(a) (i) Rationalize the denominator of (iii) Hence, or otherwise, simplify -4 +(12-√32) 3+2√2 (b) The profit function in Kwacha per day for a small scale company is given by f(x) = -16x²+64x+190, where x is the number of products sold each day. Find the number of products (x) sold each day in order to maximize the profit, and find this maximum profit. -4 (√2+1)²

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
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Q3. (a) (i) Rationalize the denominator of
(iii) Hence, or otherwise, simplify
-4
+(12-√32)
3+2√2
(b) The profit function in Kwacha per day for a small scale company is given by
f(x) = -16x²+64x+190, where x is the number of products sold each day. Find the number
of products (x) sold each day in order to maximize the profit, and find this maximum profit.
(c) (i) Simplify 250 where i = √-1.
-². Is * associative?
2
(ii) Let * be a binary operation on R defined by x * y =
(d) (i) A curve has the equation f(x) = 8 + 22₁-3. Find dy and .
d²y
(ii) Prove the identity tan + cot 0 =
cos sin
-4
(√2+1)²
Transcribed Image Text:Q3. (a) (i) Rationalize the denominator of (iii) Hence, or otherwise, simplify -4 +(12-√32) 3+2√2 (b) The profit function in Kwacha per day for a small scale company is given by f(x) = -16x²+64x+190, where x is the number of products sold each day. Find the number of products (x) sold each day in order to maximize the profit, and find this maximum profit. (c) (i) Simplify 250 where i = √-1. -². Is * associative? 2 (ii) Let * be a binary operation on R defined by x * y = (d) (i) A curve has the equation f(x) = 8 + 22₁-3. Find dy and . d²y (ii) Prove the identity tan + cot 0 = cos sin -4 (√2+1)²
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