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3 years ago

A $7.06 toy is on sale for 15% off if eve has a 25% off coupon how much will the you cost?

Mathematics

1 answer:

Evgen [1.6K]3 years ago

5 0

Answer:

Step-by-step explanation:

First you determine how much 15% of $7.06 is. ($1.06)

Then you subtract that from $7.06 which is $6.00.

Then you determine how much 25% of $6.00 is. ($1.50)

Then you subtract that off from $6.00, which gives you $4.50.

Final answer: $4.50

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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:

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

3 0

3 years ago

A triangle has a hypotenuse of 153 centimeters and a leg of 72 centimeters what is the length of the other leg

Inga [223]

Pythagorean theorem = $\sqrt{a^{2} + b^2 +c^2 }$
Since you only have $a^{2}$ and $c^2$ you change the equation to $\sqrt{c^2 - a^2 = b^2}$
Giving you $\sqrt{153^2 - 72^2$ = 135

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3 years ago

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castortr0y [4]

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4 years ago

Lance has 9 package of sports cards. Each package has 108 cards . About how many cards does Lance have?

horrorfan [7]

It would be 972 cards

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3 years ago

Read 2 more answers

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barxatty [35]

Answer: To get function g, shift f DOWN by 7 units and to the RIGHT by 2 units

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2 years ago

A $7.06 toy is on sale for 15% off if eve has a 25% off coupon how much will the you cost?​

A $7.06 toy is on sale for 15% off if eve has a 25% off coupon how much will the you cost?