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ElenaW [278]
3 years ago
6

If the surface area of a cube is increased by a factor of 2 (so that the new surface area is twice the size of the original surf

ace area), by what factor does the volume of the cube change?
Mathematics
1 answer:
Mariana [72]3 years ago
8 0

Answer:2.828

Step-by-step explanation:

Given

Surface area of a cube is increased by a factor of 2

Let the original surface area be A

such that new surface area is 2A

for volume we need to know new radius

6(a')^2=2\times 6r^2

where r'=new radius

r=original radius

a'=\sqrt{2}a

New volume(V')=(a')^3=(\sqrt{2}a)^3

V'=2\sqrt{2}a^3

Original volume=a^3

\frac{V'}{V}=\frac{2\sqrt{2}a^3}{a^3}

V'=2\sqrt{2}V=2.828V

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X(x+3) + 34 = (x +5)(x+2)
My name is Ann [436]
X(x + 3) + 34 = (x + 5)(x + 2)

First, expand to remove parentheses. 
x^{2} + 3x + 34 =  x^{2} + 2x + 5x + 10
Second, add '2x + 5x' to get '7x'.
x^{2} + 3x + 34 =  x^{2}  + 7x + 10
Third, cancel out 'x^{2}' on both sides.
3x + 34 = 7x + 10
Fourth, subtract '3x' from both sides.
34 = 7x + 10 - 3x
Fifth, subtract '7x - 3x' to get '4x'.
34 = 4x + 10
Sixth, subtract '10' from both sides.
34 - 10 = 4x
Seventh, subtract '34 - 10' to get '24'.
24 = 4x
Eighth, divide both sides by '4', leaving the 'x' by itself.
\frac{24}{4} =x
Ninth, since '24 ÷ 4 = 6', simplify the fraction to '6'.
6 = x
Tenth, switch your sides to get the answer.
x = 6

Answer: x = 6

4 0
3 years ago
Find the general solution of the given differential equation. x2y' + xy = 8 y(x) = give the largest interval over which the gene
topjm [15]
x^2y'+xy=8
xy'+y=\dfrac8x
(xy)'=\dfrac8x\implies xy=8\ln|x|+C\implies y=\dfrac{8\ln|x|}x+\dfrac Cx

which wouldn't be a valid solution over any interval containing x=0.
5 0
3 years ago
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Kryger [21]
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5 0
3 years ago
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What is the surface area of the right rectangular prism?
Mkey [24]

Answer:

1) OPTION D.

2) OPTION D.

Step-by-step explanation:

1) You can calculate the surface area of the rectangular prism with the following formula:

SA=2(wh+lw+lh)

Where w is the width, h is height  and l is the length.

The figure show you that:

l=4m\\w=3m\\h=0.5

Then, the surface area is:

 SA=2[(3m*0.5m)+(4m*3m)+(4m*0.5m)]=31m^{2})

2) You can calculate volume of the rectangular prism with the following formula:

V=lwh

Where w is the width, h is height  and l is the length.

When you substitute values, you obtain the following result:

V=4m*3m*0.5m=6m^{3}

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4 years ago
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Which interval for the graphed function has a local minimum of 0?
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Answer:

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