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2 years ago

10

You are downloading a song to your MP3 player. The ratio of pop songs to rock songs is 5:4. You download 40’pop songs. How many

rock songs do you download

2 answers:

finlep [7]2 years ago

4 0

You download 4/5 as many rock songs as pop songs (a true shame), which is 40(4/5)= 32 rock songs.

Strike441 [17]2 years ago

4 0

You download 32 rock songs, 5 : 40 is 8 and 8 * 4 is 32.

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FinnZ [79.3K]

☁️ Answer ☁️

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3 years ago

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slamgirl [31]

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2 years ago

Write equivalent expressions using distributive property. m(4+7)

yulyashka [42]

Hey there!

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2 years ago

It says solve for x and round to the nearest hundredth. <br> 1. 9 over 6 equals x over 10

emmainna [20.7K]

Answer:

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Step-by-step explanation:

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3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

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We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago