Answer:
3(5 +6) = <em>33</em>
Step-by-step explanation:
3(5+6)
so first you multiply 3 by 5
which is 15
then you multiply 3 by 6
which is 18
and that remains as 15+18
which in total equals <em>33</em>
Answer: 2
Step-by-step explanation:
The mode is the number that is shown the most.
T=-1
sinA=sin(π/2-3A), A=2nπ+π/2-3A, 4A=2nπ+π/2, A=nπ/2+π/8 where n is an integer.
Also, π-A=2nπ+π/2-3A, 2A=2nπ-π/2, A=nπ-π/4.
The hard way:
cos3A=cos(2A+A)=cos(2A)cosA-sin(2A)sinA.
Let s=sinA and c=cosA, then s²+c²=1.
cos3A=(2c²-1)c-2c(1-c²)=c(4c²-3).
s=c(4c²-3) is the original equation.
Let t=tanA=s/c, then c²=1/(1+t²).
t=4c²-3=4/(1+t²)-3=(4-3-3t²)/(1+t²)=(1-3t²)/(1+t²).
So t+t³=1-3t², t³+3t²+t-1=0=(t+1)(t²+2t-1).
So t=-1 is a solution.
t²+2t-1=0 is a solution, t²+2t+1-1-1=0=(t+1)²-2, so t=-1+√2 and t=-1-√2 are solutions.
Therefore tanA=-1, -1+√2, -1-√2 are the three solutions from which:
A=-π/4, π/8, -3π/8 radians and these values +2πn where n is an integer.
Replacing π by 180° converts the solutions to degrees.
This can be done in two ways
One method is to check the answer options in both f(x) and g(x) and select the one that matches for both.
The second is to form a quadratic equation and solving as such:
f(x) = g(x)
-x² + 4x + 12 = x + 8
x² - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4; x = -1
Only x = 4 is given in the options, so the answer is B
