Find the distance between each pair of points. If necessary, round answers to two decimal places. (-2, 3) and (3, -9)

evaluate the sum using the summation formulas and properties.

$$^20∑i=1 i^3$$

Let

$$\sin t = a , \cos t = b , \text { and } \tan t = c.$$

Write each expression in terms of a, b, and c.

$$4 \cos ( - t ) - \cos t$$

If a projectile is fired with velocity

$$v _ { 0 }$$

at an angle

$$\theta$$

, then its range, the horizontal distance it travels (in ft), is modeled by the function

$$R ( \theta ) = \frac { v _ { 0 } ^ { 2 } \sin 2 \theta } { 32 }$$

If

$$v _ { 0 } = 2200 \mathrm { ft } / \mathrm { s }$$

, what angle (in degrees) should be chosen for the projectile to hit a target on the ground 5000 ft away?

Solve the initial value problem. Confirm your answer by checking that it conforms to the slope field of the differential equation. dy/dx = (x+2) sin x and y = 2 when x = 0

Use the factor theorem to determine whether the binomial is a factor of the given polynomial.

$$z - i ; P ( z ) = z ^ { 7 } + z ^ { 6 } + z ^ { 5 } + z ^ { 4 } + z ^ { 3 } + z ^ { 2 } + z + 1$$

The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights

$$\overline{x}_M$$

and

$$\overline{x}_W.$$

Find the standard deviation of the sampling distribution. Show your work.

Tell whether each expression is completely factored. If not, factor it. (2x+3)(3x-5)

Find the prime factorization of each composite number.

$$1575$$

Solve the equation.

$$w ( w - 6 ) ^ { 2 } = 0$$

Solve each equation. If the equation has no real-number solution, write no solution.

$$9 \left( w ^ { 2 } + 1 \right) = 9$$

Name an everyday situation that requires problem-solving skills.

At time $t = 0$, a 3.0 kilogram particle with velocity ${\hat{v}} = (5.0\ \text{~m/s}){\hat{i}}\ -\ (6.0\ \text{~m/s}){\hat{j}}$ is at $x = 3.0\text{~m}, y = 8.0\text{~m}$. It is pulled by a $7.0 \text{~N}$ force in the negative x direction. About the origin, what is the particle’s angular momentum?

Circle the letter of each simple sugar. a. glucose b. sucrose c. fructose d. starch