/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 Let \(F(t)=(t+4)^{2} .\) Find \(... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 41

Let \(F(t)=(t+4)^{2} .\) Find \(t\) such that \(F(t)=13\)

Short Answer

Expert verified
The solutions are \( t = -4 + \sqrt{13} \) and \( t = -4 - \sqrt{13} \).

Step by step solution

01

Set Up the Equation

To find the value of \(t\) such that \(F(t) = 13\), start by setting \(F(t)\) equal to 13. This gives the equation \[(t + 4)^2 = 13\]
02

Take the Square Root of Both Sides

Next, take the square root of both sides to solve for \(t + 4\). This yields: \[\sqrt{(t + 4)^2} = \sqrt{13}\]which simplifies to \[t + 4 = \pm \sqrt{13}\]
03

Solve for t

Isolate \(t\) by subtracting 4 from both sides of the equation: \[t = -4 \pm \sqrt{13}\]
04

Identify the Solutions

This yields two possible solutions for \(t\): \[t = -4 + \sqrt{13} \quad \text{or} \quad t = -4 - \sqrt{13}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Square Root Property
When solving quadratic equations, the square root property is a fundamental technique. It states that if you have an equation of the form \( x^2 = k \), then \( x = \pm \sqrt{k} \). In our problem, we had \((t + 4)^2 = 13\). Taking the square root of both sides, we must remember to include both the positive and negative roots. This is why we get \(( t + 4 = \pm \sqrt{13} )\). The \

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