At the end of a delivery ramp, a skid pad exerts a constant force on a package so that the package comes to rest in a distance d. When the pad is replaced by one that requires a distance of 2d to stop the same package, what happens to the length of time it takes for the package to stop?

A box slides across a frozen pond toward the left shore as two children standing on opposite shores pull on the box with ropes. The child on the left shore pulls with a force of 3.0 N, and the child on the right shore pulls with a force of 2.0 N. At a certain instant, the speed of the box is 3.0 m/s. (a) At that instant, what is the power resulting from each force? (b) What is the power resulting from both forces? (c) Do your answers to parts a and b change as the box slides?

Solve the equation. Check your solution. 12x-28=-63+7x

Evaluate the following radicals if x=4, y=3, and z=8.

$$\sqrt [ 3 ] { x ^ { - 1 } + z ^ { - 1 } }$$

Use the discriminant to determine the number and type of solutions for the equation. Do not solve.

$$2 x ^ { 2 } = 4 x - 1$$

Multiply. Write each product in simplest form.

$$3 \sqrt { 3 a } \sqrt { 10 }$$

Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 130, 160, 150, 120, 120, 110, 170, 160, 110, 130, 90. Check the assumptions and conditions for inference.

Graph the function with the given domain. Then identify the range of the function. y = -5x + 3; domain:

$$x \leq 0$$

The potential energy of an interaction is given by $U ( x ) = a x ^ { 2 }$, where $a = + 6.4 \mathrm { J } / \mathrm { m } ^ { 2 }$. (a) If the initial speed of a 0.82-kg object in this system is 2.23 m/s at x = 0, how far does the object travel before it reaches a speed of v = 0? (b) Does your answer in part a depend on whether the object is traveling in the positive or negative x direction?

The bill for a family of four at a restaurant was $62. Simon paid$72 for the meal and tip. How much was the tip? What percent was the tip?

Use a tree diagram to find the sample space for tossing three coins. Then find each probability. P(three heads)

Three swimmers who all swim at the same speed discuss how to cross a river in the shortest amount of time. Swimmer A will swim straight across the river at a right angle to the current. Swimmer B reasons that the current will carry A downstream, meaning that A will cover a greater distance to get across and therefore will take a longer time interval. B says he will aim at an upstream angle such that, allowing for the current, he will reach the other side directly across from where he starts, thus covering the shortest distance and arriving first. Swimmer C, reasoning that the time interval needed for B to cross will be longer than B expects because some of B’s effort will be spent battling the current, plans to aim at a downstream angle, so that the current assists rather than opposes him. This way he will be traveling at the highest speed and get across first. Which swimmer gets across first?

A 55-kg acrobat must jump high and land on his brother’s shoulders. To accomplish this, he leaps from a crouched position to a height where his center of mass is 1.20 m above the ground. His center of mass is 400 mm above the ground in the crouch and 900 mm above the ground when his feet leave the ground. (a) What is the average force exerted on him by the ground during the jump? (b) What is his maximum speed?

A 10-kg dog jumps up in the air to catch a ball. The dog’s center of mass is normally 0.20 m above the ground, and he is 0.50 m long. The lowest he can get his center of mass is 0.10 m above the ground, and the highest he can get it before he can no longer push against the ground is 0.30 m. If the maximum force the dog can exert on the ground in pushing off is 2.5 times the gravitational force Earth exerts on him, how high can he jump?