Determine the quadrant adding or subtracting periods -10pi/3+2pi=-4pi/3+2pi=2pi/3
which is the second quadrant because
first quadrant is between 0 and pi/2
second quadrant is between pi/2 and pi
third quadrant is between pi and 3pi/2
fourth is between 3pi/2 and 2pi
now we find the terminal angle since it is the second quadrant we use theta'=pi-theta=pi-2pi/3=pi/3
sin(pi/3)=sqrt(3)/2 sin is positive in the second quadrant
cos(pi/3)=-0.5 cos is negative in the second quadrant
tan(pi/3)=sin(pi/3)/cos(pi/3)=-sqrt(3) tan is negative in the second quadrant
Answer:
1/5.
Explanation:
Note that the sum of infinite geometric series is equally to: a/ (1 - r). Where a = first term and r is the common ratio.
Hence, if f(x) = 3/(1 - 5x) ^2. Therefore, taking the another derivative of f(x)` = 30/ (1 - 5x)^3.
Also, f(x)`` = 450/ ( 1 - 5 )^4 and f(x)``` = 9000( 1 - 5x)^5 and f(x)```` = 225000/( 1 - 5x)^6.
If we are to use the Taylor's series formula then;
F(0) + f'(0) + f"(0)/2! × x^2 + f'''(0)/3! × x^3.
[ NOTE: f(0) = 3, f''(0) = 30, f'''(0) = 9000, f''''(0) = 225000].
450/2! = 225, 9000/ 3! = 1500 and 225000/4! = 9375..
Which gives; 3 + 30x + 225x^2 + 1500x^3 + 9375x^4. The ratio test will then give us our answer as 1/5.
As stated above, alternatively we can make use of the sum of geometric series where |x| < 1/5
To solve this problem, we must set up a system of equations. In this case, let's let Maggie's age be represented by the variable m and her brother's age be represented by the variable b. We are told that the sum of their ages is 24, which gives us our first equation: m + b = 24. We can construct our next equation from the first sentence of given information: b = 2m - 3. This makes our system of equations:
m + b = 24
b = 2m - 3
To solve, we are going to substitute the value for b in terms of m given by the second equation into the first equation for the variable b.
m + b = 24
m + 2m - 3 = 24
To simplify, we must first combine the variable terms on the left side of the equation using addition.
3m - 3 = 24
Next, we should add 3 to both sides of the equation to get the variable term alone on the left side of the equation.
3m = 27
Finally, we should divide both sides by 3 in order to get the variable m alone.
m = 9
Therefore, Maggie is 9 years old (using the first equation and substituting in this value you can find that her brother is 15 years old).
Hope this helps!
