Question 1

The orbital speed ( s ) of an earth satellite is related to its distance ( r ) from the earth's center by the formula  . If the satellite's orbital speed is  meters per second, find its altitude a (in meters) above the earth's surface, as shown in the illustration. Round the answer to the nearest meter.

Accepted Answer

E

Question 2

Find the domain and range of the function.

Accepted Answer

A

Question 3

What size is the television screen shown in the illustration? Find  if  in. and  in.

Accepted Answer

A

Question 4

A 17-foot ladder reaches a window 15 feet above the ground. How far from the wall is the base of the ladder?

Accepted Answer

The answer of A 17-foot ladder reaches a window 15...

Question 5

Find the square root without using a calculator.

Accepted Answer

To find the square root of 11, we can use the following method:
1. Start with an estimate close to the number. Since 11 is between 9 and 16, we can start with an estimate of 3 or 4.
2. Divide the number by the estimate. For example, if we start with an estimate of 3, we get:

11 / 3 = 3.666...

3. Average the estimate and the result of the division. In this case, we get:

(3 + 3.666...) / 2 = 3.333...

4. Repeat steps 2 and 3 with the new estimate until we get a satisfactory result. After a few iterations, we get:

3.3166247903554...

This value is very close to 3.31662, which is the square root of 11 rounded to five decimal places. The closest answer choice is E) 1.2, which is incorrect, so the best choice is E) 1.2 with an explanation that the square root of 11 is very close to 3.31662 and can be found using the method of successive approximations.

Question 6

Find the value without using a calculator.

Accepted Answer

The answer of Find the value without using a calculator....

Question 7

Find the square root without using a calculator.

Accepted Answer

The answer of Find the square root without using a...

Question 8

Find the domain and range of the function.

Accepted Answer

The answer of Find the domain and range of the...

Question 9

Simplify the radical.

Accepted Answer

The answer of Simplify the radical. 
...

Question 10

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

Accepted Answer

The answer of Find the square root. Assume that all...

Question 11

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

Accepted Answer

The answer of Find the square root. Assume that all...

Question 12

The formula  relates the speed  (in mph) of a car and the distance  of the skid when a driver hits the brakes. On wet pavement,  . How far will a car skid if it is going 50 mph?

Accepted Answer

We need to use the formula 11ec1e8e_2c0b_e92f_be9b_e34b70c6a8cb_TBX8967_11, which relates the speed of the car and the distance of the skid.

11ec1e8e_2c0b_e92f_be9b_e34b70c6a8cb_TBX8967_11

= 11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 / (30*11ec1e8e_2c0b_e930_be9b_253bf355e461_TBX8967_11)

Substituting the given values, we get

11ec1e8e_2c0b_e92f_be9b_e34b70c6a8cb_TBX8967_11

= 11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 / (30*0.9)

= 11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 / 27

Now, to find the skid distance at 50 mph, we can use the formula as follows:

Skid distance = 11ec1e8e_2c0b_e92f_be9b_e34b70c6a8cb_TBX8967_11 * 50^2

Substituting the value of 11ec1e8e_2c0b_e92f_be9b_e34b70c6a8cb_TBX8967_11, we get

Skid distance = (11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 / 27) * 2500

= 11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 * (2500/27)

= 11ec1e8e_2c0b_e931_be9b_099c269a6e30_TBX8967_11 * 92.59

Rounding off to the nearest foot, we get the skid distance as about 238 ft. Thus, the correct choice is C.

Question 13

A cubical box has a volume of 8 cubic feet. Substitute 8 for V in the formula  , and solve for s to find the length of each side of the box.

Accepted Answer

The answer of A cubical box has a volume of...

Question 14

Find the value.

Accepted Answer

The answer of Find the value. ...

Question 15

Find the value.

Accepted Answer

The answer of Find the value. 
...

Question 16

Find the domain and range of the function.

Accepted Answer

Since the function has no square roots or denominators, we can assume that the domain is all real numbers except where the function is undefined. In this case, there is no such point. Therefore, the domain is (-∞, ∞).

To find the range, we need to look at the graph of the function. As x approaches -4, the function approaches 0 from above. The function continues to increase as x increases, but as x approaches infinity, the function approaches 0 from below. Therefore, the range is [0, ∞).

Question 17

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

Accepted Answer

The answer of Find the square root. Assume that all...

Question 18

Find the value without using a calculator.

Accepted Answer

The answer of Find the value without using a calculator....

Question 19

The number of wrenches that can be produced at a given price can be predicted by the formula  , where  is the supply (in thousands) and  is the price (in dollars). If the demand  for the wrenches can be predicted by the formula  , find the equilibrium price.

Accepted Answer

To find the equilibrium price, we need to set the supply equal to the demand:

11ec1e8e_2c0c_1046_be9b_85a1b7d18c18_TBX8967_11 = 11ec1e8e_2c0c_375a_be9b_8fd0204dc279_TBX8967_11

Solving for P:

11ec1e8e_2c0c_3758_be9b_ef8844412edc_TBX8967_11 = 0.5

So the equilibrium price is $3.

Question 20

After joining two pieces of picture frame molding together, a frame maker checks her work by making a diagonal measurement (see the illustration). If the sides of the frame that form a right angle are  in. and  in., what measurement should the frame maker read on the yardstick?

Accepted Answer

The answer of After joining two pieces of picture frame...

Quiz 7: Radical Expressions and Equations

Find the domain and range of the function.

What size is the television screen shown in the illustration? Find if in. and in.

A 17-foot ladder reaches a window 15 feet above the ground. How far from the wall is the base of the ladder?

Find the square root without using a calculator.

Find the value without using a calculator.

Find the square root without using a calculator.

Find the domain and range of the function.

Simplify the radical.

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

The formula relates the speed (in mph) of a car and the distance of the skid when a driver hits the brakes. On wet pavement, . How far will a car skid if it is going 50 mph?

A cubical box has a volume of 8 cubic feet. Substitute 8 for V in the formula , and solve for s to find the length of each side of the box.

Find the value.

Find the value.

Find the domain and range of the function.

Find the square root. Assume that all variables are unrestricted, and use absolute value symbols if necessary.

Find the value without using a calculator.

The number of wrenches that can be produced at a given price can be predicted by the formula , where is the supply (in thousands) and is the price (in dollars) . If the demand for the wrenches can be predicted by the formula , find the equilibrium price.

After joining two pieces of picture frame molding together, a frame maker checks her work by making a diagonal measurement (see the illustration) . If the sides of the frame that form a right angle are in. and in., what measurement should the frame maker read on the yardstick?