Algebra 3 Semester 2

Write the expression as a single logarithm. 1/6ln x-1/9 ln y

B) ln(⁶√x/⁹√y)

Approximate the natural logarithm using a calculator. Round your answer to two decimal places. ln 41

C) 3.71

Find the exact length of the arc subtended by a central angle of θ=175° on a circle with radius 6 yd.

C) 35π/6 yd

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. a=80m., ?=48.4°, c=28.9m.

A) ?=112.0°, ?=19.6°, b=64.5 m.

Find the exact value of csc π/3.

B) 2√3/3

Find the exact value of sin(π/3) using the unit circle.

A) √3/2

Solve the exponential equation exactly for x. 2²x⁺¹=32

C) 2

Search and Rescue. The illustration below shows a search and rescue helicopter with a 30° field of view with a search light. If the search and rescue helicopter is flying at an altitude of 465 feet above sea level, what is the diameter of the circle illuminated on the surface of the water?

C) 249 feet

Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions. The smaller (pinion) gear has a radius of 7 cm and the larger (spur) gear has a radius of 11cm. If the pinion hear rotate 42°, how many degrees will the spur gear rotate? Round your answer to the nearest degree.

C) 27°

Write the expression as a sum or difference of logarithms. logb(x²(x+6)/√x+8)

C) 2logbx+logb(x+6)-½logv(x+8)

Use the reciprocal identity cdcθ=1/sinθ to calculate csc 60°.

C) 2√3/3

Radium-226 has a half-life of 1600 years. How long will it take 18.5 grams of radium-226 to be reduced to 5 grams? Rond to the nearest year.

C) 3,020 years

At 1 P.M. a body is found in a park. The police measure the body's temperature at 89°F. At 7 P.M. the medical examiner arrives and determines the temperature to be at 80°F. Assuming the temperature of the park was constant at 71°F, how long has the victim been dead? Round to one decimal place.

C) 3.7 hours before 1 P.M.

In 2001, the population of Pleasantville was 34,500. Their population increases by 2.4% per year. What is the expected population of Pleasantville in 2020? Round your answer to the nearest whole number.

C) 54,432

Write the expression as a single logarithm. 6log u-log v-6log z

C) log(u⁶/vz⁶)

Solve the logarithmic equation exactly. log₄(8x)-log₄(x+1)=4

C) no solution

Use the unit circle to find all the exact values of θ that make sinθ=√2/2 in the interval 0≤θ≤2π.

C) π/4, 3π/4

Evaluate cos(-315°) exactly.

C) √2/2

Evaluate cot(-1050°) exactly.

C) √3

Solve the linear system of equations for k, m, and n. -4k-5m+4n=11 -6k+6m-6n=30 -8k-7m-2n=25

C) (-4,1,0)

Find the exact valure of tan 11π/6.

C) -√3/3

Graph the system of inequalities. y≤4x+2 y≥-4x-1

A)

Match the graph with the function ƒ(x) = -e³x

A)

Match the graph with the logarithmic function. ƒ(x)=log₃(1-x)

A)

If Gabriel Deposits $1000 in a savings account that earns 1.6% interest per year compounded quarterly, how much money can he expect to be in the account in 6 years? Round your answer to two decimal places.

A) $1,096.00

If Ashley deposits $16,500.00 into a savings account that earns 1.7% interest per year compounded monthly, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

A) $17,362.70

Solve the system of linear equations by graphing the following equations. 4x+7y=-60 9x+6y=-57

A) (-1,-8)

State the domain of the logarithm function ƒ(x)=log₆(1-x²).

A) (-1,1)

Solve the system of linear equations by elimination. 6d+3f=-24 -6d-8f=14

A) (-5,2)

Evaluate sin(213°) with a calculator. Round to four decimal places.

A) -0.5446

Use a calculator to approximate the cos 2.2° to three decimal places.

A) 0.999

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places. log₇18

A) 1.49

Solve the exponential equation exactly for x. 216x=6

A) 1/3

Write the logarithmic equation in its equivalent exponential form. log 10,000=4

A) 10⁴=10,000

An engineer wants to contract a bridge across a fast moving river. Using a straight line segment between two points that are 131 feet apart along his side of the river, he measures the angles formed when sighting the point on the other side where he wants to have the bridge end. If the angles formed at points A and B are 58° and 38°, respectively, how far is it from point B to the point on the other side of the river? Round answer to one decimal place.

