Y =4
if you replaced y with 4 the equation would be true...
it's easy math
- hope you have a nice day...
Answer:
A) 10, 013/6
Step-by-step explanation:
The given arithmetic sequence {an } = {5/6 n + 2/3}
We need to find the 62th term, so plug in n = 62 in the above sequence, we get
S62 = { ![\frac{5}{6} .62 + \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D%20.62%20%2B%20%5Cfrac%7B2%7D%7B3%7D)
= {310/6 + 2/3}
= {155/3 + 2/3}
= (155 + 2)/3
S62 = 157/3
Now let's find the first term.
S1 = [5/6 (1) + 2/3]
S1 = [5/6 + 2/3]
S1 = (5 + 4)/6
S1 = 9/6
s1 = 3/2
The sum of the terms S62 = 62(3/2 + 157/3) divided by 2
= 31(9 + 314)/6
= 31(323)/6
= 10, 013/6
So the answer is A)10,013/6
Thank you.
Answer:
97%
Step-by-step explanation:
100% - 3% = 97%
Hope this helps :)
Answer:
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:
![V = l * b * h](https://tex.z-dn.net/?f=V%20%3D%20l%20%2A%20b%20%2A%20h)
Make h the subject of the formula
![h = \frac{V}{lb}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7Blb%7D)
The surface area (S) of the aquarium is:
![S = lb + 2(lh + bh)](https://tex.z-dn.net/?f=S%20%3D%20lb%20%2B%202%28lh%20%2B%20bh%29)
Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:
![C = 7 * lb + 1 * 2(lh + bh)](https://tex.z-dn.net/?f=C%20%3D%207%20%2A%20lb%20%2B%201%20%2A%202%28lh%20%2B%20bh%29)
![C = 7lb + 2(lh + bh)](https://tex.z-dn.net/?f=C%20%3D%207lb%20%2B%202%28lh%20%2B%20bh%29)
![C = 7lb + 2h(l + b)](https://tex.z-dn.net/?f=C%20%3D%207lb%20%2B%202h%28l%20%2B%20b%29)
Substitute
for h in the above equation
![C = 7lb + 2*\frac{V}{lb}(l + b)](https://tex.z-dn.net/?f=C%20%3D%207lb%20%2B%202%2A%5Cfrac%7BV%7D%7Blb%7D%28l%20%2B%20b%29)
![C = 7lb + \frac{2V}{lb}(l + b)](https://tex.z-dn.net/?f=C%20%3D%207lb%20%2B%20%5Cfrac%7B2V%7D%7Blb%7D%28l%20%2B%20b%29)
![C = 7lb + \frac{2V}{b} + \frac{2V}{l}](https://tex.z-dn.net/?f=C%20%3D%207lb%20%2B%20%5Cfrac%7B2V%7D%7Bb%7D%20%2B%20%5Cfrac%7B2V%7D%7Bl%7D)
Differentiate with respect to l and with respect to b
![=0](https://tex.z-dn.net/?f=%3D0)
![=0](https://tex.z-dn.net/?f=%3D0)
To solve for b and l, we equate both equations and set l to b (to minimize the cost)
![7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}](https://tex.z-dn.net/?f=7b%20-%20%5Cfrac%7B2V%7D%7Bl%5E2%7D%3D7l%20-%20%5Cfrac%7B2V%7D%7Bb%5E2%7D)
![7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}](https://tex.z-dn.net/?f=7l%20-%20%5Cfrac%7B2V%7D%7Bl%5E2%7D%3D7b%20-%20%5Cfrac%7B2V%7D%7Bb%5E2%7D)
By comparison:
![l =b](https://tex.z-dn.net/?f=l%20%3Db)
becomes
![7l = \frac{2V}{l^2}](https://tex.z-dn.net/?f=7l%20%3D%20%5Cfrac%7B2V%7D%7Bl%5E2%7D)
Cross Multiply
![7l^3 = 2V](https://tex.z-dn.net/?f=7l%5E3%20%3D%202V)
Solve for l
![l^3 = \frac{2V}{7}](https://tex.z-dn.net/?f=l%5E3%20%3D%20%5Cfrac%7B2V%7D%7B7%7D)
![l = \sqrt[3]{\frac{2V}{7}}](https://tex.z-dn.net/?f=l%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D)
Recall that: ![l =b](https://tex.z-dn.net/?f=l%20%3Db)
![b = \sqrt[3]{\frac{2V}{7}}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D)
Also recall that:
![h = \frac{V}{lb}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7Blb%7D)
![h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D%2A%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D%7D)
![h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B4V%5E2%7D%7B49%7D%7D%7D)
Apply law of indices
![h = \sqrt[3]{\frac{49V^3}{4V^2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%5E3%7D%7B4V%5E2%7D%7D)
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)
The dimension that minimizes the cost of material of the aquarium is:
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)