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3 years ago

Show sin^2xcos^2x=(1-cos4x)/9

1 answer:

8 0

Did you mean sin^2xcos^2x=(1-cos4x)/8?

Because I have my solution here to that problem:

sin²(x)*cos²(x) = 1/8*(1-cos(4x))

[sin(2x)/2]² = 1/8*(1-cos(4x)) 

sin²(2x)/4 = 1/8*(1-cos(4x)) 

Recall that sin²(x) = (1-cos(2x))/2 

From this, we can tell that sin²(2x) = 1-cos(4x)/2 

[(1-cos(4x)/2]/4 = 1/8*(1-cos(4x)) 

(1-cos(4x))/8 = (1-cos(4x))/8

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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Please help! solve the equation

Lesechka [4]

1. 10
2. 2
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3 0

3 years ago

Find the 10th term of the following geometric sequence. 2, 10, 50, 250, ...

defon

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

8 0

3 years ago

Write the quadratic function in the form g(x)=a (x-h)2 +kThen, give the vertex of its graph. G(x) =2x2 +20x+49Writing in the for

Snezhnost [94]

The quadratic function given to us is:

$g(x)=2x^2+20x+49$

We are asked to find the vertex form of the function.

The general formula for the vertex form of a quadratic equation is:

$\begin{gathered} g(x)=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}$

In order to write the function in its vertex form, we need to perform a couple of operations on the function.

1. Add and subtract the square of the half of the coefficient of x to the function.

2. Factor out the function with its repeated roots and re-write the equation.

Now, let us solve.

1. Add and subtract the square of the half of the coefficient of x to the function.

$\begin{gathered} g(x)=2x^2+20x+49=2(x^2+10x+\frac{49}{2}) \\ \text{half of coefficient of x:} \\ \frac{10}{2}=5 \\ \text{square of the half of the coefficient of x:} \\ 5^2=25 \\ \\ \therefore g(x)=2(x^2+10x+25-25+\frac{49}{2}) \end{gathered}$

2. Factor out the function with its repeated roots and re-write the equation.

$\begin{gathered} g(x)=2(x^2+10x+25)-2(25+\frac{49}{2}) \\ re-\text{write the above function} \\ g(x)=2(x^2+10x+25)-1 \\ \text{Let us factorize this:} \\ g(x)=2(x+5)^2-1 \end{gathered}$

Therefore, we can conclude that the Equation and vertex of the equation is:

$\begin{gathered} Equation\colon g(x)=2(x+5)^2-1 \\ \\ Vertex\colon(-5,-1) \end{gathered}$

5 0

1 year ago

Please help me, i will give brainiest !!

BARSIC [14]

Answer:

If Cora runs 1/2 mile per week and x is the number of weeks, then she will run 5+1/2x. Then determine how many weeks are in two and a half months (depends on which month it is as there are less weeks in February than in January!) but we could estimate 6.

For Hana, you will have 3+ 3/4 x

Step-by-step explanation:

First equation is y=5+1/2 x and then plug 6 in for x to solve for y. the second equation is y=3+3/4x and plug in 6.

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Answer:

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Step-by-step explanation:

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3 years ago

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