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romanna [79]
3 years ago
5

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f

orm?
Mathematics
2 answers:
inysia [295]3 years ago
7 0
Volume of the cube with side 4p = 4p x 4p x 4p = 64p³

Volume of the cube with side 2q² =  2q² x  2q² x  2q² = 8q⁶

Total Volume = 64p³ +  8q⁶

Total Volume = (4p)³ + (2q²)³

Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)

Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)

 
Answer:  (4p + 2q²)( 16p² - 8pq² + 4q⁴)
seraphim [82]3 years ago
4 0

we know that

The volume of a cube is equal to

V=b^{3}

where

b is the length side of the cube

Step 1

Find the volume of the cube 1

we have

b=4p\ units

substitute in the formula

V1=(4p)^{3}=64p^{3}\ units^{3}

Step 2

Find the volume of the cube 2

we have

b=2q^{2}\ units

substitute in the formula

V2=(2q^{2})^{3}=8q^{6}\ units^{3}

Step 3

Find the total volume

Adds volume 1 and volume 2

V=64p^{3}\ units^{3}+8q^{6}\ units^{3}

V=(64p^{3}+8q^{6})\ units^{3}

Step 4

<u>Find the volume in factored form</u>

we know that

The sum of cubes is equal to

a^{3} +b^{3} =(a+b)(a^{2} -ab+b^{2})

a=4p\ units

b=2q^{2}\ units

substitute

(64p^{3}+8q^{6})=(4p+2q^{2})((4p)^{2}-(4p)(2q^{2})+(2q^{2})^{2}

=(4p+2q^{2})(16p^{2}-8pq^{2}+4q^{4})

therefore

<u>the answer is</u>

(4p+2q^{2})(16p^{2}-8pq^{2}+4q^{4})\ units^{3}


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Ella has 0.5 lb of sugar. how much water should she add to make the following concentrations? Tell Ella how much syrup she will
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Answer:

For 50% syrup, add 0.5 lb of water for 1 lb of syrup; for 5% syrup, add 9.5 lb of water for 10 lb of syrup; for 75% syrup, add 0.17 lb of water for 0.67 lb of syrup; for 1.5% syrup, add 32.8 lb of water for 33.3 lb of syrup.

Step-by-step explanation:

Let x represent the amount of water added.  This means the total mass of the syrup is represented by 0.5+x.

To find percentages, we divide the part by the whole.  For a 50% syrup, we need the part (sugar) compared to the whole (sugar + water) to equal 50%, or 0.50:

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Using the distributive property, we have

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Subtract 0.25 from each side:

0.5-0.25 = 0.25+0.5x-0.25

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Divide both sides by 0.5:

0.25/0.5 = 0.5x/0.5

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For 50% syrup, add 0.5 lb of water.  This makes the total mass 0.5+0.5 = 1 lb.

For 5% syrup, we change the equation to equal 0.05 (5% = 5/100 = 0.05) and leave everything else the same:

Multiply both sides by 0.5+x:

Using the distributive property,

0.5 = 0.05(0.5)+0.05(x)

0.5 = 0.025 + 0.05x

Subtract 0.025 from both sides:

0.5-0.025 = 0.025+0.05x-0.025

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Divide both sides by 0.05:

0.475/0.05 = 0.05x/0.05

x = 9.5

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For 75% syrup, set the equation equal to 0.75:

Using the distributive property,

0.5 = 0.75(0.5)+0.75(x)

0.5 = 0.375 + 0.75x

Subtract 0.375 from each side:

0.5 - 0.375 = 0.375 + 0.75x - 0.375

0.125 = 0.75x

Divide both sides by 0.75:

0.125/0.75 = 0.75x/0.75

0.17 = x

For 75% syrup, add 0.17 lb of water; the total mass is 0.17+0.5 = 0.67 lb.

For 1.5% syrup, set the equation equal to 0.015:

Using the distributive property,

0.5 = 0.015(0.5) + 0.015(x)

0.5 = 0.0075 + 0.015x

Subtract 0.0075 from each side:

0.5-0.0075 = 0.0075 + 0.015x - 0.0075

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Divide both sides by 0.015:

0.4925/0.015 = 0.015x/0.015

32.8 = x

For 1.5% syrup, use 32.8 lb of water; the total mass is 32.8+0.5 = 33.3 lb.

I hope this is right and have a good day

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Answer:

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Then, the distance covered by the car is 4x since was going 4 kph.

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We know that the total distance covered is 640 km.

Using this information, we can set up the equation 4x+7x+35=640.

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Answer:

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Step-by-step explanation:

Information given

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Solution to the problem

The margin of error is given by this formula:

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And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

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