A) 111.7 feet

Use the properties of logarithms to simplify the expression. 3³log₃⁵

A) 125

Find the area of the triangle described. Round to the nearest integer. b=373, c=372, a=87

A) 16,092

An apple pie is taken out of the oven with an internal temperature of 344°F. It is placed on a rack in a room with a temperature of 74°F. After 37 minutes, the temperature of the pie is 225°F. What will be the temperature of the pie 50 minutes after coming out of the oven? Round to one decimal place.

A) 197.1°F

A tracking station has two telescopes that are 2.8 miles apart. The telescopes can lock onto a rocket after it is launched and record the angles of elevation to the rocket. Is the angles of elevation from telescope A and B are 27° and 53.5°, respectively, then how far is the rocket from telescope B? Round to one decimal place.

A) 2.8 miles

If the measure of the angle H is (3x)° and the angle E is (10x - 56)°, what is the measure of angle H to the nearest degree?

A) 24°

A triangular garden measures 41 feet by 23 feet by 22 feet........

A) 27.50

Some students are painting a mural on the side of a building...

A) 30°

Some very destructive beetles have made their way into a forest preserve...

A) 490. 1 square miles

Glide slope of an airplane. The glide slope of an airplane is the angle between the flight path approaching the runway and the ground. An airliner approaches a runway on a glide slope of approximately 3°. How high is an airplane above the ground if the distance from the runway to a point on the ground directly below the airplane is 10,034 feet? Round your answer to the nearest foot.

A) 526 ft

An airplane door is 8 feet high. If a slide attacked to the bottom of the open door is at an angle of 26° with the ground, and the angle is formed by the line of sight from where the slide touches the ground to the top of the door is 32°, then how long is the slide?

A) 65 feet

A parking lot is to have the shape of a parallelogram that has adjacent slide measuring 234 feet and 332 feet. The angle between the two sides is 58°. What is the area of the parking lot? Round to the nearest integer.

A) 65,883 square feet

Convert 7/19π radians to degrees. Round the answer to one decimal place.

A) 66.3°

In 2002 the population of Stony Creek was 7,500. Their population increases by 0.75% per year. What is the expected population in Stony Creek in 2022? Round your answer to the nearest whole number.

A) 8,714

Solve the given triangle and round to one decimal place. α+β+γ=180° b=224.0 ft, ?=23.4°, ?=48.2°

A) ?=108.4°, c=420.5 ft, a=535.2 ft.

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. a=190m., b=214 m., c=213 m.

A) ?=52.8°, ?=64.0°, ?=63.2°

Write the exponential equation in its equivalent logarithmic form. (¼)⁴=(¹/₂₅₆)

A) log¼(1/256)=4

Match the graph to the system of inequalities

A) y<2x y<-3x

Match the graph with the logarithmic function.

A) ƒ(x)=log₄(1-x)-1

Ferris Wheel. If the Ferris Wheel is centered at the origin and travels in a counterclockwise direction. A car starts at (-100,0) and before completing 6 rotations it is stopped at (50,-50√3). Through what angle has the car rotated?

C) 1920°

Solve the system of linear equations by substitution. 4x+6y=-32 5x-8y=22

B) (-2, -4)

Solve the system of linear equations by graphing the following equations. -2x-6y=34 -5x+8y=-53

B) (1,-6)

Solve the system of linear equating by elimination. 8t+12q=32 24t+4q=224

B) (10,-4)

Solve the logarithmic equation. Round your answer to three decimal places. log₂(1-x)+log₂(4-3x)=3

B) -0.475

Solve the exponential equation. Make sure to isolate the base to power first. Round your answer to three decimal places. 4e²x-8ex-9=0

B) 1.031

A 35 foot slide leaning against the bottom of a building's window makes a 49° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 38°. How tall is the window? Round to the nearest integer.

