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3 years ago

What are the sides of a rectangular prism increased by if the volume increases from 54 mm3 to 3456 mm3?

Mathematics

1 answer:

kotykmax [81]3 years ago

6 0

Answer:

The sides of the original rectangular prism have been increased by a scale factor of 4

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x---> volume of the increased rectangular prism

y---> volume of the original rectangular prism

$z^{3}=\frac{x}{y}$

substitute

$z^{3}=\frac{3,456}{54}=64$

$z=4$ -----> the scale factor

therefore

The sides of the original rectangular prism have been increased by a scale factor of 4

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Which system of equations could be graphed to solve the equation below? log Subscript 0. 5 Baseline x = log Subscript 3 Baseline

Vanyuwa [196]

You can use the fact that two expressions in equality can be considered to be equal to a third variable(not used in given context).

The system of equations that could be graphed to solve the equation given is

$y = \log_{0.5}(x)\\\\$
$y = \log_3(2+x)$

<h3>How can we form a system of equations from an equation?</h3>

Suppose the equation be $a = b\\$

Let there is a symbol $c$ such that we have $a = b = c$

It is because a and b are same measure (that is exactly what a = b means)

and we gave another name c to that measure.

Thus, we have

$a = c\\b = c$

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<h3>Using the above method to find the system of equations needed</h3>

Since the given equation is $log_{0.5}(x) = log_2(2+x)$

The 2d graphs are usually expressed as $y = f(x)$ on X-Y plane.

Taking the equation's expressions equal to y, we get

$log_{0.5}(x) = log_2(2+x) = y$

or, we get system of equations as

$y = log_{0.5}(x)\\\\y = log_3{(2 + x)}$

Their graph is plotted below. The intersection point of both curves is the solution to the given equation as it satisfies both the equations of the system of equations formed from the given equation.

Thus,

The system of equations that could be graphed to solve the equation given is

$y = \log_{0.5}(x)\\\\$
$y = \log_3(2+x)$

Learn more about solutions to system of equations here:

brainly.com/question/14550337

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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