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3 years ago

Find the area on the interior of the solid lines

Mathematics

1 answer:

labwork [276]3 years ago

3 0

The total area of the rectangle would be 768.
The area of the the circle ( 2 semi circles added ) would be 452.16.
If you subtract these two areas you get your answer.
768-452.16=315.84
*The way pi is used can change the value of the decimal.*

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Two numbers have a difference of 24. What is the sum of their squares if it is a minimum?

seraphim [82]

Let "a" and "b" be some number where:

a - b = 24

We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.

So we can first substitute for "a" where a = b+24

So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576

Then we take the derivative and set it equal to zero:

4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12

Thus "a" must equal 12.

So:
a = 12
b = -12

And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.

The smallest sum is 288.

3 0

3 years ago

If the measure of angle is θ is 7pi/4 , which statements are true?

Hoochie [10]

Answer:

$\checkmark$ $\sin\theta=-\frac{\sqrt{2}}{2}$

$\checkmark$ $\tan \theta = -1$

$\checkmark$ The measure of the reference angle is $45^{\circ}$

Step-by-step explanation:

The reference angle of an angle is the magnitude of the smallest angle it makes with the x-axis. In this case, we have $360-315=\boxed{45^{\circ}}$ (*Note: $\frac{7\pi}{4}=315^{\circ}$ , use $\pi=180^{\circ}$ to convert to degrees)

8 0

3 years ago

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What is 25 times 4. Just Asking For My First Brainly Question

mash [69]

Answer: 100

Step-by-step explanation:

25*4 = 100

4 0

4 years ago

Read 2 more answers

Which statement describing this experiment is true?

Andru [333]

Answer:c

Step-by-step explanation:

4 0

3 years ago

13. Write

Bingel [31]

First off, we factor out the expression:

$\displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }$

In the bracket, separate 8 out of the expression.

$\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}$

In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

$\displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}$

So we add +9 in x^2-6x.

$\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}$

Convert the expression in the small bracket to perfect square.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}$

Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}$

Then we distribute 2 in.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\$

$\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }$

Remember that negative multiply positive = negative.

Hence the vertex form is y = 2(x-3)^2-2 or first choice.

4 0

3 years ago