B) 11 feet

Phytoplankton are microscopic plants that live in the ocean. Phytoplankton grow abundantly in oceans around the world and are the foundation of the marine food chain. One variety of phytoplankton growing in tropical waters is increasing at a rate of 16% per month, If it is estimated that there are 50 million in the water, how many will there be in 8 months? Utilize formula N=N₀ert where N represents the population of phytoplankton. Round to the nearest million.

B) 180 millions

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places. log₇.₃14.9

B) 2.04

Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius 7/4 in and arc length 5/7 in.

B) 20/49 radians

Height of a building. The angle of elevation of a stake in the ground to the top of a building is 21°. What is the height of the building if the distance from the stake to the base of the building is 60.5 m? Round your answer to one decimal place.

B) 23.2 m

Height of a palm tree. A palm tree casts a shadow that is 48.8 feet long. At the same time, a man of height 63.9 inches cast a shadow that is 80.7 inches long. How tall is the palm tree?

B) 38.6 feet

Use a calculator to approximate the length of the arc on a circle with central angle θ=1.3 radians and radius r=3.9 yd. Round your answer to two decimal digits.

B) 5.07 yd

A rope is to be tied from the top of a tent 8 feet high to stake in the ground. If the angle between the ground and the rope is to be 56°, how far from the base of the tent should the rope be staked? (round to two decimal places.)

B) 5.40

Given ƒ(x) = 4³⁻ⁿ, evaluate ƒ(0.1). Round your answer to two decimal places.

B) 55.72

If secθ=-25/24, and the terminal side of θ lies in quadrant II, find sin θ.

B) 7/25

Match the function with the graph and the model name h(t)=1-ln(t+2)

B) Logarithmic

What type of triangle is the following?

B) Obtuse Equilateral Triangle.

Match the function with the graph and the model name. Logistic

B) P(t)=100/1+3e⁻⁰°²t

State in which quadrant or on what axis the terminal side of a 717° angle in standard position lies.

B) QIV

Solve right triangle ABC if A=44° and c=14.8 m. Round lengths to one decimal point.

B) a=10.3 m, b=10.6 m, B=46°

Calculate sinθ if the terminal side of θ is defined by the line y=14x, x≥0, and θ is the smallest positive angle in standard position.

B) √197/197

Find the exact value of csc(3π/4) using the unit circle. Rationalize the denominator, if necessary.

B) √2

Find the exact value of cos(π/4) using the unit circle.

B) √2/2

Solve the system of linear equations by substitution. 3x-8y=-20 6x-5y=-29

C) (-4,1)

If Vu deposits $5,500.00 in a savings account that earns 3% interest per year compounded quarterly, how much money can she expect to be in the account in 6 years? Round your answer to two decimal places.

D) $6,580.27

Solve the system of linear equations by elimination. -2x-2y=12 -4x+6y=54

D) (-9,3)

For the exponential function ƒ(x) = 1-e⁻², state the y-intercept. Round your answer to two decimal places

D) (0,0)

Clock. What is the measure of the angle an hour hand on a clock makes if it starts at 3:00 am on Tuesday and continues until 5:00 am on Thursday?

D) -1500°

Solve the exponential equation exactly for x. 10x²⁻³ = 10

D) -2,2

Solve the exponential equation. Round your answer to two decimal places. 4(10³x)=32

D) 0.30

A substance has an approximate hydrogen ion concentration of about 1.24x10⁻¹²°¹. Calculate its pH value.

D) 12.0

Solve the logarithmic equation. Round your answer to three decimal places. ln(9x)=6

D) 44.825

Use the triangle to write secθ, if A=4, B=3, and C=5,

D) 5/3

Use the triangle to write cscθ, if A=4, B=3, and C=5.

D) 5/4

A health food company mixes dried fruit with walnuts to make trail blend mix....

D) d=55 pounds, w=10 pounds

Write the expression as a sum or difference of logarithms. logv(x¹/₈/z³/₂)

D) ¹/₈log bx-³/₂logbx

Use the unit circle to find all the exact values of θ that make tanθ=√3/3 in the interval 0≤θ≤2π.

D) π/6, 7π/6

Write the expression as a single logarithm. 3log u+2log v

log (u³v²)