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3 years ago

2/9 rational or irrational

Mathematics

1 answer:

marishachu [46]3 years ago

4 0

Answer: Rational

Step-by-step explanation: Let's first go over what a rational number is. A rational number is any number that you can write in the form $\frac{a}{b}$ where a and b are integers and b ≠ 0.

The fraction $\frac{2}{9}$ would be a rational number because it's in the form of $\frac{a}{b}$ . Therefore, 2/9 is a rational number.

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If tests are worth 60% of your grade, and you have a 76.8% in that class, and you fail that test, what will be your grade?

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Answer:

Step-by-step explanation:

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3 years ago

- 30 = 12 – 6r Pls help

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Answer: r = 7

Step-by-step explanation:

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PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLIEST

Anna11 [10]

Using Pythagorean, a^2 + b^2 = c^2
16 +x^2 = 36.69
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And finally take the square root of that, giving you 4.87

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2 years ago

Four grey regular polygons join together as shown in the diagram please answer part b

Wittaler [7]

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2 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