Answer:
x = 18 cm
y = 9 cm
Step-by-step explanation:
An open-top box will have minimum surface area when it is in the shape of half a cube. The whole cube would have volume 2×2916 = 5832 cm³, so its side length would be ∛5832 cm = 18 cm.
The dimensions of the box are x = 18 cm; y = 9 cm.
__
The surface area is x^2 +4xy, where y = 2916/x^2. That is, the surface area is ...
S = x^2 +11664/x
Setting the derivative to zero, we find ...
dS/dx = 0 = 2x -11664/x^2
x^3 = 5832 . . . . . . . . may look familiar
x = ∛5832 = 18
y = 2916/18^2 = 9
In the question, it is already mentioned that the water tank holds = 24,000 gallons
In the given question it is also mentioned that the need is to find the time required to use 2/3 of the total water that the tank holds.
So the need is to find the amount of water that equals 2/3 of the total water in the tank.
Then
Quantity of water that needed to be used = [24000 * (2/3)] gallons
= 16000 gallons
In the problem it is also mentioned that the average rate of consumption per day is 650 gallons.
So
650 gallons of water used in = 24 hours
16000 gallons of water will be used in = [(24/650) *16000] hours
= 590.77 hours
So the time required to consume 2/3 of the total water in the tank is 590.77 hours.
Answer:
x=2√3
Step-by-step explanation:
Let's solve your equation step-by-step.
x2
3
=4
Step 1: Simplify both sides of the equation.
1
3
x2=4
Step 2: Divide both sides by 1/3.
1
3
x2
1
3
=
4
1
3
x2=12
Step 3: Take square root.
x=±√12
x=2√3 or x=−2√3
The equation is y = -3/6x + 3/2
Answer:
793 liters of washing fluid is needed
Step-by-step explanation:
step 1
Find the slant height of the triangular faces of pyramid
we know that
The lateral area of a square pyramid is equal to the area of its four triangular faces
so
![LA=4[\frac{1}{2}bl]](https://tex.z-dn.net/?f=LA%3D4%5B%5Cfrac%7B1%7D%7B2%7Dbl%5D)
where
b is the base of triangle (is the same that the length of the square base)
l is the slant height
To find out the slant height we need to apply the Pythagorean Theorem
so

we have


substitute



step 2
Find the lateral area of the pyramid
![LA=4[\frac{1}{2}bl]](https://tex.z-dn.net/?f=LA%3D4%5B%5Cfrac%7B1%7D%7B2%7Dbl%5D)
we have


substitute
![LA=4[\frac{1}{2}(35.42)(27.96)]](https://tex.z-dn.net/?f=LA%3D4%5B%5Cfrac%7B1%7D%7B2%7D%2835.42%29%2827.96%29%5D)

step 3
Find out how much window washing fluid is needed
we know that
2 L of washing fluid cover 5 square meters
so
using proportion

Round up
793 liters of washing fluid is needed