Question

Number Theory: Please show all work.

Solve each of the following equations for the unknown variable X ≡ 0, 1, 2, 3, 4, 5, 6 mod 7.

(i) 2X + 5 ≡ 6 mod 7.

(ii) 3X + 5 ≡ 6 mod 7.

Answer #1

For each part, find all possible solutions to the given
equations (if any exist).
i ) x = 7 mod 9, x =3 mod 4
ii) 3x^2 +1 = 0 mod 10
iii) 3x+7 = 9 mod 10

Please show complete, step by step
working.
Solve the following equations for 0 ≤ x ≤ 2π, giving
your answers in terms of π where appropriate
i) cos
x = -√3/2
ii) 2 sin
2x = 1
iii) cot x =
1/√3
b) Solve the following for 0° ≤ q ≤
360°,
i) sin^2Q = 3/4
ii) 2 sin^2Q - sinQ = 0 {Hint: factor out sinθ)

please show all work Evaluate each of the following limits, for
after lim the part with x-> and then a number is below the lim
and then after is the fraction part
1) lim x->3 (x^2-2x-3/x^2-5x+6)
2) limx->2 (x-2/square root(2x)-2)
3) lim x->inf (3x^5-7x^3/-5x^5+x^3-9)

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 -...

Please solve the following and show the workings.
Solve the following equations:
i) 3 4x = 4
ii) 2000 = 500 e 0.2x
iii) logx3 + logx 27 = 2
Express as a single logarithm :
1/3 log27 + 3 log 7 - 6 log2

i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 =
ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks)
c) Solve the following pairs of simultaneous equations 2x + y =
7 and x - 2y = -1

Use Gauss-Jordan Elimination to solve the following system of
equations. Please show all the wotk identifying what row operations
you are doing in each step
2x-4y+6z-8w=-10
x-2y+z+w=2
-2x+4y+z+2w=-3
-x+3y-3z+5w=6

Differential Equations. Please write clearly and show all
work
1. Solve by Laplace Transforms: x'' + x = 4*delta(t - 2*pi) The
initial conditions are: x(0) = 0 = x'(0).

find the derivative of each of the following show all work and
circle answer please
part 1) f(x)= x+2/x^2+2
part 2) f(x)=2tan(x)+sin(3x)-10
part 3) f(x)=x^2 . cos(x^3-2)
part 4) f(x)=ln((x^7 sqrt(x^3+1)/(3x^2+8)^5))

1a) Find all the integer solutions of each of the following
linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 15x + 18 y =17.
1b) Find all solutions in positive integers of each of the
following linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 7x + 15 y = 51.

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