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2 years ago

Write the phrase as a rate in simplest form. 320miles on 34gallons

Mathematics

2 answers:

Katena32 [7]2 years ago

7 0

Answer:

160/17 miles per gallon

Step-by-step explanation:

The typical rate of distance and gallons is distance per gallons, so divide the distance by the number of gallons.

(320 miles)/(34 gallons) = 160/17 miles per gallon

tankabanditka [31]2 years ago

7 0

Answer:

9.41 miles per gallon

Step-by-step explanation:

For every 320 miles, you use 34 gallons.

320 miles/34 gallons

The unit rate is 9.41 ( $\frac{160}{17}$ or $9 \frac{7}{17}$ ) miles per gallon

I hope I helped!

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~ Zoe

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2 years ago

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2 years ago

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2 years ago

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2 years ago

Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$

Therefore we have:

$\frac{H-8}{r_1} =\frac{H}{r_2}$

We put in the numerical values of $r_1$ , $r_2$ and solve for $H$ :

$\boxed{H=\frac{8r_2}{r_2-r_1} =\frac{8*13.677}{13.68-9.12} =24\:feet.}$

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2 years ago