(1/4)^3z-1=16^z+2x 64^z-2

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 2916cm3. Deter

aleksklad [387]

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

4 0

3 years ago

a water tank holds 24,000 gallons. how many hours will it take for 2/3 of the water to be used if the water is used at an averag

Likurg_2 [28]

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.

8 0

4 years ago

If x^2/3 = 4, what is x^2

nikklg [1K]

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

5 0

3 years ago

Find the equation of the line that passes through (-5,4) and (1,1)

pav-90 [236]

The equation is y = -3/6x + 3/2

5 0

3 years ago

A written explanation solving the question how much fluid is needed using the Pythagorean method and finding the area of the tri

Alecsey [184]

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

$LA=4[\frac{1}{2}bl]$

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

$l^2=(b/2)^2+h^2$

we have

$b=35.42\ m$

$h=21.64\ m$

substitute

$l^2=(35.42/2)^2+21.64^2$

$l^2=781.9337$

$l=27.96\ m$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bl]$

we have

$l=27.96\ m$

$b=35.42\ m$

substitute

$LA=4[\frac{1}{2}(35.42)(27.96)]$

$LA=1,980.6864\ m^2$

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

$\frac{2}{5}\ \frac{L}{m^2}=\frac{x}{1,980.6864}\ \frac{L}{m^2}\\\\x=1,980.6864(2)/5\\\\x= 792.27\ L$

Round up

793 liters of washing fluid is needed

6 0

3 years ago