Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.
A multiplicative inverse is the same thing as a reciprocal, which is basically just flipping the fraction and changing the sign. Therefore the multiplicative inverse of -1/9 is 9
The answer would be true because 4+5 is > 8
Answer:
The value of annuity is 
Step-by-step explanation:
From the question we are told that
The periodic payment is 
The interest rate is 
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is 
The value of the annuity is mathematically represented as
![P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=P_v%20%20%3D%20%20P%20%2A%20%20%5B1%20%20-%20%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7B-t%20%2A%20n%7D%20%5D%20%2A%20%5B%5Cfrac%7B%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
(reference EDUCBA website)
substituting values
![P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ]](https://tex.z-dn.net/?f=P_v%20%20%3D%20250%20%2A%20%20%5B1%20%20-%20%281%20%2B%20%5Cfrac%7B0.05%7D%7B4%7D%20%29%5E%7B-10%20%2A%204%7D%20%5D%20%2A%20%5B%5Cfrac%7B%281%20%2B%20%5Cfrac%7B0.05%7D%7B4%7D%20%29%7D%7B%20%5Cfrac%7B0.08%7D%7B4%7D%20%7D%20%5D)
![P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ]](https://tex.z-dn.net/?f=P_v%20%20%3D%20%20250%20%2A%20%20%5B1%20%20-%20%281.0125%20%29%5E%7B-40%7D%20%5D%20%2A%20%5B%5Cfrac%7B%281.0125%20%29%7D%7B0.0125%7D%20%5D)
![P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ]](https://tex.z-dn.net/?f=P_v%20%20%3D%20%20250%20%2A%20%20%5B0.3916%20%5D%20%2A%20%5B%5Cfrac%7B%281.0125%29%7D%7B0.0125%7D%20%5D)
Answer:
x = 70; the labeled angles are 110º and 70º.
Step-by-step explanation:
The full degrees will add up to 180º. There are 2x and +40.
Equation: 
Solve: 
Since x=70, 70+40 will equal to 110.
Therefore, "x = 70; the labeled angles are 110º and 70º." is correct.
