Ummmmm 923,000?that's my best guess
sinx-✓(1-3sin2x)=0
-✓(1-3sin2x)=-sinx
apply squared both sides
(-✓(1-3sin2x)^2=(-sinx)^2
1-3sin2x=sin2x
collect like terms
-3sin2x-sin2x+1=0
-4sin2x+1=0
-4sin2x=-1
devide both sides by -4
sin2x=-1/-4
sin2x=0.25
sinx*sinx =0.25
[sinx]^2 = 0.25
apply square root both sides
<h2>✓(sinx)2 = ✓0.25</h2>
<h2>sinx=0.5</h2><h2> </h2><h2>x=sin^-(0.5)</h2>
<h2>x=30°</h2>
<h3>check quadrant where sin is positive, sin is +ve in second quandrant</h3>
180-x= Theta(X)
180-30=X
X=150°
therefore, all angles for sinx -✓(1-3sin2x)=0 are (X= 30° and 150°)
Answer:
Part 1.
Juice = 8 L.
Lemonade = 32 L.
Part 2.
20 L punch Josie can make.
Part 3.
New ratio juice : lemonade = 2 : 9
Step-by-step explanation:
Part 1.
1+4 = 5 parts altogether, 1 parts for juice and 4 parts for lemonade.
40 : 5 = 8 L is 1 part.
Juice - 1 part - 8 L.
Lemonade - 4 parts - 4*8 = 32 L.
Part 2.
1 parts of juice needs 4 parts of lemonade
4 L of juice needs x L of lemonade
1 : 4 = 4 : x
x = 4*4/1 = 16 L lemonade
4+ 16 = 20 L punch Josie can make
Part 3.
It was 4 L of juice and 16 L of lemonade.
After 2 L lemonade was added, we have 4 L of juice and (16+2) = 18 L of lemonade.
4 L juice : 18 L lemonade = 4/2 L juice : 18/2 L lemonade =
= 2 L juice: 9L lemonade
New ratio juice : lemonade = 2 : 9