Answer:
huh
Step-by-step explanation:
what does that mean
Part A
The four plastic sides comprises of two equal squares of area
![x^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20)
each and two equal rectangles of area
![xy](https://tex.z-dn.net/?f=xy)
each.
Given that t<span>he total area of the four plastic sides is to be
![1200in^2](https://tex.z-dn.net/?f=1200in%5E2)
, thus:
![2x^2+2xy=1200 \\ \\ \Rightarrow x^2+xy=600 \\ \\ \Rightarrow xy=600-x^2](https://tex.z-dn.net/?f=2x%5E2%2B2xy%3D1200%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%2Bxy%3D600%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20xy%3D600-x%5E2)
The volume of the figure is given by: Volume = Area of base x depth
![V=(xy)x=x(600-x^2)=600x-x^3](https://tex.z-dn.net/?f=V%3D%28xy%29x%3Dx%28600-x%5E2%29%3D600x-x%5E3)
Part B:
For maximum volume, the derivative of V with respect to x will equal 0.
![\frac{dV}{dx} =0 \\ \\ \Rightarrow600-3x^2=0 \\ \\ \Rightarrow3x^2=600 \\ \\ \Rightarrow x^2=200 \\ \\ \Rightarrow x=\pm \sqrt{200} =\pm14.14](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdx%7D%20%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow600-3x%5E2%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow3x%5E2%3D600%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%3D200%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%3D%5Cpm%20%5Csqrt%7B200%7D%20%3D%5Cpm14.14)
But dimensions has to be positive, thus the value of x which produces maximum volume is x = 14.14
Recall that
![xy=600-x \\ \\ \Rightarrow y= \frac{600}{x} -x \\ \\ = \frac{600}{14.14} -14.14 \\ \\ =42.43-14.14 \\ \\ =28.29](https://tex.z-dn.net/?f=xy%3D600-x%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20y%3D%20%5Cfrac%7B600%7D%7Bx%7D%20-x%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B600%7D%7B14.14%7D%20-14.14%20%5C%5C%20%20%5C%5C%20%3D42.43-14.14%20%5C%5C%20%20%5C%5C%20%3D28.29)
Therefore, the </span><span>dimensions that will maximize the volume of the shelter is x = 14.14 and y = 28.29</span>
for the first question you would want to to multiply 52*1.5 because 52 is the original price and 1.5 is the mark up. by multiplying these together you get 78. next you need to add the tax. For tax you should multiply 78*.1 (this answer is 7.8) and add the answer to 78, getting the total of 85.8. I really hope this helps :-)
Answer:
35
Step-by-step explanation:
Since the triangles are similar, we can write a ratio
25 ?
---- = -----
5 7
Using cross products
25*7 = 5 ?
Divide each side by 5
25*7/5 = 5?/5
35 = ?
What you have to do for this is to divide the total worth ($200,000.00) by the number of shares.
So this means that we need to count:
200 000 ÷4 000
here's a trick:
if you divide two numbers with many 0s at the end, you can always erase the SAME mount of 0s at the end (this is equivalent to dividing by 10).
so
200 000 ÷4 000
is equivalent to :
200 ÷4
which is 50! (4*50=200)
so the answer is that each share was worth 50 dollars.