Around 70-80 depending on how many people I’m texting
Let the square base of the container be of side s inches and the height of the container be h inches, then
Surface are of the container, A = s^2 + 4sh
For minimum surface area, dA / ds + dA / dh = 0
i.e. 2s + 4h + 4s = 0
6s + 4h = 0
s = -2/3 h
But, volume of container = 62.5 in cubed
i.e. s^2 x h = 62.5
(-2/3 h)^2 x h = 62.5
4/9 h^2 x h = 62.5
4/9 h^3 = 62.5
h^3 = 62.5 x 9/4 = 140.625
h = cube root of (140.625) = 5.2 inches
s = 2/3 h = 3.47
Therefore, the dimensions of the square base of the container is 3.47 inches and the height is 5.2 inches.
The minimum surface area = s^2 + 4sh = (3.47)^2 + 4(3.47)(5.2) = 12.02 + 72.11 = 84.13 square inches.
Answer: Andre picked 252 pounds of apples
Step-by-step explanation:
Let x = number of pounds of apple picked by Jane.
Let y = number of pounds of apple picked by Andre
Let z = number of pounds of apple picked by Maria
Andre picks three times as many pounds as maria. It means that
y = 3z
Jane picks two times as many pounds as Andre. It means that
x = 2y
The total weight of the apples is 840 pounds. It means that
x + y + z = 840 - - - - - - - - - 1
We will substitute z = y/3 and x = 2y into equation 1
2y + y + y/3 = 840
Cross multiplying with 3
6y + 3y + y = 2520
10y = 2520
y = 2520/10 = 252
x = 2y = 252× 2 = 504
z = y/3 = 252/3 = 84
The solution to the problem is as follows:
x^3-x^2 +x -1= x^2(x-1) +(x-1)=(x-1)(x^2+1) ,(common factor x-1
<span>
(x^2-1)=(x-1)(x+1) </span>
<span>
LCM=(x-1)(x^2+1)(x+1) </span>
<span>
=(x^2-1)(x^2+1)=x^4-1
I hope my answer has come to your help. God bless and have a nice day ahead!
</span>
The ODE is exact, since


so there is solution
such that


Integrating both sides of the first PDE wrt
gives

Differentiating both sides wrt
gives


Then the solution to the ODE is

# # #
Alternatively, we can see that the ODE is homogeneous, since replacing
and
reduces to the same ODE:



This tells us we can solve by substituting
, so that
, and the ODE becomes



which is separable as

Integrating both sides gives


and solving in terms of
,


