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3 years ago

A point is refected across the x-axis. The new point is (5,-3.5).What is the distance between the two points?

1 answer:

5 0

When a point is reflected across the x-axis, it's y value is flipped. Here is a formula for your future reference:

X-axis reflection: (x,-y)

Using your given coordinates, you simply plug the numbers in, resulting in final coordinates of (5,3.5).

Because the problem asks for the distance between the two points, you now have to find the difference between -3.5 and 3.5, which is 7.

There you go; the distance between the points is 7 units.

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

3 0

3 years ago

I really need help with this question , can someone help me?

Alexxx [7]

I'm too late but here ya go anyway :)

x = 180 - (31 + 40) is the answer.

8 0

3 years ago

36^ - 1/2 Wich is equivalent? A -18<br> B -6<br> C- 1/18<br> D- 1/6

STatiana [176]

Answer:

3rd

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What is the domain of the square root function graphed below?

Nikolay [14]

The domain of a function is the set of all values x can have.
From the graph, we see the least value of x is 3. x can be any value greater than or equal to 3.

The domain is

$x \ge 3$

5 0

3 years ago

A fast typist can type 120 words in 100 seconds. At that rate, how many seconds would it take to type 258 words?

Alexeev081 [22]

Answer: 215 seconds

Step-by-step explanation:

This is a ratio problem so you can set up the ratio like this:

120 words : 100 second.

If you divide both sides of the ratio by 120 you get:

1 word: 0.8333 seconds

Multiply both sides of the ratio by 258 and you get:

258 words: 215 seconds.

Therefore typing 258 will take them 215 seconds.

5 0

3 years ago