Find the general solution to the exact differential equation. dy/dx = sin x - eˉ˟ + 8x³

Evaluate the expression. 36. 13² - 5²

Solve the initial value problem using the Fundamental Theorem. (Your answer will contain a definite integral.) dy/dx = sin (x²) and y = 5 when x = 1

Determine whether the function is bounded above, bounded below, or bounded on its domain.

$$y=2-x^2$$

Find the speed of sound in mercury, which has a bulk modulus of

$$2.8 \times 10 ^ { 10 }$$

Pa and a density of

$$1.36 \times 10 ^ { 4 } \mathrm { kg } / \mathrm { m } ^ { 3 }$$

.

Methane, ethane, and propane are also hydrocarbons, but they are not major components of gasoline. What prevents them from being part of this mixture?

Evaluate the expression when a = 4, b = -5, and c = -8. 43. -b + c

Experiments have shown that, for airflow at $T_{\infty}=35^{\circ} \mathrm{C}$ and $V_{1}=100 \mathrm{m} / \mathrm{s}$, the rate of heat transfer from a turbine blade of characteristic length $L_{1}=0.15 \mathrm{m}$ and surface temperature $T_{s, 1}=300^{\circ} \mathrm{C}$ is $q_{1}=1500 \mathrm{W}$. What would be the heat transfer rate from a second turbine blade of characteristic length $L_{2}=0.3 \mathrm{m}$ operating at $T_{s, 2}=400^{\circ} \mathrm{C}$ in airflow of $T_{\infty}=35^{\circ} \mathrm{C}$ and $V_{2}=50 \mathrm{m} / \mathrm{s} ?$ The surface area of the blade may be assumed to be directly proportional to its characteristic length.

Which of the following functions are solutions of the differential equation $y^{\prime \prime}+y=\sin x$ ? (a) $y=\sin x$

(b) $y=\cos x$

(c) $y=\frac{1}{2} x \sin x$

(d) $y=-\frac{1}{2} x \cos x$

Which of the following functions are solutions of the differential equation $y^{\prime \prime}+y=\sin x ?$ $y=\cos x$

Zalmon walks 3/4 of a mile in 3∕10 of an hour. What is his speed in miles per hour? (A). 0.225 miles per hour (B). 2.3 miles per hour (C). 2.5 miles per hour (D). 2.6 miles per hour.

Determine whether the statement is true or false. Justify your answer. The parametric equations $x = at + h$ and $y = bt + k$, where $a \neq 0$ and $b \neq 0$, represent a circle centered at (h, k) when a = b.

Full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized on the top of the next page. Use a 0.05 significance level to test the claim that IQ scores of people with low lead levels vary more than IQ scores of people with high lead levels.

$$\begin{aligned} \text { Low Lead Level: } n & = 78 , \overline { x } = 92.88462 , s = 15.34451 \\ \text { High Lead Level: } n & = 21 , \overline { x } = 86.90476 , s = 8.988352 \end{aligned}$$

Graph each equation by writing two linear equations. $y=-|x-5|$