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3 years ago

Cos(x/3)cos(x/3)=1/2(1+cos(2x/3))

Mathematics

2 answers:

TEA [102]3 years ago

6 0

This follows from the half-angle identity for cosine.

$\cos^2\theta=\dfrac{1+\cos2\theta}2$

aleksklad [387]3 years ago

4 0

Answer:

it's true, don't have a step by step explanation just did it on my test.

Step-by-step explanation:

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when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3><u>Solution:</u></h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = $a^2$

6 is subtracted from the square of a number = $a^2 - 6$

5 times the number = $5 \times a$

<em><u>So we can frame a equation as:</u></em>

6 is subtracted from the square of a number = 5 times the number

$a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0$

<em><u>Let us solve the above quadratic equation</u></em>

For a quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here in this problem,

$a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6$

Substituting the values in above quadratic formula, we get

$\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}$

We have two solutions for "a"

$\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}$

We have asked negative solution. So a = -1

Thus the negative solution is -1

6 0

3 years ago

What is the length of the hypotenuse of a right triangle with legs of length 6 and 4 ?

liberstina [14]

Answer:

6²+4²=h²

36+16=h²

$\sqrt{52} = h \: \: \: \: \: \\ hyphotenuse \: is \: 2 \sqrt{13 \:} \\ or \: 7.2111$

6 0

3 years ago

Figures are similar. Find x.

katrin [286]

Answer:

24.3

Step-by-step explanation:

18/20 = x/20 (similar triangles)

8 0

3 years ago

Browns department store is having a 1/4 off sale. How much would a shirt that regularly sells for 36.00 cost during the sale?

nadya68 [22]

Since the shirt is 25 percent off your paying for 75 percent of the shirt. 0.75(36) is 27. The shirt will cost 27.00

4 0

3 years ago

Subtract. –21 – (–13)<br> a. –34<br> b. –8<br> c. 8<br> d. 34

Angelina_Jolie [31]

-21 - (-13)

-21 + 13

= -8

The answer B)

6 0

3 years ago