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1 year ago

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The ratio 1331 : x is equivalent to the ratio

="x^{2} : 1331" alt="x^{2} : 1331" align="absmiddle" class="latex-formula">. what is the value of x?

1 answer:

Marrrta [24]1 year ago

6 0

Answer:

121

Step-by-step explanation:

Set up the equation 1331/x=x^2/1331

Cross multiply and simplify the answer.

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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

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

At x = $\frac{-1}{2}$ ,

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

We know that if $f''(a)>0$ then x = a is a point of minima.

So, $x=\frac{-1}{2}$ is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

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A stretched spring has a length of 12 inches when a weight of 2 lbs is attached to the spring. The same spring has a length of 1

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The way I figured this one out was saying that if it takes 2lbs to stretch it to 12 inches and 5lbs to stretch to 18 inches that means that 3 additional pounds = 6 inches. Therefore, each additional pound is 2 inches. We know already that with 2 lbs it was 12 inches in length and we can also say that 2 lbs = 4 inches. So subtract 4 from 12 and you end up with the answer of 8 inches.

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2 years ago

What is the slope of (-5,-1) (5,5)? Explain.

ArbitrLikvidat [17]

Step-by-step explanation:

$slope = \frac{ - 1 - 5}{ - 5 - 5} = \frac{ - 6}{ - 10} = \frac{ 3}{ 5} \\$

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3 years ago

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Match each mathematical expression with its simplified form.<br> (2 +9+4)<br> (3 + 1 + 4 + 8)

katen-ka-za [31]

Answer:

15 and 16

Step-by-step explanation: To get simplified form, you add the numbers in parentheses together. (2+9+4)= 15 and (3+1+4+8)=16

For problem 1. 2+9=11 11+4=15

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