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3 years ago

How do I do this help

Mathematics

1 answer:

tatuchka [14]3 years ago

5 0

6÷40.5= $6.75 per hour
8÷54= $6.75 per hour
y= 6.75x

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Step-by-step explanation:

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Three more than twice a number is less than negative thirteen. Solve the inequality for the unknown number.

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Answer:

Step-by-step explanation:

The number = x

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Among all right circular cones with a slant height of 24, what are the dimensions (radius and height) that maximize the volum

aleksklad [387]

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

$r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2$

Once this is defined, we proceed to define the volume of a cone,

$v=\frac{1}{3}\pi r^2 h$

Substituting,

$v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)$

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

$\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)$

$\frac{dv}{dh} = 0$ then $\rightarrow \frac{1}{3}\pi(576-3h^2)=0$

$h_1=-8\sqrt{3}\\h_2=8\sqrt{3}$

<em>We select the positiv value.</em>

We have then,

$r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}$

We can now calculate the maximum volume,

$V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99$

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