Answer:
x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.
Step-by-step explanation:
V= x^2y = 500
Surface area A = x^2 + 4xy.
From the first equation y = 500/x^2
So substituting for y in the equation for the surface area:
A = x^2 + 4x * 500/x^2
A = x^2 + 2000/x
Finding the derivative:
dA/dx = 2x - 2000x^-2
dA/dx = 2x - 2000/x^2
This = 0 for a minimum/maximum value of A, so
2x - 2000/x^2 = 0
2x^3 - 2000 = 0
x^3 = 2000/ 2 = 1000
x = 10
Second derivative is 2 + 4000/x^3
when x = 10 this is positive so x = 10 gives a minimum value of A.
So y = 500/x^2
= 500/100
= 5.
If you would like to know the solution to the system of equations, you can do this using the following steps:
y = –5x + 3
<span>y = 1
</span>_______________
1 =<span> –5x + 3</span>
5x = 3 - 1
5x = 2 /5
x = 2/5 = 0.4
(x, y) = (0.4, 1)
The correct result would be (0.4, 1<span>).</span>
Answer:
$1,800
Step-by-step explanation:
If Mo pays 1/2 of the rent then he is paying 50%. Charlie is paying another 25%. This leaves the remaining 25% that Andy pays. Since Andy's payment amount is 450 then that means that 450 is equal to 25% of the total rent. Therefore, we simply need to multiply this amount by 4 to get the 100% of the overall rent.
450 * 4 = $1,800
Finally, we can see that the total rent amount is $1,800
-4/3+1/3y I hope thats right
Answer:
Step-by-step explanation:
Amount of kool - aid that the pitcher can hold = 
gallons
There are 6 smaller containers in which this kool - aid is to be adjusted.
Also, the volume of the smaller containers is equal to each other i.e. the containers are identical to each other in terms of volume.
To find:
The amount of kool - aid that each container can hold?
Solution:
Volume of all the smaller containers combined = Volume of the kool - aid available
Let the volume of one smaller container = 
of kool - aid is the amount that each smaller can hold.
