Find equations for the tangent plane and normal line to the surface given at the prescribed point.

$$x^{3}+2 x y^{2}-7 x^{3}+3 y+1={0} \text { at } P_{0}(1,1,1)$$

Why is the sky blue?

simplify the expression algebraically and use a graphing utility to confirm your answer graphically. cos(3π/2 - x)

Differentiate the function given.

$$g(x)=\sec ^{2} x-\tan ^{2} x+\cos x$$

For each pair consisting of a and an observed significance level (p -value), indicate whether the null hypothesis would be rejected.

$$\alpha = .05 , p -value = .10$$

Among persons aged 15 to 24 years in the United States, the leading causes of death and number of deaths in a recent year were as follows: accidents, 12,015; homicide, 4651; suicide, 4559; cancer, 1594; heart disease, 984; congenital defects, 401. To make a pie chart, you need one additional piece of information. What is it?

Write the following expression as a single power of 3.

$$3 \cdot 3^2 \cdot 3^4 \cdot 3^8 \cdot 3^{16}$$

Investigate the difference between compounding annually and simple interest. Find the interest for a one-year CD for $5,000 at an interest rate of 6%, compounded annually.

Which term is used to describe salt-tolerant plants?

Find $y ^ { \prime }$

$$y = \sin \frac { 3 } { x }$$

Once started, a(n) _ reaction tends to keep going.

Find the center and radius of the circle, and sketch its graph.

$$x ^ { 2 } + y ^ { 2 } = 9$$

Use a special right triangle to find the tangent of the given angle measure. 30°

Rank the following types of radiation for the damage they can cause in the human body from highest to low est: (a) gamma rays; (b) alpha particles; (c) electrons or beta particles.