How long (in seconds) will it take you to swim 100 meters if you swim at $1.25 \mathrm{~m} / \mathrm{sec}$ ?

In the following sentence, underline any incorrect verb form and write the correct form above it. If all the verbs in a sentence are correct, write C after the sentence.

Either I have leaved my keys somewhere, or they have fell out of my pocket.

In each case, express the given vector field V in the standard form $\sum v_{i} U_{i}.$ (a) $2 z^{2} U_{1}=7 V+x y U_{3}$ (b) $V(\mathbf{p})=\left(p_{1}, p_{3}-p_{1}, 0\right)_{p}$ for all $\mathbf{p}.$ (c) $V=2\left(x U_{1}+y U_{2}\right)-x\left(U_{1}-y^{2} U_{3}\right)$ (d) At each point $\mathbf{p}, V(\mathbf{p})$ is the vector from the point $\left(p_{1}, p_{2}, p_{3}\right)$ to the point $\left(1+p_{1}, p_{2} p_{3}, p_{2}\right)$ (e) At each point $\mathbf{p}, V(\mathbf{p})$ is the vector from $\mathbf{p}$ to the origin.

When writing a function that accepts a two-dimensional array as an argument, which size declarator must you provide in the parameter for the array?

Find an equation of the tangent line to the curve at the given point. $y=\ln \left(x^2-3\right), \quad(2,0)$

Simplify the following given expression. Assume all variables are positive.

$$\sqrt[6]{2 x^6}$$

Solve the given problems.

The vertical cross-section of a culvert under a road is elliptical. The culvert is $18$ m wide and $12$ m high. Find an equation to represent the perimeter of the culvert with the origin at road level and $2.0$ m above the top of the culvert.

The chemical reaction of hydrogen with oxygen produces water.

$$2 \mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(g) \longrightarrow 2 \mathrm{H}_2 \mathrm{O}(g)$$

How many moles of $\mathrm{H}_2$ are needed to react with $5.0$ moles of $\mathrm{O}_2$ ?

A human being can swim at a maximum rate of 7.4 feet per second. The function y = 7.4x describes how many feet y a person can swim in x seconds. Graph the function. Use the graph to estimate the maximum number of feet a person can swim in 4.5 seconds.

Write two different proportions using each set of numbers. Use cross products to justify your answer. A. $1.80,$1.20, 14, 21 B. 1, 3.5, 31.50, 9.0 C. 11.7, 8424, 0.02, 14.4

Solve the first-order differential equation by separating variables.

$$y'=\dfrac{x^2+1}{3y^2}$$

Determine a rotation $\mathbf{x}=P \mathbf{x}^{\prime}$ that removes the cross-product terms, and give its equation in the $x^{\prime} y^{\prime} z^{\prime}$-system. Name the quadric.

$$2 x^2+3 y^2+23 z^2+72 x z+150=0$$

Factor. Assume that variables used as exponents represent positive integers.

$$2 x^{2 n}+11 x^n+5$$

Simplify each expression. Assume all variables are nonzero.

$$3^2 \cdot 3^{-5}$$