Quiz 6: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. Calculate the arc length of the curve $$y=\frac{2}{5}x^{5/2}$$ from $$x=0$$ to $$x=4$$.

   • $$4.0$$
   • $$6.3$$
   • $$8.2$$
   • $$9.1$$

2. Using linear interpolation between the points $$(3,7)$$ and $$(7,15)$$, determine the value of $$y$$ when $$x=5$$.

   • $$9$$
   • $$10$$
   • $$11$$
   • $$12$$

3. A force $$F=\langle2,5,-1\rangle$$ $$N$$ acts on an object that undergoes a displacement $$d=\langle4,-2,3\rangle$$ $$m$$. Calculate the work done by the force.

   • $$-6$$
   • $$-5$$
   • $$11$$
   • $$13$$

4. A dataset consists of the following sorted values: $$10,14,18,22,26,30,34,38,42,46$$. Determine the $$60$$ th percentile using the interpolation method.

   • $$28.0$$
   • $$30.0$$
   • $$31.6$$
   • $$32.4$$

5. Evaluate the limit using L'Hôpital's rule: $$\lim_{x\to0}\frac{\sin(5x)}{x}$$

   • $$0$$
   • $$1$$
   • $$5$$
   • undefined

6. A plane passes through the points $$A(2,0,0)$$, $$B(0,3,0)$$, and $$C(0,0,4)$$. Which of the following is the equation of the plane?

   • $$\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$$
   • $$2x+3y+4z=1$$
   • $$x+y+z=4$$
   • $$2x+y+z=4$$

7. The radius of a sphere is increasing at a rate of $$1$$ $$cm/s$$. Determine the rate at which the volume is increasing when the radius is $$2$$ $$cm$$.

   • $$8\pi$$ $$cm^3/s$$
   • $$12\pi$$ $$cm^3/s$$
   • $$16\pi$$ $$cm^3/s$$
   • $$32\pi$$ $$cm^3/s$$

8. Calculate the geometric mean of the values $$3$$, $$9$$, and $$27$$.

   • $$6$$
   • $$9$$
   • $$12$$
   • $$15$$

9. Given $$f(x,y)=x^2+2xy$$, find the directional derivative at the point $$(1,2)$$ in the direction of the vector $$\langle1,2\rangle$$.

   • $$2\sqrt{2}$$
   • $$2\sqrt{3}$$
   • $$4$$
   • $$2\sqrt{5}$$

10. Events occur according to a Poisson distribution with a mean rate of $$\lambda=3$$ per hour. Calculate the probability that exactly $$1$$ event occurs in one hour.

    • $$0.05$$
    • $$0.15$$
    • $$0.22$$
    • $$0.37$$