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2 years ago

Which explanation justifies how the area of a sector of a circle is derived?.

Mathematics

1 answer:

kifflom [539]2 years ago

7 0

Step-by-step explanation:

We know the area of a circle is

$\pi {r}^{2}$

That is when the cricle is 360 degrees full, so another formula is

$\frac{360}{360} \pi {r}^{2}$

If we the find the area of the sector with angle x, then that formula will be

$\frac{x}{360} {\pi}r^{2}$

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Can anyone help me with this question 9 2/3 think you to who ever help me

Whitepunk [10]

Answer:

29/3

Step-by-step explanation:

Cauze 3 × 9 + 2 = 29/3

The denominater will be the same

8 0

3 years ago

Read 2 more answers

Michael cuts a piece of wood for a project. The first cut is shown and can be represented by the equation . The second cut needs

Verdich [7]

Short Answer: A
Remark
The second cut is going to have the same slope as the original line. The lines are parallel.

Step One
You need to find the slope. That is the main part of this problem. You can pick any 2 points on the graph to do that.

Point one
(- 11, 10) That point is on the upper left of the line

Point Two
The y intercept is a handy point in this question. It is right on the y axis. Each square counts as 2, so it is at (0,6)

Formula
slope = m = (y2 - y1) / (x2 - x1)

Givens
y2 = 10
y1 = 6
x2 = -12 Each square counts as 2 in the x direction.
x1 = 0

Substitute and solve.
m = (10 - 6) / (-12 - 0)
m = 4/ - 12
m = - 1/3

Step Two
Find the y intercept of the new line using the given point.

So far what we have is
y = (-1/3)x + b
The point used for the second line is (0,-2)
-2 = (-1/3)*0 + b
b = - 2

Answer
The second line is
y = (-1/3)x - 2

8 0

4 years ago

HELP FAST WILL GIVE BRAINLIEST AND 5 STARS ALSO 30 POINTS!

xeze [42]

The answer is A because the diagram shows

6 0

3 years ago

Find cot and cos If sec = -3 and sin 0 > 0

Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given $\displaystyle \large{\sec \theta = -3}$ and $\displaystyle \large{\sin \theta > 0}$ . What we have to find are $\displaystyle \large{\cot \theta}$ and $\displaystyle \large{\cos \theta}$ .

First, convert $\displaystyle \large{\sec \theta}$ to $\displaystyle \large{\frac{1}{\cos \theta}}$ via trigonometric identity. That gives us a new equation in form of $\displaystyle \large{\cos \theta}$ :

$\displaystyle \large{\frac{1}{\cos \theta} = -3}$

Multiply $\displaystyle \large{\cos \theta}$ both sides to get rid of the denominator.

$\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}$

Then divide both sides by -3 to get $\displaystyle \large{\cos \theta}$ .

Hence, $\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}$

__________________________________________________________

Next, to find $\displaystyle \large{\cot \theta}$ , convert it to $\displaystyle \large{\frac{1}{\tan \theta}}$ via trigonometric identity. Then we have to convert $\displaystyle \large{\tan \theta}$ to $\displaystyle \large{\frac{\sin \theta}{\cos \theta}}$ via another trigonometric identity. That gives us:

$\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}$

It seems that we do not know what $\displaystyle \large{\sin \theta}$ is but we can find it by using the identity $\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}$ for $\displaystyle \large{\sin \theta > 0}$ .

From $\displaystyle \large{\cos \theta = -\frac{1}{3}}$ then $\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}$ .

Therefore:

$\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}$

Then use the surd property to evaluate the square root.

Hence, $\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}$

Now that we know what $\displaystyle \large{\sin \theta}$ is. We can evaluate $\displaystyle \large{\frac{\cos \theta}{\sin \theta}}$ which is another form or identity of $\displaystyle \large{\cot \theta}$ .

From the boxed values of $\displaystyle \large{\cos \theta}$ and $\displaystyle \large{\sin \theta}$ :-

$\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}$

Then rationalize the value by multiplying both numerator and denominator with the denominator.

$\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}$

Hence, $\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}$

Therefore, the second choice is the answer.

__________________________________________________________

Summary

Trigonometric Identity

$\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}$

Surd Property

$\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}$

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

5 0

2 years ago

Find the perimeter of the triangle. Please help! That one is 2x+5 if you cannot see.

Paul [167]

2x3x5=30
3 is from the amount of sides in the triangle

6 0

4 years ago