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3 years ago

PLEASE HELP!!!

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

D. 2 3 • 3 2 • 5

Step-by-step explanation:

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Solve the equation for all real values of x. cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

Step-by-step explanation:

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

Which expression correctly represents "twice the sum of four and a number"?

Lesechka [4]

Answer:

2(4+x)

Step-by-step explanation:

"Twice the sum of" tells us it will be the equation times two

"the sum of four and a number" is easy, thats 4 + x

The second number is x because the number is not specified so we need a place holder, x in this case, to tell us that the number is not given.

All this put together = twice the sum of four and a number, or 2(4+x)

7 0

3 years ago

The average of 11 numbers in a list is 14. If the average of 9 of the numbers in the list is 9, than what is the average of the

liberstina [14]

Total value of 11 numbers
14*11
154

Total value of 9 numbers
9*9
81

Total value of other 2 numbers
154 - 81
73

So average of other 2 numbers
73 / 2
36.5

3 0

3 years ago

4/5w-12=2/3w what is the step by step answer to those equation?

Mariulka [41]

Kulay, there is no such thing as a "step by step answer" here. You seem to want a "step by step solution."

I must assume that by 4/5 you actually meant (4/5) and that by 2/3 you meant (2/3). Then your equation becomes:

(4/5)w - 12 = (2/3)w.

The LCD here is 5*3, or 15, so mult. every term by 15:

12w - 180 = 10w.
Add 180 to both sides, obtaining 12 w - 180 + 180 = 10w + 180.

Then 12w = 10w + 180. Simplifying, 2w = 180. What is w?

4 0

3 years ago

suppose you have a coupon for 20% discount you buy a game that costs $38 the sales tax rate is 5.5% sales tax applies to the cos

Lostsunrise [7]

$32.072 ≈ $32.07
20% of $38 is equal to $7.60
$38 - $7.60 = $30.40
5.5% of $30.40 = 1.672
$30.40 + $1.672 = $32.072

6 0

3 years ago

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