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3 years ago

A height of 26 feet and a diameter of 5.6 feet. What is the volume of the geode, rounded to the nearest tenth?

Mathematics

1 answer:

7nadin3 [17]3 years ago

8 0

Answer:

Therefore,

The volume of the geode, rounded to the nearest tenth is 640.1 feet³.

Step-by-step explanation:

Given:

Geode shaped approximately like a cylinder. such that

Height = h = 26 feet

Diameter = d = 5.6 feet

$Radius = r =\dfrac{d}{2}=\dfrac{5.6}{2}=2.8\ feet$

To Find:

volume of the geode = ?

Solution:

Geode shaped approximately like a cylinder,

So, Volume of Cylinder is given by,

$\textrm{Volume of Cylinder}=\pi r^{2}h$

Where,

Height = h

Radius = r

pi = 3.14

Substituting the values we get

$\textrm{Volume of Cylinder}=3.14\times 2.8^{2}\times 26=640.05\approx 640.1\ feet^{3}$

Therefore,

The volume of the geode, rounded to the nearest tenth is 640.1 feet³.

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A car that travels along the highway to Denver at a steady speed. When it begins, it is 300 miles from Denver. After 3 hours, it

umka21 [38]

Answer: $y=-40x+300$

Step-by-step explanation:

This car follows a line, hence its motion can be modeled by the Line equation.

In fact, we already have two points of the line, if we call $x$ the time in hours and $y$ the traveled distance in miles:

Point 1: $(x_{1},y_{1})=(0,300)$

Since we are told the car's initial position is 300 miles in the time 0 h

Point 2: $(x_{2},y_{2})=(3,180)$

Since we are told the car's final position is 180 miles after 3h

<u />

<u>Let's find the Slope $m$ : </u>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=-40$ This is the slope of the line

Now, the equation of the line is:

$y=mx+b$

We already know the slope, now we have to find the intersection point with the y-axis ( $b$ ) with any of the given points. Let's choose Point 1: $(x_{1},y_{1})=(0,300)$

$300=-40(0)+b$

Isolating $b$ :

$b=-300$

Then, the equation of the line is:

$y=-40 x+300$

7 0

3 years ago

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A theater is divided into a red section and a blue section. The red section has 350 seats, and the rest of the seats are in the

coldgirl [10]

850.

68,750 = 350(75) + 50x
68, 750 = 26,250 + 50x
-26250
42,500 = 50x / 50
850 = x

5 0

3 years ago

An archeologist discovered two artifacts buried beneath the ground. She found the first artifact at an elevation of -8:2/7 meter

8090 [49]

Answer:

Option D is the correct choice.

Step-by-step explanation:

We are provided angle of elevations of two artifacts buried beneath the ground and we are asked to find distance between these two elevations.

We will find distance between these elevations by taking the difference of two.

$35:\frac{4}{7}--8:\frac{2}{7}$

$35:\frac{4}{7}+8:\frac{2}{7}=43:\frac{6}{7}$

Since we know that distance is always positive so option A is incorrect.

Therefore, option D is the correct choice and distance between these two elevations is $43:\frac{6}{7}$ .

5 0

2 years ago

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Write an equation that has a graph with the shape of y = x^2, but shifted left 3 units.

svetoff [14.1K]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf % template detailing
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

now, with that template in mind, let's see

$\bf y=x^2\implies 
\begin{array}{llll}
y=(&1x&-0)^2\\
&B&C
\end{array}$

so, just change C to +3, thus C/B is 3/1

6 0

2 years ago

I need help again if I don't get this right then I'll have to do the lesson all over again and I'm already 10 lessons behind!

xxTIMURxx [149]

<h3>♫ - - - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - - - ♫</h3>

➷ It would be option D

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

6 0

3 years ago

Read 2 more answers