Wristwatch Wholesale

Help with math!?

1. Find k such that f (x) = (x ^ 3) – (kx ^ 2) + k ^ 4 + x-factor – 2. 2. What is the remainder when f (x) = (-4x ^ 17) + (x ^ 9) – (x ^ 5) + 8x is divided by x + 1. 3. The monthly income from the sale of wristwatches x is represented X-(40 – 0.2x) dollars. The wholesale price of each watch is $ 32. How many watches must be sold each month to achieve a profit (income – Costs) of at least $ 50? The result is at least $ 50 if at least (in white) watches and not more than (white) watches are sold.

Theorem the rest are told that for a polynomial f (x), the remainder to the division by (xa) is f (a). It follows that (Xa) is a factor of f (x) corresponds exactly f (a being 0). Thus, 1. f (2) = 2 ^ 3 – k * 2 ^ 2 + 2k + 4 ………. = 8 – 2k + 4k + 4 ………. = 12 – 2k ………. = 0 when k = 6 2. It is easier than first. Simply replace x = -1. Without a calculator or mechanical assistance, I would not consider replacing a value other than -1, 0 or 1. -1 At a power strange is -1, all power, even it is 1. (I guess you know) is f = (-1) …………….. = 4 -1 1-8 …………….. = – 4 3. The wholesale price of watches is $ 32x x Profit = 40x – 0.2x ^ 2 – 32x …….. = 8x – 0.2x ^ 2 …….. = 0.2x (40 – x) The graph of this function is concave down parabola. We must find the values of x for which it equals 50, then it is over 50 for all x between these values. To solve 8x – 0.2x ^ 2 = 50, multiply both sides by -5:-40x + x ^ 2 = – 250 x ^ 2 – 40x + 250 = 0 using the quadratic formula (slightly simplified) I x = 20 + / – sqrt (20 ^ 2 – 250) [you will use 40 instead of 20, 4 * 250, and divide by 2. same result.] x = 20 + 12.2 or 20 – 12.2. = 32.2 or 7.8 the number sold must be an integer, is therefore at least 8 and not more than 32.

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