Question

Solve 2sin(x)=3−4cos(x) for the first 2 positive solutions.

Answer #1

1. Solve sin(x)= √2/2 over the interval [0,2π).
2. Solve 4cos(x)+1=3 over the interval [0,2π).
3. Solve cos^2(x)+6=7 over the interval [0,2π).
4. How many solutions are there for the equation
4cos(x)+5=6 over the interval [0,2π).

Find the first two positive solutions to the system of 3
congruence equations x ≡ 3 (mod 9) x ≡ 9 (mod 12) x ≡ 7 (mod 22)
(notice how the m1, m2, m3 are not co-prime!)

PLEASE SOLVE ALL 8 QUESTIONS SHOWING STEP-BY-STEP
SOLUTIONS.
Solve for the unknown variable on the interval 0 is (less than
or equal to) x (less than or equal to) 2pi.
1. 4 cos^2 x - 3 =0
2. Square root of 2 sin 2x = 1
3. 3cot^2 x-1 = 0
4. cos^3 x = cos x
5. sin x - 2sin x cos x = 0
6. 2sin^2 x- sin x-3 = 0
7. csc^2 x- csc x -...

For the following exercises, find all exact solutions on [0,
2π)
23. sec(x)sin(x) − 2sin(x) = 0
25. 2cos^2 t + cos(t) = 1
31. 8sin^2 (x) + 6sin(x) + 1 = 0
32. 2cos(π/5 θ) = √3

Evaluate the integral ∫x^2cos(3x)dx..
Select one:
a. 1/3x^2sin(3x)+2/27sin(3x)−2/9xcos(3x)+C
1/3x^2sin(3x)+2/27sin(3x)−2/9xcos(3x)+C
b. 1/3x^2sin(3x)−2/27sin(3x)+2/9xcos(3x)+C
13x^2sin(3x)−2/27sin(3x)+2/9xcos(3x)+C
c. x/2sin(x)−2/9sin(x)+2/3xcos(x)+C
x^2sin(x)−2/9sin(x)+2/3xcos(x)+C
d. x^2sin(x)+2/9sin(x)−2/3xcos(x)+C

Solve the following equations algebraically. Be sure to check
for extraneous solutions.
A). (9^2x)(1/3)^(x+2) = 27(3^x)^-2
B). 3^x+4 = 2^1-3x
C). log base 3(x-2) + log base 3 (x-4) =2

a.
find all possible EXACT solutions for 2sin (3x) + sqrt3 = 0
b. find all exact solutions of 3cos(2x) + 5sin(x)=-1 on
[0,2pi)

Solve for x. Discard extraneous solutions.
Please show the steps!
log(x) = 2 − log(x − 21)
2 log(x) − log(7x − 1) = 0
log_4 (3x − 2) − log_4 (4x + 1) = 2
log3 (x 2 − 6x) = 3
log(x − 2) − log(2x − 3) = log(2)

1. Consider the function f(x) whose second derivative is
f″(x)=10x+2sin(x). If f(0)=2 and f′(0)=3, what is f(x)?

Solve the system of equations. Find all solutions. 5x + 7y = 31
x 2 + y 2 = 13

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