Which statement is true about the graph of the equation 2x + y

A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

3 years ago

Find the ratio in which the line segment joining - 2 - 3 and 5 and 6 is divided by x– axis

nexus9112 [7]

Answer:

x axis ?

Step-by-step explanation:

4 0

3 years ago

Please help me- thank you

Kruka [31]

Answer:

a) The profit will be: $Profit=y^2-99500$

b) Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

Step-by-step explanation:

Cost of Bicycles= $y^2+10y+100,000$

Revenue generated = $2y^2+10y+500$

Find a polynomial that represent profits

The formula used for finding profit is:

$Profit = Total \ Revenue - Total \ Cost\\Profit= 2y^2+10y+500 - (y^2+10y+100,000)\\Profit= 2y^2+10y+500 - y^2-10y-100,000\\Profit=2y^2-y^2+10y-10y+500-100,000\\Profit=y^2-99500$

So, the profit will be: $Profit=y^2-99500$

If the company can produce bicycles y= 300

The profit will be:

$Profit=y^2-99500\\Profit=(300)^2-99500\\Profit=90000-99500\\Profit=-9500$

Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

5 0

3 years ago

The effect of global climate change on the US economy was investigated by researchers at Carnegie Mellon University. To gauge th

AURORKA [14]

Answer:

Please see the attached file for the complete answer.

Step-by-step explanation:

Download pdf

4 0

3 years ago

Plz help Events A and B are independent. Let event A be the event that a person chooses and buys a certain pear from the grocery

kompoz [17]

Hi all

Answer:

I had this question on my MAP testing just today, and I answered with

C. Choosing a certain book does not affect the choice of a pear,

D. Choosing a certain pear does not affect the choice of a book.

These are the answers I think are correct.

7 0

3 years ago

Which statement is true about the graph of the equation 2x + y - 5 = 0?