University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

144

Pages:

2
Author:

Bailey Ayala

Question 1 x = -8 when y = -1/4 in an inverse variation. Find y when x = 4. Answer: The equation for an inverse variation: $ y = \frac{k}{x} $ Solve for k: $ -1/4 = \frac{k}{-8} $ $ k = (-1/4) \times (-8) $ $ k = 2 $ Substitute $ k = 2 $ to find y: $ y = \frac{2}{x} $ When $ x = 4 $: $ y = \frac{2}{4} $ $ y = \frac{1}{2} $ Question 2 Find the exact value of tan(11π/3) using the unit circle. Answer: Remove full rotations of 2π until the angle is between 0 and 2π: $ 11\pi/3 - 2\pi = 11\pi/3 - 6\pi/3 = 5\pi/3 $ Apply the reference angle by finding the angle between 0 and $\pi/2$ (2π): The quadrant: $ 5\pi/3 $ is in the fourth quadrant. Make the expression negative because tangent is negative in the second quadrant: $ \tan\left(\frac{5\pi}{3}\right) = \tan\left(\frac{\pi}{3}\right) $ The exact value of $\tan(\frac{\pi}{3}) = \sqrt{3} - \sqrt{3} = 0$ (Decimal: -1.73205.) Question 3 For the function that is described by the provided characteristics, write an equation in terms of x and y. A sine curve with a period of π, an amplitude of 3, a right phase shift of π/2, and a vertical translation up 2 units. Answer: The phase shift is $\frac{\pi}{2}$, so $ x - \frac{\pi}{2} = x \times 2 $. The amplitude is 3 so $ a = 3 $. The period is $\frac{2\pi}{b} = \pi$, so $ b = 2 $. The vertical translation is 2 units so $ d = 2 $. Equation is: $ y = 3 \sin\left(2\left(x - \frac{\pi}{2}\right)\right) + 2 $ $ y = 3 \sin(2x - \pi) + 2 $ Question 4 h varies jointly as f and g. Find h when f = 20, g = 15, and k = 4. Answer: Given that h varies jointly as f and g, then we can write: $ h = k \cdot f \cdot g $ where k is the constant of proportionality. When $ f = 20 $, $ g = 15 $, and $ k = 4 $: $ h = 4 \times (20) \times (15) $ $ h = 1200 $ Question 5 A back-to-back stem plot is particularly useful for (A) identifying outliers. (B) comparing data distributions. (C) merging two sets of data. (D) graphing home runs. (E) measuring stems from leaves. Answer: A back-to-back stem plot has information for each set of data, and you can compare the spread and locate outliers. The correct answer is: (A) identifying outliers.