$$\theta = 0^\circ, 180^\circ, 270^\circ$$

Question 1

Solve for $$x in $$the equation $$16x + 4 = 83x - 2. $$What is the value of $$x$$?

Accepted Answer

$$x = 0.087$$

Question 2

Which of the following is the correct solution for $$x in$$ $$x = \log_3$ 181$$? (Round to the nearest thousandth)

Accepted Answer

$$x = 5.672$$

Question 3

If $$\ln 2x = 5$$, what is the value of $$x$$? (Round to the nearest thousandth)

Accepted Answer

$$x = 74.207$$

Question 4

A $$20-$$meter road sign casts a $$30-$$meter shadow. What is the angle of elevation to the sun? (Round to the nearest degree)

Accepted Answer

$$33^\circ$$

Question 5

What is the future value if $$1560 is invested at 5$$\%$$ compounded monthly for 2$ years? (Round to the nearest cent)

Accepted Answer

$$1727.98$$

Question 6

Given $$\log_a x = 2.2$$, $$\log_a y = 1.8$$, and $$\log_a z = 5.1$$, evaluate $$\log_a (x^2$ y z).$$

Accepted Answer

$$11.3$$

Question 7

Find the exact value of $$y = \sin$$^{-1}$$(-1). $$Which of the following is correct?

Accepted Answer

$$y = -\frac{\pi}{2}$$

Question 8

Solve for $$x in$$ $$\log_5$ (8 - 3x) = 3. $$What is the value of $$x$$?

Accepted Answer

$$x = -117$$

Question 9

Which of the following is the correct solution for $$x in$$ $$13x = 6$$?

Accepted Answer

$$x = 0.462$$

Question 10

What amount should be invested now to obtain $$20,000 in 12$ years, if interest is 6$$\%$ compounded quarterly? (Round to the nearest cent)

Accepted Answer

$$9,920.00$$

Question 11

Given $$\sec 	heta = -1$$ and $$\sin 	heta \u003e 0$$, what is the value of $$	heta in$$ $$[0, 2\pi)$$?

Accepted Answer

$$	heta = \pi$$

Question 12

Which of the following is the correct solution for $$x in$$ $$3x - 4 = 72x + 5$$?

Accepted Answer

$$x = -0.127$$

Question 13

Solve for $$x in$$ $$\ln 5 + 4x - \ln 3 + x = \ln 3. $$What is the value of $$x$$?

Accepted Answer

$$x = 0.366$$

Question 14

Which of the following is the correct value for $$	heta = \arcsin\left(-\frac{3}{2}ight)$$?

Accepted Answer

No solution exists

Question 15

Solve for $$x in$$ $$\log_x + \log_{x^2$} = 3. $$Which of the following is correct?

Accepted Answer

$$x = 10$$^{1}$$

Question 16

Which of the following is the correct value for $$y = \arccos(-2)$$?

Accepted Answer

No solution exists

Question 17

If $$\cos 	heta = 1/5$$ and $$	an 	heta \u003e 0$$, which quadrant is $$	heta in$$?

Accepted Answer

Quadrant III

Question 18

Solve for $$x in$$ $$-2\sin^2$ x = 3\sin x + 1$$ for $$x in$$ $$[0, 2\pi). $$Which of the following is a solution?

Accepted Answer

$$x = \arcsin(-0.5)$$

Question 19

Which of the following is the correct solution for $$2	an^2$ 	heta \sin 	heta - 	an^2$ 	heta = 0$$ for $$	heta in$$ $$[0^\circ, 360^\circ)$$?

Accepted Answer

$$	heta = 0^\circ, 180^\circ, 270^\circ$$

Question 20

If $$y = 3\sin 12x$$, what is the period of the function?

Accepted Answer

$$\frac{\pi}{12}$$

Precalculus Final Exam Practice – Step-by-Step Study Guidance

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