Related rates Quiz 1

Question 1

There are three quantities $$x,y,z$$ such that $${{x}^{3}}+{{y}^{2}}{{z}^{2}}={{(y+z)}^{2}}+1$$ .So if $$x=1,y=2,z=2,y^\prime=-2,z^\prime=-1$$ then find the value of $$x^\prime $$?

Accepted Answer

$$-8$$

Answer

$$3$$

Answer

$$-3$$

Answer

$$8$$

Question 2

Suppose $$s$$ is the distance covered by a car by acceleration $$a$$ in time $$t$$ be represented as $$s=\dfrac{1}{2}a{{t}^{2}}$$. If acceleration is changing at the rate of $$2m/{{s}^{2}}$$. Then find the rate of change in distance when $$a=2,t=3$$?

Accepted Answer

$$15$$

Answer

$$-5$$

Answer

$$-15$$

Answer

$$-10$$

Question 3

The base and height of a right-angled triangle is increasing at the rate of $$4,0.5$$ respectively. What will be the rate of change in hypotenuse when the base$$=5$$ and height$$=12$$?

Accepted Answer

$$2$$

Answer

$$-2$$

Answer

$$-1$$

Answer

$$1$$

Question 4

What is the $${{\dfrac{1}{4}}^{th}}$$ of the ratio of rate of change of $$r$$ with respect to time $$t$$ in the equation: $$2{{r}^{3}}+4rh-4{{r}^{2}}h+2r{{h}^{2}}+{{h}^{2}}=0$$ when $$r=3,h=4,h^\prime=1$$ and when $$r=0,h=1,h^\prime=2$$

Accepted Answer

$$16:3$$

Answer

$$2:1$$

Answer

$$1:1$$

Answer

$$4:3$$

Question 5

The height of an isosceles triangle is decreasing at a rate of $$8cm/min$$, while its area is increasing at a rate of $$15c{{m}^{2}}/min$$. If at that moment the area is $$50c{{m}^{2}}$$ and the base is $$5cm$$ long, how fast is the base changing?

Accepted Answer

$$3.5cm/min$$

Answer

$$7cm/min$$

Answer

$$-7cm/min$$

Answer

$$-3.5cm/min$$