Answer:
x=4+√23 , 4-√23
Step-by-step explanation:
x^2-4x=4x+7
x^2-8x-7=0
now solving from quadratic equation
x=4+√23 , 4-√23
Expand the left side using the angle sum identity for sine:
sin(<em>x</em> + <em>π</em>/2) = sin(<em>x</em>) cos(<em>π</em>/2) + cos(<em>x</em>) sin(<em>π</em>/2)
cos(<em>π</em>/2) = 0 and sin(<em>π</em>/2) = 1, so the right side reduces to
sin(<em>x</em> + <em>π</em>/2) = cos(<em>x</em>)
as required.
Standard Equation for trig function: y = A cos (B (x - H))+ K
*Here, we are just dealing with A (amplitude) and B (period)
Period = 2π/ b
8 = 2π/ b
Solve for b: 2π/8 or π/4
Equation: y = 2 cos (π/4 (x))
Annual interest is P*r^t, r is 0.05 here, t is 9/12=3/4=0.75
P*0.05^0.75=120
use your calculaor: P= 120÷ (0.05)^0.75=1135
so he invested about 1135 dollars
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