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2 years ago

If 6:2:8:x, then a. 2x=14 b. 2x=48 c. 6x=10 d. 6x=16

Mathematics

1 answer:

Annette [7]2 years ago

3 0

Answer:

D) 6x=16

Step-by-step explanation:

6 : 2 = 8 : x

=> x = 8/(6/2 )

=> x = 8/3

=> 6x = (8/3) * 6 = 8 * 2 = 16

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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

Aldon and Jamal raised the same amount of money for the school fundraiser. Aldon

Naddika [18.5K]

Answer: $5

Step-by-step explanation: This can be represented by the equation

40 + 12T = 25 + 15T

We just solve for T.

Subtract 12T from both sides

40 = 25 + 3T Subtract 25

15 = 3T Divide by 3

5 = T

7 0

3 years ago

Write 10 5/12 as an equivalent improper fraction.

allochka39001 [22]

125/12 would be your equivalent improper fraction

3 0

2 years ago

Read 2 more answers

£99 is shared in the ratio 6 : 5 What is the larger share?

nordsb [41]

Answer:

Step-by-step explanation:

6x + 5x = 99

11x = 99

x=99/11

x=9

6x = 6x9 = 54

5x = 5x9 = 45

ans: 54

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2 years ago

If the market price for chair is $24 in the marginal cost for the chairs seven dollars the marginal revenue from the chair would

joja [24]

$17 (it's just the market price - the marginal cost)

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3 years ago