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3 years ago

A rectangular prism has a volume of 24 in³. For a school project, Sharon applies a scale factor of 3 to the prism.

Mathematics

1 answer:

siniylev [52]3 years ago

6 0

Answer:

The volume ratio of the enlarged prism to the original prism is equal to

$27$

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-----> the volume of the enlarged prism

y-----> the volume of the original prism

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

we have

$z=3$

$y=24\ in^{3}$

substitute

$3^{3}=\frac{x}{24}$

$x=(27)(24)=648\ in^{3}$ -----> volume of the enlarged prism

the volume ratio of the enlarged prism to the original prism is equal to

$3^{3}=27$

Verify

$\frac{648}{24}=27$ -----> is correct

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3 years ago

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Answer:

option 4

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ = $\sqrt{ab}$

Given

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= 6 $\sqrt{2}$ - 15 $\sqrt{12}$

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4 years ago

The graph of f '(x) is continuous and decreasing with an x-intercept at x = 2. Which of the following statements must be true? (

bixtya [17]

Answer:

The graph of f is always concave down ⇒ the first answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Remember that : If f(x) is a function then the solutions to the

equation f′(x) = 0 gives the maximum and minimum values to f(x)

- The value of x gives maximum if f′′(x) is negative and minimum if

f′′(x) is positive.

- Inflection points of the function f(x) are found the solutions of the

equation f′′(x) = 0

* Lets solve the problem

- The graph of f'(x) is continuous means that the graph is unbroken line

- The graph of f'(x) decreasing with an x-intercept at x = 2 means

f'(2) = 0

- The differentiation of a function equal to zero at the critical point

(minimum or maximum) of the function

∵ f'(x) = 0 at x = 2

∴ The x-coordinate of the critical point of f(x) is 2

- If the differentiation of the function is decreasing, then the critical

point of the function is maximum point

∵ f'(x) is decreasing

∴ The critical point of the f(x) is maximum point

- That means the slope of curve is negative

∴ The graph of f is concave down at x = 2

* The right answer is the graph of f is always concave down

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3 years ago

Gem and her three friends are going on a holiday. There is a buy 2 get one free offer on plane tickets. Tickets cost £600 each.

VLD [36.1K]

Answer: £450

Step-by-step explanation:

If they bought 2 tickets, they could get an extra ticket for free. As there are three of them, they would buy 2 tickets, get one for free and then buy another ticket to make it four.

In that case they would have only paid for 3 tickets.

The total cost of 3 tickets is:

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= £1,800

The 4 of them would therefore have to pay:

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3 years ago