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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.4, Problem 69E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Psychology Early in the twentieth century, an intelligence test called the Stanford-Binet Test (more commonly known as the IQ test) was developed. In this test, an individual’s mental age M is divided by the individual’s chronological age C and the quotient is multiplied by 100. The result is the individual’s IQ.

I Q ( M , C ) = M C × 100

Find the partial derivatives of IQ with respect to M and with respect to C. Evaluate the partial derivatives at the point (12, 10) and interpret the result. (Source: Adapted from Bernstein/Clark-Stewart/Roy/Wickens, Psychology, Fourth Edition)

To determine

To calculate: The value of the partial derivative of IQ with respect to M and with respect to C, also calculate the value of the partial derivative at the point (12,10) and interpret the result if the function for IQ level is modelled by IQ(M,C)=MC×100.

Explanation

Given information:

The provided function for IQ level is IQ(M,C)=MC×100. Where, M is mental age and C is chronological age.

Formula used:

Consider the function z=f(x,y) then for the value of ∂z∂x consider y to be constant and differentiate with respect to x and the value of ∂z∂y consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided IQ function is,

IQ(M,C)=MC×100

Partially derivative of the function IQ(M,C)=MC×100 with respect to M.

IQM(M,C)=∂∂M(MC×100)=100C∂∂M(M)=100C

Substitute (M,C)=(12,10) in the derivative IQM(M,C)=100C.

IQM(12,10)=10010=10

Partially derivative of the function IQ(M,C)=MC×100 with respect to C

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 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Find the X value corresponding to z=0.25 of the following distributions. =40and=4 =40and=8 =40and=16 =40and=32

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Probability and Statistics for Engineering and the Sciences

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics

In Exercises 19 to 26, show that the given set has a cardinality of K by establishing a one-to-one corresponden...

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For Problems 19-28, use the following set designations. N= x|x is a natural number Q= x|x is a rational number ...

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Mathematical Applications for the Management, Life, and Social Sciences

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Solve each equation using the quadratic formula (when necessary, round result to three significant digits): 3x2...

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Let H be a normal subgroup of finite group G. If the order of the quotient group G/H is m, prove that gmH for a...

Elements Of Modern Algebra

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Contemporary Mathematics for Business & Consumers

Write each expression in terms of i. 64

Trigonometry (MindTap Course List)

Mean Value Theorem Consider the graph of the function f(x)=x2+5 (see figure). (a) Find the equation of the seca...

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Calculus: Early Transcendental Functions (MindTap Course List)

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Finite Mathematics for the Managerial, Life, and Social Sciences

For Review Exercises 26 to 29, sketch, if possible, the polygon described. A quadrilateral that is equiangular ...

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Self Check How much will she have in the account 60 weeks after her first deposit. A student deposits 50 in a n...

College Algebra (MindTap Course List)

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Mathematics For Machine Technology

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