Math Problem Statement

Use the variable u for the inside function to express each of the following as a composite function. ( a) y = (8t ^ 2 - 5) ^ 2 NOTE: u(t) is the inside function and y(u) is the outside function. u(t) = y (u) = ( b ) P = 8e ^ (-0.5t) NOTE: u(t) is the inside function and P(u) is the outside function . u(t) =; P(u) = C 5 ( y^ 6 +7)

Solution

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Math Problem Analysis

Mathematical Concepts

Composite Functions
Exponential Functions
Polynomial Functions

Formulas

u(t) = 8t^2 - 5, y(u) = u^2
u(t) = -0.5t, P(u) = 8e^u
u(y) = y^6 + 7, C(u) = 5u

Theorems

Chain Rule for Differentiation

Suitable Grade Level

Grades 11-12