4 sin^2 θ + 13cos^2 θ = 7
sin^2 θ = 1 - cos^ θ
4 - 4cos^2 θ + 13cos^2 θ = 7
9cos^2 θ = 3
cos^2 θ = 1/3
cos θ = # (1/3) # - square root
Square root of (1/3) has +1/3 and -1/3 as values of cos
Find the key angle by doing the cos inverse of #1/3
K.A = cos^-1 #(1/3) = 0.955
θ lies in all 4 quadrants
The values of θ are:
θ = 0.955, 2.186, 4.096, 7.23
Ignore 0.955, 2.186, 4.096, 7.23 as they are out of range pi/2 = 1.571
The the value of θ = 0.955 = 0.96 (to 2 d.p) radian
Hope it helped!
Basically, ur just solving for y
6x + 4y = 8...subtract 6x from both sides
4y = -6x + 8....now divide both sides by 4
y = (-6/4)x + 8/4...reduce
y = -3/2x + 2 <=== slope intercept form
$1.40+$1.60=$3
$180-$3=$177
Her mother added $177 to her piggy bank
He will only need approximately 118 cartons
Hope this helps!
