Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer is 7950,72. You can solve it's task on calculator.
Assuming that the pool was drained at a constant rate, the speed at which it was drained can be expressed as a function of time. In this case, the pool level will be expressed in feet per hour.
The time changed by 4 hours (6-2), and the level of the pool changed by -8 feet (2-10). Diving the feet by the hours to get the rate of decreasing depth, we find that the rate equals -2 feet/hour.
The percent of the purchase price for Julio’s down payment was C. 18%
<h3>What is Interest Rate?</h3>
This refers to the amount of money that is added to a loan collected by a person, for when he makes repayment.
Hence,
Given that
- PMT monthly payment 1558.09
- R interest rate 0.05875
- K compounded monthly 12 because the payment is monthly
- N time 20 years
- Pv present value?
We use the formula Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv= 1,558.09×((1−(1+0.05875÷12)^(−12×20))÷(0.05875÷12))
=219,684.92
Next thing to do is make a subtraction to get the down payment:
267,900−219,684.92=48,215.08
Then the percentage would be:
48,215.08÷267,900= 18% approx.
Read more about interest rates here:
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