Explanation Given: The sensitivity S to a drug depends on the dosage d in milligrams according to the equation: S = 650 d − 2 d 2 Formula used: The standard form of equation of vertical parabola with its vertex at ( h , k ) is: y = a ( x − h ) 2 + k For the above parabola, if a < 0 then the parabola open downwards and maximum value of the equation occurs at x = h and the maximum value is given as, y = k Calculation: Consider the provided parabolic equation, S = 650 d − 2 d 2 Rewrite the equation as, S = − 2 d 2 + 650 d Form this,

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ISBN: 9780135909942

Author: TOBEY/SLATER

Publisher: PEARSON

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 9.2, Problem 42E

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To calculate: The maximum sensitivity S to a drug and the dosage d in milligrams that produce the maximum sensitivity.

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Chapter 9.2, Problem 41E

Chapter 9.2, Problem 43E

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

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part b please

Chapter 9 Solutions

INTERMEDIATE ALGEBRA - 18 WEEK MML CODE

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The maximum sensitivity S to a drug and the dosage d in milligrams that produce the maximum sensitivity.

Solution Summary: The author explains that the maximum sensitivity to a drug depends on the dosage d in milligrams according to the equation.

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Chapter 9 Solutions