Stronger muscles and bones, and greater energy, are examples of physical activity's (a) physical benefits. (b) mental benefits. (c) emotional benefits. (d) social benefits.

Consider a pair of planets for which the distance between them is decreased by a factor of 5. Show that the force between them becomes 25 times as strong.

An electron is moving east in a uniform electric field of 1.50 N/C directed to the west. At point A, the velocity of the electron is $4.50 \times 10 ^ { 5 } \mathrm { m } / \mathrm { s }$ toward the east. What is the speed of the electron when it reaches point B, 0.375 m east of point A?

A function f(x) is transformed to the function g(x) = -f(-x). Find the point on f(x) that transforms to the point (-5, -1).

Write true or false for each statement .

$$\{3,6,9,10\}\subseteq\{3,9,11,13\}$$

Prove that A(m,n+1)$\gt$A(m,n) whenever m and n are nonnegative integers.

If there is no change in concentrations, why is the equilibrium state considered dynamic?

State with i. Remove perfect squares from radicals when possible. $\sqrt{-81}$

Show that if the denominations of coins are $c^0, c^1,...,c^k$, where $k$ is a positive integer and $x$ is a positive integer, $c\gt 1$, the greedy algorithm always produces change using the fewest coins possible.

Why do you think NPP in human-cultivated land is lower than that in several natural ecosystem types such as temperate and tropical forest?

a) State a possible equation for a polynomial function whose graph extends

i) from quadrant III to quadrant I ii) from quadrant II to quadrant I iii) from quadrant II to quadrant IV iv) from quadrant III to quadrant IV

b) Compare your answers to those of a classmate. Discuss what is similar and different between your answers.

Use symmetry to evaluate the double integral.

$$\iint _ { \mathcal { R } } x ^ { 3 } d A , \quad \mathcal { R } = [ - 4,4 ] \times [ 0,5 ]$$

Find the indefinite integral (most general antiderivative) in the Exercise. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

$$\int \frac{6 d r}{(r-\sqrt{2})^{3}}$$

Find the absolute extrema if they exist, as well as all values of $x$ where they occur, for the below function, and specified domain. If you have one, use a graphing calculator to verify your answers.

$$f(x) = 5x^{2/3} + 2x^{5/3}; \ \ \ \ [-2, 1]$$