Sketch the graph of the height of a particle against time if velocity is positive and acceleration is negative.

There are two relationships that are often mistaken for causation. A common response is when some other reason may cause the same result. A confounding variable is when there are other variables that are unknown or unobserved. a. In North Carolina, the number of shark attacks increases when the temperature increases. Therefore, a temperature increase appears to cause sharks to attack. List two or more common responses that could also cause this result. b. A company claims that their weight loss pill caused people to lose 20 pounds when following the accompanying exercise program. List two or more confounding variables that could have had an effect on this claim.

Find the exact value, if any, of each composite function. If there is no value, write, "It is not defined." Do not use a calculator. $\sin \left(\sin ^{-1} 0.2+\tan ^{-1} 2\right)$

An object of mass M = 2.00 kg is attached to a spring with spring constant k = 22.0 N/m whose unstretched length is L = 0.110 m , and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 1.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 1.00 radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

a) Given the angular speed of ω = 1.00 radians/s , find the radius R(ω) at which the mass rotates without moving toward or away from the origin. Assume that, at a certain angular speed ω2, the radius R becomes twice L.

b) Find ω2. Express your answer in radians per second.

Determine whether each function is (a) continuous from the left. (b) continuous from the right. at the numbers c and d. $f(x)=\sqrt{(x+1)(x-5)}$ at c=-1 and d=5

Use a radical symbol to denote and evaluate the principal nth root (if it exists) of the number. Then find any other real nth roots of the number.

$$\begin{matrix} \text{Number} & \text{n}\\ \text{27} & \text{3}\\ \end{matrix}$$

You are researching the price of MP3 players. You found an average price of $58.80. One MP3 player costs$56 and another costs $62. Find the price of the third MP3 player.

The essential elements of a hand winch are shown. The toothed wheel and the handle OA pivot independently about the same axis through O. When bearing against the radial flank of a tooth, the pawl BC locks at the $20^{\circ}$ angle shown. When separated from the tooth flank, the pawl can rotate clockwise relative to OA to allow clockwise rotation of OA relative to the winch drum in preparation for another pull. A lock not shown prevents clockwise rotation of the toothed wheel during repositioning of the handle. If P = 400 N, determine the tensions ${T}_{{1}}$ and ${T}_{{2}}$. Neglect friction at the base of the winch.

Invitations are sold in packs of 3. Emily needs 77 invitations for her party. How many packs of invitations does she need?

A 5-mm-thick stainless steel strip $(k=21 \mathrm{W} / \mathrm{m} \cdot \mathrm{K},$ $\left.\rho=8000 \mathrm{kg} / \mathrm{m}^{3}, \text { and } c_{p}=570 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ is being heat treated as it moves through a furnace at a speed of 1 cm/s. The air temperature in the furnace is maintained at $900^{\circ} \mathrm{C}$ ith a convection heat transfer coefficient of $80 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}.$ If the furnace length is 3 m and the stainless steel strip enters it at $20^{\circ} \mathrm{C},$ determine the temperature of the strip as it exits the furnace.

Perform the indicated operation(s) and write the result in standard form. $(5+6 i)^{2}$

The blades of the portable fan generate a 1.2-lb thrust T as shown. Compute the moment $M_O$ of this force about the rear support point O. For comparison, determine the moment about O due to the weight of the motor-fan unit AB, whose weight of 9 lb acts at G.

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Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%. What are the units of C'(r)? What is the practical meaning of C'(r)? What is its sign?