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3 years ago

A red candle is 11 2/5 inches tall. The label claims that the candle will melt 1 1/8 inch every hour it burns. If the label is c

orrect, for how many hours will the candle burn?

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

3 0

$11\frac{2}{5}\ inches\ burn\ in\ x\ hours\\\\
1\frac{1}{8}\ inches\ burn\ in\ 1\ hour\\\\cross\ multiplication\\\\
11\frac{2}{5}=1\frac{1}{8}x\ \ \ \ | divide\ by\ 1\frac{1}{8}\\\\
\frac{\frac{57}{5}}{\frac{9}{8}}=x\\\\\frac{57}{5}*\frac{8}{9}=x\\\\
x=\frac{456}{45}=10\frac{2}{15}\\\\
Candle\ will\ burn\ in \ 10\frac{2}{15}\ hours.$

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Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume $V$ of a solid pyramid can be given as:

$\displaystyle V = \frac{1}{3} \cdot b \cdot h$ ,

where

$b$ is the area of the base of the pyramid, and
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Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be $x$ cm.

At the vertice of this pyramid, $x = 0$ and the length of a side of the square is also $0$ .
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As a result, the length of a side of the square will be

$\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x$ .

The area of the square will be

$\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}$ .

Integrate the area of the horizontal cross-section with respect to $x$

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$\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}$ .

In other words, the volume of this pyramid is 16 cubic centimeters.

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mezya [45]

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Step-by-step explanation:

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scZoUnD [109]

<h3>Answer: 2x^2 + 6x - 4</h3>

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Work Shown:

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Step-by-step explanation:

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