Answer:
x = 28,000
Step-by-step explanation:
"What" is our unknown, x; "is" is an equals sign; 70% expressed as a decimal is .70; "of" means to muliply.
Our equation, then, is
x = .70(40,000) so
x = 28,000
Check the picture below.
now, you can pretty much count the units off the grid for the segments ST and RU, so each is 7 units long, and are parallel, meaning that the other two segments are also parallel, and therefore the same length each.
so we can just find the length for hmmmm say SR, since SR = TU, TU is the same length,
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{-5}~,~\stackrel{y_2}{5})\qquad \qquad % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ SR=\sqrt{[-5-(-2)]^2+[5-1]^2}\implies SR=\sqrt{(-5+2)^2+(5-1)^2} \\\\\\ SR=\sqrt{(-3)^2+4^2}\implies SR=\sqrt{25}\implies SR=5](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0AS%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%0AR%28%5Cstackrel%7Bx_2%7D%7B-5%7D~%2C~%5Cstackrel%7By_2%7D%7B5%7D%29%5Cqquad%20%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%5B-5-%28-2%29%5D%5E2%2B%5B5-1%5D%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B%28-5%2B2%29%5E2%2B%285-1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%28-3%29%5E2%2B4%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B25%7D%5Cimplies%20SR%3D5)
sum all segments up, and that's perimeter.
Answer:
A. 14x14x28
B. The maximum volume is 5488 cuibic inches
Step-by-step explanation:
The problem states that the box has square ends, so you can express volume with:
![v=x^{2} y](https://tex.z-dn.net/?f=v%3Dx%5E%7B2%7D%20y)
Using the restriction stated in the problem to get another equation you can substitute in the one above:
![4x+y=84\\\\](https://tex.z-dn.net/?f=4x%2By%3D84%5C%5C%5C%5C)
Substituting <em>y</em> whit this equation gives:
![v=x^{2} (84-4x)\\\\v=84x^{2} -4x^{3}](https://tex.z-dn.net/?f=v%3Dx%5E%7B2%7D%20%2884-4x%29%5C%5C%5C%5Cv%3D84x%5E%7B2%7D%20-4x%5E%7B3%7D)
Now find the limit of <em>x</em>:
![\frac{84x^{2}-4x^{3}}{dx}=168x-12x^{2}\\\\x=\frac{168}{12}=14](https://tex.z-dn.net/?f=%5Cfrac%7B84x%5E%7B2%7D-4x%5E%7B3%7D%7D%7Bdx%7D%3D168x-12x%5E%7B2%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B168%7D%7B12%7D%3D14)
Find the length:
![y=84-4(14)=28](https://tex.z-dn.net/?f=y%3D84-4%2814%29%3D28)
You can now calculate the maximum volume:
![v=(14)^{2}(28)= 5488](https://tex.z-dn.net/?f=v%3D%2814%29%5E%7B2%7D%2828%29%3D%205488)
First of all, the identity property of multiplication (which is what this is I'm assuming) is that the number 1 multiplied by any other number is that number itself. (An example would be 2 multiplied by 1, which would be two) So in this problem, this rule applies too, since 2/3 multiplied by 1 would be 2/3!
Hope this helped :)