the pair of equations x=3t and y=5t-t^2 . The particle moves along”; “If a particle moves along a curve with constant speed, then”; “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) ,…”. Work carefully, check explanations for misses, then retake to track improvement before test day.
Questions in this quiz (10)
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
If a particle moves along a curve with constant speed, then
- velocity magnitude equals zero
- velocity and acceleration perpendicular
- acceleration constant
- straight line motion
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
- $$3$$
- $$6$$
- $$9$$
- $$12$$
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?
- $$-6$$
- $$-10$$
- $$-14$$
- $$-30$$
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?
- $$-\frac1{8\pi}$$
- $$-\frac1{6\pi}$$
- $$-\frac1{4\pi}$$
- $$-\frac1{2\pi}$$
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?
- $$360$$
- $$720$$
- $$1080$$
- $$180$$
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 $$t=5$$.
- $$0.85$$
- $$1.12$$
- $$1.38$$
- $$1.75$$
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
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
At what values of $$x$$ is Mean Value Theorem satisfied for $$f(x)=x^3-3x^2+2x+4$$ on $$[0,3]$$
- $$1$$
- $$2$$
- $$1,2$$
- $$0$$