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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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10.1022 rounded to the nearest hundredth​
ivanzaharov [21]

Answer:

10.10

Step-by-step explanation:

4 0
3 years ago
Help plz find the equation​
tatiyna

                                              Question # 1

Step-by-step Explanation:

Given

\frac{1}{2}\div \frac{2}{3}

solving

\frac{1}{2}\div \frac{2}{3}

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}

=\frac{1}{2}\times \frac{3}{2}

\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}

=\frac{1\times \:3}{2\times \:2}

\mathrm{Multiply\:the\:numbers:}\:1\times \:3=3

=\frac{3}{2\times \:2}

\mathrm{Multiply\:the\:numbers:}\:2\times \:2=4

=\frac{3}{4}

Therefore, completing the blanks:

\frac{1}{2}\div \frac{2}{3}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}

                                             Question # 3

Step-by-step Explanation:

Given

\frac{2}{5}\div \frac{3}{4}

solving

\frac{2}{5}\div \frac{3}{4}

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}

=\frac{2}{5}\times \frac{4}{3}

\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}

=\frac{2\times \:4}{5\times \:3}

\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8

=\frac{8}{5\times \:3}

\mathrm{Multiply\:the\:numbers:}\:5\times \:3=15

=\frac{8}{15}

Therefore, completing the blanks:

\frac{2}{5}\div \frac{3}{4}=\frac{2}{5}\times \:\frac{4}{3}=\frac{8}{15}

                                                Question # 5

Step-by-step Explanation:

Given

\frac{3}{4}\div \frac{5}{7}

solving

\frac{3}{4}\div \frac{5}{7}

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}

=\frac{3}{4}\times \frac{7}{5}

\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}

=\frac{3\times \:7}{4\times \:5}

\mathrm{Multiply\:the\:numbers:}\:3\times \:7=21

=\frac{21}{4\times \:5}

\mathrm{Multiply\:the\:numbers:}\:4\times \:5=20

=\frac{21}{20}

Therefore, completing the blanks:

\frac{3}{4}\div \frac{5}{7}=\frac{3}{4}\times \:\frac{7}{5}=\frac{21}{20}

6 0
3 years ago
Elena has some bottles of water that each hold 17 fluid ounces.
Svet_ta [14]

Answer:

17b = w

Step-by-step explanation:

17 times the number of bottles = the number of ounces of water

Then you just plug in the numbers you are given

17(51) = w

17 x 51 = 867

<u>51 bottles of water holds 867 ounces</u>

<u />

17b = (51)

divide both sides by 17

51/17 = 3

b = 3

<u>It would take 3 bottles of water to hold 51 ounces</u>

6 0
2 years ago
Evaluate 12.7 - x for x= 8.41
agasfer [191]

Answer:

x=  

10

429

​  

 

​  

≈2.071231518

x=−  

10

429

​  

 

​  

≈−2.071231518

Step-by-step explanation:

12.7−xx=8.41

Multiply x and x to get x  

2

.

12.7−x  

2

=8.41

Subtract 12.7 from both sides.

−x  

2

=8.41−12.7

Subtract 12.7 from 8.41 to get −4.29.

−x  

2

=−4.29

Divide both sides by −1.

x  

2

=  

−1

−4.29

​  

 

Expand  

−1

−4.29

​  

≈4.29 by multiplying both numerator and the denominator by 100.

x  

2

=  

−100

−429

​  

 

Fraction  

−100

−429

​  

≈4.29 can be simplified to  

100

429

​  

=4.29 by removing the negative sign from both the numerator and the denominator.

x  

2

=  

100

429

​  

 

Take the square root of both sides of the equation.

x=  

10

429

​  

 

​  

 

x=−  

10

429

​  

 

​  

 

3 0
3 years ago
Read 2 more answers
Find the product of 2 and (3.7 × 10^-4)
Blizzard [7]

Answer:

74000

Step-by-step explanation:

1.      10^-4=10000

2.      10000*3.7=37000

3.      37000*2=74000

8 0
3 years ago
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