Which of the following statements explains how to solve for w in the equation A = lw?

Mathematics

1 answer:

gladu [14]3 years ago

6 0

Answer:

Divide both sides by l.

Step-by-step explanation:

The equation that we have to solve in this problem is

$A=lw$

where

A is the area

l is the length

w is the width

Here we want to solve the equation for w, the width. It means that we have to isolate this variable.

In order to do so, we proceed as follows:

1) We divide by l on both sides:

$\frac{A}{l}=\frac{lw}{l}$

2) We simplify l on the right side, so we get:

$\frac{A}{l}=w$

So, we have solved for w.

Therefore, the correct answer is

Divide both sides by l.

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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

irina [24]

Answer:

x-coordinates of relative extrema = $\frac{-1}{2}$

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

$f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}$

Differentiate with respect to x

$f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}$

$f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}$

Differentiate f'(x) with respect to x

$f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1$