A beetle that has an inertia of $4.0 \times 10 ^ { - 6 } \mathrm { kg }$ sits on the floor. It jumps by using its muscles to push against the floor and raise its center of mass. (a) If its center of mass rises 0.75 mm while it is pushing against the floor and then continues to travel up to a height of 300 mm above the floor, what is the magnitude of the force exerted by the floor on the beetle? (b) What is the beetle’s acceleration during the motion?

Solve each subtraction problem using algebraic addition: Describe how to change a subtraction problem into an addition problem.

Willie Lohmann travels from city to city for business. Every other year he buys a used car for about $15,000. The dealer allows about$8000 as a trade-in allowance, so Willie spends $7000 every other year for a car. Willie keeps accurate records of his expenses, which total 32.3¢ per mile. Willie's employer has two plans to reimburse car expenses: A. Actual expenses: Willie will receive all his operating expenses, and$3500 each year for the car's decline in value. B. Standard mileage rate: Willie will receive 56.5¢ per mile but no operating expenses and no depreciation allowance. If Willie travels 18,000 miles per year, which method gives him the larger reimbursement? At what annual mileage do the two methods give the same reimbursement?

Suppose a jogger has to exert a force of 25 N against air resistance to maintain a velocity of +5.0 m/s. At what rate is the jogger expending energy?

Find the side length in each right triangle. If b = 24 and c = 26, find a.

Write the statement in if-then form. Dianna will go to the movie if she finishes her homework.

Find the indicated term for the geometric sequence with first term,

$$a_1$$

and common ratio, r.

$$Find \ a _ { 40 } , \text { when } a _ { 1 } = 6 , r = - 1$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. If I know the measures of the sides and angles of an oblique triangle, I have three ways of determining the triangle's area.

In a carnival game, the player throws a ball at a haystack. For a typical throw, the ball leaves the hay with a speed exactly one-half of the entry speed. (a) If the frictional force exerted by the hay is a constant 6.0 N and the haystack is 1.2 m thick, derive an expression for the typical entry speed as a function of the inertia of the ball. Assume horizontal motion only, and ignore any effects due to gravity. (b) What is the typical entry speed if the ball has an inertia of a 0.50 kg?

The Declaration of Independence was signed in 1776. The U.S. Constitution was ratified in 1789. How many years passed between these two events?

Two 1.0-kg blocks, one gray and one tan, are lined up along a horizontal x axis. The gray block is at x = -4.0 m, and the tan one is at x = +4.0 m. A constant force of 1.0 N is exerted on the gray block in the positive x direction through a distance of 2.0 m. Taking the two blocks as the system and ignoring friction, calculate the following over the interval required for the gray block to move from x = -4.0 m to x = -2.0 m: (a) the work done on the system, (b) the change in the energy of the system, (c) the change in the kinetic energy of the system’s center of mass, and (d) the value of $F \Delta x _ { \mathrm { cm } }$, where F = 1.0 N and $\Delta x _ { \mathrm { cm } }$ is the displacement of the system’s center of mass. (e) If the blocks collide totally inelastically, what is the energy of the system after the collision?

Evaluate the limit, if it exists. Use the Limit Laws when possible. $\lim _{x \rightarrow \infty} \frac{2 x}{x-4}$

(a) What is a vaccine? (b) Briefly outline how vaccination provides protection against disease:

Evaluate the integral.

$$\int \frac { x ^ { 2 } + 2 x - 1 } { x ^ { 3 } - x } d x$$