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3 years ago

Solve: sin2x cosx + cos 2x sin x = √3/2 for 0

Mathematics

1 answer:

artcher [175]3 years ago

5 0

Answer:

$x=\frac{\pi }{9}+\frac{2k\pi }{3} ,\frac{2\pi }{9}+\frac{2k\pi }{3}$

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The maximum value of 12 sin 0-9 sin²0 is: -

jeka57 [31]

Answer:

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be $\theta$ rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

$f(\theta) = 12sin(\theta) - 9 sin^2(\theta)$

Taking the first derivative of this with respect to $\theta$ and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of $f(\theta)$ w.r.t $\theta$ is

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)$

And setting this = 0 gives

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0$

Eliminating $cos(\theta)$ on both sides and solving for $sin(\theta)$ gives us

$sin(\theta) = \frac{12}{18} = \frac{2}{3}$

Plugging this value of $sin(\theta)$ into the original equation gives us

$12(\frac{2}{3}) - 9(\frac{4}{9} ) = 8 - 4 = 4$

This is the maximum value that the function can acquire. The attached graph shows this as correct

3 0

2 years ago

IS THIS CORRECT?! I HAVE A BACK SIDE TOO, IF ANYTHING IS WRONG PLS PLS LMK!!

Fudgin [204]

The only error you made is on problem 3. Everything else is correct. Nice work.

-------------------------------------------------------

Here is how to solve problem 3

Plug x = 1 into the equation and solve for y

-3x + y = 1

-3*1 + y = 1 ... replace x with 1

-3 + y = 1

y - 3 = 1

y - 3 + 3 = 1 + 3 .... add 3 to both sides

y = 4

<h3>The answer is 4</h3>

-------------------------------------------------------

Verifying the answer:

Plug (x,y) = (1,4) into the equation. Both sides should be the same number after simplifying both sides.

-3x + y = 1

-3*1 + 4 = 1 ..... replace x with 1; replace y with 4

-3 + 4 = 1

1 = 1

The answer is confirmed.

If you were to graph -3x + y = 1, which is equivalent to y = 3x+1, you'll find that the point (1,4) is on this line.

4 0

3 years ago

How many digits are written when 1000 to the power of 2015 is expressed as a numeral?

PtichkaEL [24]

Answer: There are 6046 digits will be written on expansion upto 2015th power.

Step-by-step explanation:

Since we have given that

$1000^{2015}$

We have to find the number of digits ,

So,

$1000^{2015}\\\\=(10^3)^{2015}\\\\=10^{6045}$

Since we know that

$10^n\text{ has n+1 number of digits }$

so,

$10^{6045}\text{ has 6046 number of digits }$

Hence, there are 6046 digits will be written on expansion upto 2015th power.

6 0

3 years ago

What are two solutions of 3 + 4 |x/2 + 3| = 11?

Alex

3 + 4abs(x/2 + 3) = 11 Subtract 3
4 abs(x/2 + 3) = 11 - 3
4 abs(x/2 + 3) = 8 Divide by 4
abs(x/2 + 3) = 8/4
abs(x/2 + 3) = 2

Solution 1
x/2 + 3 = 2 Subtract 3
x/2 = 2 - 3
x/2 = - 1 Multiply by 2
x/2 *2 = - 2
x = - 2

Solution 2
x/2 + 3 = - 2
x/2 = - 2 - 3
x/2 = - 5 Multiply by 2
x = -5 * 2
x = -10

Solutions
x = - 2 <<<< answer 1
x = -10 <<<< answer 2

3 0

4 years ago

What percent of 630 is 270

Tatiana [17]

I don't Clearly understand your question but I think it is 0.428571

8 0

3 years ago