Answer:
2500000
Step-by-step explanation:
50^3*20=2,500,000
Hope this helps!
~Animaljamissofab ♥
Lan wants to run less than 7/12 miles. It says to find out a fraction with a denominator of 4 and which is less than 7/12.
Let's assume the required fraction to be x/4 such that x/4 is less than 7/12.
![\frac{x}{4} < \frac{7}{12} \\\\ 3*\frac{x}{4} < \frac{7}{12}*3 \\\\ \frac{3x}{4} < \frac{21}{12} \\\\ \frac{3x}{4} < \frac{7}{4} \\\\ 3x < 7](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%7D%20%3C%20%5Cfrac%7B7%7D%7B12%7D%20%5C%5C%5C%5C%203%2A%5Cfrac%7Bx%7D%7B4%7D%20%3C%20%5Cfrac%7B7%7D%7B12%7D%2A3%20%5C%5C%5C%5C%20%5Cfrac%7B3x%7D%7B4%7D%20%3C%20%5Cfrac%7B21%7D%7B12%7D%20%5C%5C%5C%5C%20%5Cfrac%7B3x%7D%7B4%7D%20%3C%20%5Cfrac%7B7%7D%7B4%7D%20%5C%5C%5C%5C%203x%20%3C%207%20)
So we must have multiples of 3's that should be less than 7, we have only two choices 3 < 7 or 6 < 7.
It means x = 1 or x = 2, and the required fraction would be 1/4 or 2/4.
2/4 is simplified to 1/2 and the question says to have denominator 4.
Hence, final answer is 1/4
![g(x) = x^2 - 2 \text{ is even function }](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20-%202%20%5Ctext%7B%20is%20even%20function%20%7D)
<em><u>Solution:</u></em>
Given that,
![g(x) = x^2 - 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20-%202)
We have to find whether the above function is odd or even
If a function is: y = f(x)
If f(-x) = f(x), the function is even
If f(-x) = - f(x), the function is odd
Which is,
![\mathrm{Even\:Function:\:\:A\:function\:is\:even\:if\:}f\left(-x\right)=f\left(x\right)\mathrm{\:for\:all\:}x\in \mathbb{R}\\\\\mathrm{Odd\:Function:\:\:A\:function\:is\:odd\:if\:}f\left(-x\right)=-f\left(x\right)\mathrm{\:for\:all\:}x\in \mathbb{R}](https://tex.z-dn.net/?f=%5Cmathrm%7BEven%5C%3AFunction%3A%5C%3A%5C%3AA%5C%3Afunction%5C%3Ais%5C%3Aeven%5C%3Aif%5C%3A%7Df%5Cleft%28-x%5Cright%29%3Df%5Cleft%28x%5Cright%29%5Cmathrm%7B%5C%3Afor%5C%3Aall%5C%3A%7Dx%5Cin%20%5Cmathbb%7BR%7D%5C%5C%5C%5C%5Cmathrm%7BOdd%5C%3AFunction%3A%5C%3A%5C%3AA%5C%3Afunction%5C%3Ais%5C%3Aodd%5C%3Aif%5C%3A%7Df%5Cleft%28-x%5Cright%29%3D-f%5Cleft%28x%5Cright%29%5Cmathrm%7B%5C%3Afor%5C%3Aall%5C%3A%7Dx%5Cin%20%5Cmathbb%7BR%7D)
From given,
![g(x) = x^2 - 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20-%202)
Replace x with -x
![g(-x) = (-x)^2 - 2\\\\g(-x) = x^2 - 2](https://tex.z-dn.net/?f=g%28-x%29%20%3D%20%28-x%29%5E2%20-%202%5C%5C%5C%5Cg%28-x%29%20%3D%20x%5E2%20-%202)
Therefore,
![g(x) = g(-x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20g%28-x%29)
Thus the function g(x) is even
Answer:
1/6
Step-by-step explanation:
since 31/6 is 5 1/6