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3 years ago

The sum of three consecutive numbers is 3072. What are the three numbers?

Mathematics

1 answer:

inn [45]3 years ago

6 0

Answer:

1023, 1024, 1025

Step-by-step explanation:

i just took 3072 and divided it by 3 to get 1024 and then i subtracted one from the first number and added 2 onto the last number

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

IceJOKER [234]

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

<u>Step-by-step explanation:</u>

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

How do you solve this?

liberstina [14]

Answer:

The answer is

Step-by-step explanation:

To solve the expression , use the rules of indices

Since the bases are the same and are multiplying we add the exponents

That's

<h3> ${a}^{x} \times {a}^{y} \times {a}^{z} = {a}^{x + y + z}$ </h3>

So we have

We have the final answer as

Hope this helps you

3 0

4 years ago

What is 9365+643-9433+7.99999 repeating

nika2105 [10]

It is 780.99999 sorry if i'm incorrect

5 0

4 years ago

PLEASE HELP Geometry

iogann1982 [59]

It is c vtrbvrvrrvbtbtebtvyvvuubiii

6 0

4 years ago

these cards are put int a bag. One card is chosen at random. (1,2,3,4,5,6,7,8,9,10) a.) what is the probability of choosing the

Rama09 [41]

Answer:

There are 10 cards in total.

The probability of choosing card with the number 4 is 1/10.

The probability of choosing card with the number 1 is 2/10 = 1/5 (since there are 2 cards with the digit 1 - 1, 10)

5 0

4 years ago

Read 2 more answers