Math Mod Unit 9 Practice Test

Given two trig ratios, find the third without using a calculator. sin=35 , cos=45 , tan= _____

3/4

Choose the degree measures of both acute angles. legs 5 cm and 8 cm

- 58° - 32°

Find the lengths of the sides of a right triangle when sinA=0.625.

- √39 - 8 - 5

What force is required to compress a spring with spring constant k=750 N/m 0.3 meters?

-225 N

In the equation y=7,893(1+0.23)x , what is the growth or decay rate?

0.23

Nobelium-253 has a half-life of 102 seconds. How much of a 10 gram sample will remain after 400 seconds?

0.66 g

If y=kx and x=8 when y=6 , what is the constant of proportionality?

0.75

The squirrel population in a certain park is 3,000 and is increasing by 15% each year. 1) Is the population in a state of growth or decay? 2) Write a model for this situation. 3) Using the model you wrote, how many squirrels will be present after 4 years?

1) growth 2) A(t) = 3,000(1 + 0.15)^t 3) 5,247

In the equation y=5,702(1+0.32)x , what is the growth or decay factor?

1.23

Convert 5π/8 radians to degrees.

112.5°

What was the initial quantity of nobelium-253, which has a half-life of 102 seconds, if after 102 seconds, there are 57 g in the sample?

114 g

Lago is flying a kite in his back yard. He has let out 20 meters of kite string and the string makes an angle of elevation with the ground of 48°. How high is the kite flying, to the nearest tenth of a meter?

14.9 m

If a projectile has a mass of 0.25 kg, what is the force needed to accelerate it at 9 m/s2?

2.25 N

Wind resistance varies jointly as an object's surface area and velocity. If an object traveling 55 miles per hour with a surface area of 24 square feet experiences a wind resistance of 330 Newtons, how fast must a car with 48 square feet of surface area travel in order to experience a wind resistance of 252 Newtons?

21 miles per hour

In the equation y=3,487(1.12)x , what is the initial value?

3,487

Vanadium-49 has a half-life of 500 days. How much of a 45 gram sample will remain after 130 days?

37.58 g

If y varies jointly as x and z , and y=20 when x=15 and z=6 , find y when x=4 and z=5.

4 4/9

If y varies directly as x and inversely as z , and y=5 when x=4 and z=3 , find y when x=3 and z=7.

45/28

A force of 550 Newtons will compress a spring of 11 meters. What is the spring constant of the spring?

50 N/m

Find the measure, to the nearest hundredth of a degree, of the larger acute angle in a right triangle with sides 8, 15, and 17 cm.

61.93°

A weather balloon with a volume of 5 liters at a pressure of 1.25 will have what volume when the pressure is 0.75?

8 1/3 L

If y varies jointly as x and z , and y=7 when x=8 and z=9 , find z when y=5 and x=6.

8 4/7

3sin(2π9x)

amplitude: 3 period: 9

6sin(2π2x)

amplitude: 6 period: 2

The amount of time it takes a decaying substance to decrease by _____ is called half-life.

half

The ratio of the length of the leg adjacent to an acute angle to the length of the ____ is called the cosine of a right triangle.

hypotenuse

The ratio of the length of the _____ opposite an acute angle to the length of the leg adjacent to the acute angle is called the tangent of a right triangle.

leg

A description of a real-world system using __________ language and concepts is called a mathematical model.

mathematical

The ratio of the length of the leg ____ an acute angle to the length of the hypotenuse is called the sine of a right triangle.

opposite

Joint variation is a relationship where one variable varies directly as the _____ of two other variables.

product

The hypotenuse is the longest side in a right triangle, opposite the ___ angle.

right

Inverse variation is a relationship where one variable gets ______ as the other gets larger and the product of the two variables is a constant.

smaller

Complementary angles are two angles the _____ of whose measures are 90 degrees.

sum

Direct variation is a relationship where one variable is equal to some constant _____ the other variable.

times

Convert 45∘ to radians.

π/4