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svet-max [94.6K]

3 years ago

6

Mason is driving on a long road trip. He currently has 12 gallons of gas in his car. Each hour that he drives, his car uses up 1

.5 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?

1 answer:

egoroff_w [7]3 years ago

6 0

After 2 hours it should have 9 gallons of gas left

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The sum of two consecutive even numbers is 54. Find the numbers.

Reil [10]

Hi! the numbers are 26 and 28!

26+(26+2) =54

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3 years ago

What is the square root of 378904

zvonat [6]

Simplify the following:

sqrt(378904)

sqrt(378904) = sqrt(8×47363) = sqrt(2^3×47363):

sqrt(2^3 47363)

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2 sqrt(2) sqrt(47363)

sqrt(2) sqrt(47363) = sqrt(2×47363):

2 sqrt(2×47363)

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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:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

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:

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

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3 years ago

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Answer:

Your answer is y.

Step-by-step explanation:

4y+2y-5y given

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