What is the simplest form of x^4 y^7 / 3 square root x^10 y^4

Is the function even or odd?

sweet [91]

Answer:

$f(\theta)=\cos(\theta)$ is an even function.

Step-by-step explanation:

Recall when it means when a function is even or odd. An even function has the following property:

$f(-x)=f(x)$

And an odd function has the following property:

$f(-x)=-f(x)$

So, let's test some values for cos(x).

Let's use π/3:

$f(\pi/3)=\cos(\pi/3)$

From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).

Now, let's find -π/3. This is the same as 5π/3. Thus:

$f(-\pi/3)=\cos(-\pi/3)$

And again from the unit circle, we can see that this is 1/2.

Therefore, despite the negative, the function outputs the same value.

Cosine is an even function.

Notes:

Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!

6 0

3 years ago

1. If $18,000 is invested at 6% compounded monthly, what is the amount after 7 years?

stira [4]

P = 18,000
R=6%
T=7 years

A = P ( 1 + 1 divided by r) raised to n
Substitute the numbers an u will fin the answer

8 0

3 years ago

mix 2parts red with 3parts cream and 1part blue how much cream and blue paint do i need to mix with 4litres of red

vagabundo [1.1K]

The 4 litres of red has to be 2 parts of the mixture, so each part will be 2 litres. Therefore 3 parts of cream will be 6 litres and the one part of blue will be 2 litres.

7 0

3 years ago

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Translate ƒ(x) = |x| so that it's translated up by 5 units and vertically stretched by a factor of 3. What's the new function g(

zavuch27 [327]

Given:

The parent absolute function is

$f(x)=|x|$

To find:

The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.

Solution:

The translation is defined as

$g(x)=kf(x+a)+b$ .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

Parent function is translated up by 5 units. So, b=5

It is vertically stretched by a factor of 3. So, k=3.

There is no horizontal shift. So, a=0.

Now, putting k=3, a=0 and b=5 in (1), we get

$g(x)=3f(x+0)+5$

$g(x)=3f(x)+5$

$g(x)=3|x|+5$ $[\because f(x)=|x|]$

Therefore, the correct option is D.

5 0

3 years ago

The exact solution to the equation x^3 = 125 is +5 true or false

Natasha2012 [34]

Answer:

True

Step-by-step explanation:

5 0

3 years ago

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