How much lower was the 6am temperature in Juneau than in Los Angeles

I need to solve the equation please help me

lesantik [10]

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:

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

4 0

2 years ago

Can u help me with the whole page

hram777 [196]

10. he owes more than
11. she spent $55, she is $55 in debt
12. yes. -12 and 12 have the same absolute value, they ate both the same distance from 0
13. yes
14. not the opposite but the inverse

6 0

2 years ago

The inequality 94 – 3 log2x ≤ 88 describes noise exposure level (in decibels) in terms of the number of hours, x, it takes to re

Damm [24]

Answer:

4

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the product? Assume

morpeh [17]

What the person said

6 0

2 years ago

0.66666667 as a fraction

Ierofanga [76]

Answer:

__________________________________________

The correct answer is: " $\frac{2}{3}$ " .

__________________________________________

Note: Let's assume that this given decimal value is really:

"0.66666666666666666....." ;

(non-terminating; but repeating the singing digit, "7" ; yet rounded to:

" 0.66666667 " ;

then: " 0.666... " = $\frac{666}{999}$ ;

= (666 ÷ 111) / (999 ÷ 111) ;

= 6/9 ;

= (6÷3)/(9÷3) ;

= 2/3 ;

= " $\frac{2}{3}$ "

→ which is our answer.

____________________________________________

Or: " 0.6666... " = 666 ÷ 999 = ? ;

using calculator :

= 0.66666667 ;

→ which is the "rounded off" number of "0.6666..." ;

— (infinitely repeating) ;

→ So 666 ÷ 999 =

→ " $\frac{666}{999}$ " ;

= " $\frac{2}{3}$ " ;

→ Either use a "fraction calculator" ;

or simplify as aforementioned.

____________________________________________

Hope this answer is helpful to you!

Best wishes to you in your academic pursuits

— and within the "Brainly" community!

____________________________________________

7 0

2 years ago

Read 2 more answers