Thursday, May 03, 2018

Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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August 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.

10. lridium-192 is an isotope of iridium and has a half-life of 73.83 days. If a laboratory experiment begins with 100 grams of Iridium-192, the number of grams, A, of Iridium-192 present after t days would be A = 100(1/2)(t/73.83).
Which equation approximates the amount of Iridium-192 present after t days?

1) A = 100(73.83/2)t
2) A = 100(1/147.66)t
3) A = 100(0.990656)t
4) A = 100(0.116381)t

Answer: 3) A = 100(0.990656)t
100(1/2)(t/73.83) = 100((1/2)(1/73.83)) (t)
(1/2)(1/73.83) = 0.99065551184
So 100(1/2)(t/73.83) = 100(0.990656) (t)

11. The distribution of the diameters of ball bearings made under a given manufacturing process is normally distributed with a mean of 4 cm and a standard deviation of 0.2 cm. What proportion of the ball bearings will have a diameter less than 3.7 cm?

1) 0.0668
2) 0.4332
3) 0.8664
4) 0.9500

Answer: 1) 0.0668
Enter normCdf(0,3.7,4,0.2) into your calculator.
You'll find "normCdf" using 2nd VARS, which gives you the DISTRIB menu, where it is option 2.
The 0 is your lower boundary, and 3.7 is your upper boundary. You want everything less than 3.7.
The 4 is your mean, and the 0.2 is your standard deviation.
You will get an answer of 0.066807.

12. A polynomial equation of degree three, p(x), is used to model the volume of a rectangular box. The graph of p(x) has x intercepts at −2, 10, and 14. Which statements regarding p(x) could be true? A. The equation of p(x) = (x − 2)(x + 10)(x + 14). B. The equation of p(x) = −(x + 2)(x − 10)(x − 14). C. The maximum volume occurs when x = 10. D. The maximum volume of the box is approximately 56

1) A and C
2) A and D
3) B and C
4) B and D

Answer:4) B and D
The zeroes are -2, 10 and 14, so statement A is incorrect but B could be true.
Since 10 is a zero, it does not make sense that it would also be a maximum value. The line will be either increasing or decreasing as it passes through x = 10. In either case, x = 10 is not a maximum point. This eliminates statement C, so only Choice 4 is left.
Putting p(x) = −(x + 2)(x − 10)(x − 14) into the calculator, you will see that the maximum is 56, so statement 4 could be true if statement 2 is true.

Comments and questions welcome.

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