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3 years ago

What happens to the volume of a rectangular prism when its length is tripled?

Mathematics

1 answer:

earnstyle [38]3 years ago

3 0

The volume of a rectangular prism is represented by the following equation:

$V=wlh$

where w is the width , l is the length, and h is the height

Replace $l$ with $3l$ since the length is tripled

$V_0=w(3l)h$

$=3(wlh)$

From this, we see that this new volume is 3x larger than the original. Thus, the volume is tripled when its length is tripled.

Let me know if you need any clarifications, thanks!

You might be interested in

Which function has zeros at x=-2 and x=5?

Licemer1 [7]

Answer:

$x^{2} - 3x - 10$

Step-by-step explanation:

To start, lets form our polynomial factors from our zeroes.

x = -2

x + 2 = 0

x = 5

x - 5 = 0

Now lets put these into factored form by moving them into parenthesis and multiplying them with each other!

(x+2)(x-5)

We can start moving them out! I am going to use FOIL, but you could also use distributive or any other method/property.

x · x = x²

x · -5 = -5x

x · 2 = 2x

2 · 5 = 10

Now lets put our terms into our polynomial function, based on the order of the powers.

$x^{2} - 3x - 10$

We are done! Hope this helps!

7 0

3 years ago

Write the equation of the line that includes the point (3,3) and has a slope of 2.

-Dominant- [34]

Answer:

y = 2x - 3

Step-by-step explanation:

We are given the slope, m = 2

Our standard formula of a line is y = mx + b, so we can substitute for the x and y values of the point (3, 3). If you did not know, the x-value and the y-value are both 3 because the point (3, 3) = (x, y).

So, our equation looks like this:

3 = (2)(3) + b

We can solve for b:

3 = 6 + b

b = -3

And now we have our equation of a line:

y = 2x - 3

7 0

3 years ago

Greatest Common Factor (GCF) 1. 12a - 27

Ilya [14]

Answer:

Step-by-step explanation:

The factors of 12a are ...

2×2×3×a

The factors of 27 are ...

3×3×3

The only common factor is 3.

_____

12a -27 = 3(4a -9)

8 0

3 years ago

This equation shows how the total number of pieces Lamar has learned depends on the number of weeks he has taken piano lessons.

Dominik [7]

Answer:

19 weeks

Step-by-step explanation:

Given equation:

P = w

Where,

w = the number of weeks he has taken piano lessons

p = the total number of pieces he has learned

how many weeks of piano lessons will Lamar need before he will be able to play a total of 19 pieces?

Find w when p = 19

P = w

p = 19

Since P = w

19 = w

Therefore,

w = 19

Lamar need 19 weeks before he will be able to play a total of 19 pieces

3 0

3 years ago

Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1]

Alekssandra [29.7K]

$\green{\large\underline{\sf{Solution-}}}$

Given expression is 

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

$\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

Hence, 

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

4 0

3 years ago