For the function in this exercise, find the general antiderivative. Check your answer by differentiation. $f ( x ) = e ^ { \sin x } \cos x$

Solve. $\frac{24+36+22+18}{4}$

What is the solution of 22 + v = -65? (A) -87 (B) -43 (C) 43 (D) 87

Simplify the complex fraction.

$$\frac { 1 + \frac { 6 } { x } + \frac { 8 } { x ^ { 2 } } } { 1 + \frac { 1 } { x } - \frac { 12 } { x ^ { 2 } } }$$

Find the surface area of the volume generated when the following curves revolve around the x-axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. $y = \sqrt { x } \text { from } x = 2 \text { to } x = 6$

Consider a rectangle that has a perimeter of 120 ft. Use the graph of B(I) to find the dimensions of the rectangle with a perimeter of 120 feet that has each area. Explain your answer.

$$500 ft^2$$

$$700 ft^2.$$

Find the domain and range of each function.

$$f ( x ) = 1 + x ^ { 2 }$$

Solve the system of linear equations given below. $6x+15y=15 \\ 7x-3y=-3$

Surface tension forces can be strong enough to allow a double-edge steel razor blade to "float" on water, but a single-edge blade will sink. Assume that the surface tension forces act at an angle $\theta$ relative to the water surface. $\textbf{(a)}$ The mass of the double-edge blade is $0.64 \times 10^{-3} \mathrm{kg}$ , and the total length of its sides is 206 $\mathrm{mm}$ . Determine the value of $\theta$ required to maintain equilibrium between the blade weight and the resultant surface tension force.$\textbf{(b)}$ The mass of the single-edge blade is $2.61 \times 10^{-3} \mathrm{kg}$, and the total length of its sides is 154 $\mathrm{mm}$.

Graph the region represented by the line. $y < 2$

The Earth

$$\text { (mass } = 6.0 \times 10 ^ { 24 } \mathrm { kg } )$$

rotates around the Sun in an orbit that is approximately circular, with a radius of

$$1.5 \times 10 ^ { 11 } \mathrm { m }$$

. a. Estimate the orbital speed of the Earth around the Sun. b. Determine the centripetal acceleration experienced by the Earth. c. Deduce the magnitude of the gravitational force exerted on the Sun by the Earth.

Write reactions that correspond to the following enthalpy changes: the standard enthalpy of neutralization of barium hydroxide solution by hydrochloric acid

Write a two-page essay comparing the current GDP and the real GDP. What role does the government play in measuring the real GDP? Use text from the lesson and research in the library or on the internet for more information about the government role in measuring the real GDP.

Determine the open t-intervals on which the curve is concave downward or concave upward. x = 3t², y = t³ - t