A mass $m$ is gently placed on the end of a freely hanging spring. The mass then falls $30$ cm before it stops and begins to rise. What is the frequency of the oscillation?

A bar of steel has the minimum properties $S_{e}=40 \mathrm{kpsi}, S_{y}=60 \mathrm{kpsi}, \text { and } S_{u t}=80 \mathrm{kpsi}$. The bar is subjected to a steady torsional stress of 15 kpsi and an alternating bending stress of 25 kpsi. Find the factor of safety guarding against a static failure, and either the factor of safety guarding against a fatigue failure or the expected life of the part. For the fatigue analysis use:a) Goodman criterion. b) Gerber criterion. c) Morrow criterion.

Differentiate the functions. $f(p)=\sqrt{3} p^{4}$

Calculate the mass/mass percent concentration for the following solution.

$2.50$ g K$_{2}$Cr$_{2}$O$_{7}$ in $95.0$ g of solution

Find the reference angle for the given angle. $\frac{7 \pi}{10}$

At what points (x, y, z) in space are the functions continuous?

$$f ( x , y , z ) = e ^ { x + y } \cos z$$

Which of the following sentences are equivalent to the statement. All circles are round. a. If it’s round, it’s a circle. b. Roundness is a necessary property of circles. c. Something that isn’t round can’t be a circle. d. Some round things are circles.

Calculate the mass/mass percent concentration for the following solution.

$65.0$ g C$_{6}$H$_{12}$O$_{6}$ in $125.0$ g of solution

What did Marx see in the working class that made him think it had the power to rise up in revolution?

A farmer has determined that her cornfield will yield corn (in bushels) according to the formula $B(x, y)=4 x^{2}+y^{2}+600$ where x denotes the amount of water (measured in hundreds of gallons) used to irrigate the field and y the number of pounds of fertilizer applied to the field. The fertilizer costs $10 per pound and water costs$15 per hundred gallons. If she can allot $500 to prepare her field through irrigation and fertilization, use a Lagrange multiplier to determine how much water and fertilizer she should purchase in order to maximize her yield.

Sketch in standard position the angle described and then find its measure.

$$\frac { 1 } { 6 }$$

of a clockwise revolution.

Given that $25.0 \mathrm{~mL}$ of mercury has a mass of $340.0 \mathrm{~g}$, calculate (a) the density of mercury and (b) the mass of $120.0 \mathrm{~mL}$ of mercury.

Explain how to add two functions.

The three-toed sloth often is camouflaged by algae. Which type of symbiosis does this represent and why?