Suppose P is a formula in propositional logic containing n variables. Approximate the worst-case complexity of an algorithm that runs through all possible true/false values of the n variables to see if there is an assignment that makes P true.

Evaluate the following integrals using integration by parts. $\int_{0}^{1} \sin ^{-1} y d y$

Solve the system using substitution.

$$\begin{array}{l}{y=2 x+5} \\ {y=6 x+1}\end{array}$$

Suppose f is differentiable on $(-\infty, \infty), f(5.99)=7$, and f(6)=7.002. Use linear approximation to estimate the value of f'(6).

Solve and check the solution. c - 4 = 67

A ring is made out of gold and copper. Gold has a density of 19.3 g/cm$^{3}$. Copper has a density of 9 g/cm$^{3}$. Mass m, density d, and volume v are related by the formula m = dv. The ring has a volume of 8.4 cm$^{3}$, and a mass of 104.44 g. Let a = volume of gold. mass of gold = dv = 19.3a Let c = volume of copper. mass of copper = dv = 9c Solve the following system by elimination to find out how many grams of gold are in the ring.

$$\begin{aligned} a+c &=8.4 \\ 19.3 a+9 c &=104.44 \end{aligned}$$

What two accounts are affected when a business buys supp lies on account?

Solve each proportion. $\frac{3}{x+1}=\frac{1}{2}$

If a shaft diameter is dimensioned $20 \pm 0.2$, determine the diameter of the shaft at MMC and at LMC.

Use the proportion $\frac{m}{n}=\frac{p}{q}$. Identify the following. the means

Find as many arithmetic progressions of three squares as you can by examining the sequence of squares of integers.

Write the decimal as a fraction or mixed number in simplest form. -0.454

Describe the sequence of transformations from f(x)=|x| to g. Then sketch the graph of g by hand. Verify with a graphing utility. g(x)=5-|x-1|

Describe the graph of $f^{-1}$ when (i) f is increasing and always positive. (ii) f is increasing and always negative. (iii) f is decreasing and always positive. (iv) f is decreasing and always negative.