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s2008m [1.1K]
3 years ago
8

I need to solve the equation please help me

Mathematics
1 answer:
lesantik [10]3 years ago
4 0

Answer:

\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

Step-by-step explanation:

We are given the equation:

4\sin^2(x)+6\sin(x)+2=0

First, we can divide everything by 2:

2\sin^2(x)+3\sin(x)+1=0

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

2u^2+3u+1=0

Solve for u. Factor:

(2u+1)(u+1)=0

Zero Product Property:

2u+1=0\text{ or } u+1=0

Solving for both cases:

\displaystyle u=-\frac{1}{2}\text{ or } u=-1

And by substitution:

\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

\displaystyle x=\frac{3\pi}{2}+2n\pi

All together, our solutions are:

\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

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The sum of all the ages of Dylan and Renee is 57 years . 9 yrs ago , Dylans age was 2 times Renee's age. How old is Dylan now?​
Ugo [173]

Answer:

Step-by-step explanation:

let present age of

Dylan=x

Renee=y

x+y=57

9 years ago

x-9=2(y-9)=2y-18

x=2y-18+9=2y-9

so  2y-9+y=57

3y=57+9=66

y=66/3=22

x+22=57

x=57-22=35

Dylan's present age=35 years

3 0
2 years ago
Alaina needs to sell 225 boxes in order to be the top seller. She sells thin mints and samoas to all of her customers for a tota
Digiron [165]

Answer:

94 boxes of samoas

131 boxes of thin mints

Step-by-step explanation:

m=mints

s=samoas

s+m=225    m=225-s

s(2.5)+m(3)=628

2.5s+3m=628

substitute for m

2.5s+3(225-s)=628

2.5s+675-3s=628

reduce

-0.5s=-47

s=94

m=131

4 0
3 years ago
If 1 kg of milk had 0.264 kg of fat, then find the amount fat in 12.5 kg of milk.<br>​
beks73 [17]

1 kg--> 0.264 kg fat

:. 12.5 kg--> (0.264*12.5) 3.3 kg fat

Mark me brainliesttt :))

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3 years ago
Solve for x (5x-3)/4 = x/3 + 1 and please show working out
Mila [183]
(5x-3)/4 = x/3 +1  
5x-3 = 4x/3 +4 
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(11/3)x = 7 
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4 0
3 years ago
The ordered pair (1, -2) is a solution to the system of linear equations.
vesna_86 [32]

Answer:

False

Step-by-step explanation:

2x + y = 0

Try (1, -2)

2(1) + (-2) = 0

2 + (-2) = 0

0 = 0

The solution works on the first equation.

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-1 - 4 = 5

-5 = 5

The solution does not work in the second equation.

Answer: False

3 0
3 years ago
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