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1 year ago

What will the new demensions of the rectangle below be after a dilation within scale factor of 9\4

Mathematics

1 answer:

timurjin [86]1 year ago

3 0

Answer

The new dimensions of the rectangle after dilation by scale factor of (9/4) include

New length = 72 feet

New width = 18 feet

Explanation

The relationship between new length, original length and scale factor of dilation is given as

New length = (Original length) × (Scale factor)

For this question,

Scale factor = (9/4)

Original length = 32 feet

New length = (Original length) × (Scale factor)

New length = 32 × (9/4) = 72 feet

New width = (Original width) × (Scale factor)

Original width = 8 feet

Scale factor = (9/4)

New width = (Original width) × (Scale factor)

New width = 8 × (9/4) = 18 feet

Hope this Helps!!!

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2 years ago

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2 years ago

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X - the number of questions he answered correctly
y - the number of questions he answered incorrectly

There were 40 questions on the test.
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3 years ago

Given LaTeX: f\left(x\right)=x^{^3}-3x+4f ( x ) = x 3 − 3 x + 4, determine the intervals where the function is increasing and wh

Vedmedyk [2.9K]

Answer:

Increasing: $x$ and $x>1$ .

Decreasing: $-1$

Step-by-step explanation:

We have been given a function $f(x)=x^3-3x+4$ . We are asked to determine the intervals, where the function is increasing and where it is decreasing.

First of all, we will find critical points of our given function by equating derivative of our given function to 0.

Let us find derivative of our given function.

$f'(x)=\frac{d}{dx}(x^3)-\frac{d}{dx}(3x)+\frac{d}{dx}(4)$

$f'(x)=3x^{3-1}-3+0$

$f'(x)=3x^{2}-3$

Let us equate derivative with 0 as find critical points as:

$0=3x^{2}-3$

$3x^{2}=3$

Divide both sides by 3:

$x^{2}=1$

Now we will take square-root of both sides as:

$\sqrt{x^{2}}=\pm\sqrt{1}$

$x=\pm 1$

$x=-1,1$

We know that these critical points will divide number line into three intervals. One from negative infinity to -1, 2nd -1 to 1 and 3rd 1 to positive infinity.

Now we will check one number from each interval. If derivative of the point is greater than 0, then function is increasing, if derivative of the point is less than 0, then function is decreasing.

We will check -2 from our 1st interval.

$f'(-2)=3(-2)^{2}-3=3(4)-3=12-3=9$