Aannsswweerr: -3/4-7b
Step-by-step explanation: I smart for a 3yrs old kid. And I don't even need a diAper but my 17 yrs old sister does so she weirdo...
HEY, I also have good news. I JUST GOT POTY TRANED!! YA Boi.
My sis told me she was on her period but then I told her there was this thing called subject and predicate and how she isnt supposed to have a period at the end of her statement because it wouldnt make any sense... and ya, it didnt go well cause' she put on a tantrum.
But the weird thing is that Google said this "Tantrums are most common between the ages of one and four, then decrease when children start school." SO HOW COME I DIDN"T HABE A TANTRUM and SHE HAD ONE!!.. life makes no sense
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of ![\dfrac{d }{dx}(V)=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%20%7D%7Bdx%7D%28V%29%3D0)
![\dfrac{d}{dx}(99x^2-4x^3) =0](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%2899x%5E2-4x%5E3%29%20%3D0)
⇒ 198x - 12x² = 0
![12x \Big({\dfrac{33}{2}-x}}\Big)=0](https://tex.z-dn.net/?f=12x%20%5CBig%28%7B%5Cdfrac%7B33%7D%7B2%7D-x%7D%7D%5CBig%29%3D0)
By solving for x:
x = 0 or x = ![\dfrac{33}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B33%7D%7B2%7D)
Again:
V = 99x² - 4x³
![\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdx%7D%3D%20198x%20-12x%5E2%20%5C%5C%20%5C%5C%20%5Cdfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%3D198%20-24x)
At x = ![\dfrac{33}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B33%7D%7B2%7D)
![\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%5CBig%7C_%7Bx%3D%20%5Cfrac%7B33%7D%7B2%7D%7D%3D198%20-24%28%5Cdfrac%7B33%7D%7B2%7D%29)
![\implies 198 - 12 \times 33](https://tex.z-dn.net/?f=%5Cimplies%20198%20-%2012%20%5Ctimes%2033)
= -198
Thus, at maximum value;
![\dfrac{d^2V}{dx^2}\le 0](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%5Cle%200)
Recall y = 99 - 4x
when at maximum x = ![\dfrac{33}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B33%7D%7B2%7D)
![y = 99 - 4(\dfrac{33}{2})](https://tex.z-dn.net/?f=y%20%3D%2099%20-%204%28%5Cdfrac%7B33%7D%7B2%7D%29)
y = 33
Finally; the volume V = x² y is;
![V = (\dfrac{33}{2})^2 \times 33](https://tex.z-dn.net/?f=V%20%3D%20%28%5Cdfrac%7B33%7D%7B2%7D%29%5E2%20%5Ctimes%2033)
![V =272.25 \times 33](https://tex.z-dn.net/?f=V%20%3D272.25%20%5Ctimes%2033)
V = 8984.25 inches³
Answer:
f = 1
Step-by-step explanation:
The price of the fries would be $2.50, the price of the drink would be $2.50, and the price of the cheeseburger wold be $7.50.
We can write a set of equations to represent the prices, if 'f' is fries, 'd' is drink, and 'c' is cheeseburger:
c = 3f
f = d
Using these equations, we can then write out the sum of the items also, as it would be c + f + d = 12.50, but as we know that c = 3f and d = f, we can write it as 3f + f + f = 12.50, and then solve:
3f + f + f = 12.50
5f = 12.50
÷ 5
f = $2.50
Now that we know the price of the fries, we know that the price of the drink is the same, so the drink is also $2.50. Then, we can multiply 2.50 by 3 as we know that the cheeseburger is 3 times the cost of the fries, and 2.50 × 3 = 7.50.
I hope this helps!
Answer:
So the vectors are linearly independent.
Step-by-step explanation:
So if they are linearly independent then the following scalars in will have the condition a=b=c=0:
a(2,3,1)+b(2,-5,-3)+c(-3,8,-5)=(0,0,0).
We have three equations:
2a+2b-3c=0
3a-5b+8c=0
1a-3b-5c=0
Multiply last equation by -2:
2a+2b-3c=0
3a-5b+8c=0
-2a+6b+10c=0
Add equation 1 and 3:
0a+8b+7c=0
3a-5b+8c=0
-2a+6b+10c=0
Divide equation 3 by 2:
0a+8b+7c=0
3a-5b+8c=0
-a+3b+2c=0
Multiply equation 3 by 3:
0a+8b+7c=0
3a-5b+8c=0
-3a+9b+6c=0
Add equation 2 and 3:
0a+8b+7c=0
3a-5b+8c=0
0a+4b+13c=0
Multiply equation 3 by -2:
0a+8b+7c=0
3a-5b+8c=0
0a-8b-26c=0
Add equation 1 and 3:
0a+0b-19c=0
3a-5b+8c=0
0a-8b-26c=0
The first equation tells us -19c=0 which implies c=0.
If c=0 we have from the second and third equation:
3a-5b=0
0a-8b=0
0a-8b=0
0-8b=0
-8b=0 implies b=0
We have b=0 and c=0.
So what is a?
3a-5b=0 where b=0
3a-5(0)=0
3a-0=0
3a=0 implies a=0
So we have a=b=c=0.
So the vectors are linearly independent.