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3 years ago

Find the domain of the graphed function!

Mathematics

1 answer:

ArbitrLikvidat [17]3 years ago

8 0

Answer:

Step-by-step explanation:

you can see that the graph only extends from 2 to 5, and because of the closed circles you know its ≤ not < for the signs

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If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

Question 8 is the one I’m having trouble on it

salantis [7]

Just multiply 30 times 2,000 and also multiply 30 times 700. The reason you will multiply it by 30 is because in 1 month there is 30 days. 30 x 2,000= 60000 30 x 700 = 21000 I’m only 9 btw so sorry if I didn’t give a lot of detail lol

4 0

3 years ago

Madison earned $80 last month pet sitting in her

xeze [42]

Answer:

Step-by-step explanation:

Subtract

4 0

3 years ago

Read 2 more answers

Please explain how to divide 1,344 by 24 using the box method? I know the answer is 56, but I am not sure how to get this answer

Maslowich

Answer:

Step-by-step explanation:

Given that divisor is 24 and dividend is 1344 and we are to use box method.

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Box Method, or the Area Model, is one of these strategies. It is a mental math based approach that will enhance number sense understanding. Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible.

For example this method is shown below:

I step is to find in multiples of 10 or 100 the greatest divisor

24) 1344( 500

1200

--------

144

Step 2: Next step is to divide 144 by 24

24)144( 6

144

----

Thus we find that quotient is quotient in I step + quotient in 2nd step

= 50+6 = 56

and remainder is zero.

7 0

3 years ago

What is 12/21 divided by 3/14

sladkih [1.3K]

To do this problem, you gotta cross-multiply. SO, $\frac{12}{21}$ multiplied by $\frac{14}{3}$

12 times 14 = 168
21 times 3 = 63
Then the final answer is $\frac{168}{3}$

5 0

3 years ago