Mathematics

Abstract algebra proof...prove d divides b

Let a,b,n be integers with n>1 and let d=gcd(a,n).If the equation [a]x=[b] has a solution in Z/nZ, prove that d divides b.-To say that [a]x = [b] has a solution in Z/nZ means that there is an integer

One more exponents question ;)

One more I forgot to put on the last question: simplify please, to where theres no negative exponents if you could! (5x^-3)^3-(5x^-3)^3 =5^3 * x^-9 =125/(x^9)-Hey secret sorrow, i guess the question

How to complete the square of 6x^2-9x-2

Full solution please :) thanks.-f(x) = 6x²-9x-2 Complete the Square Formula: ax²+bx+c → a(x+b/2a)²+(c-b²/4a) → a(x+h)²+k 6x²-9x-2, a = 6, b = -9, c = -2 → (6)[x+(-9)/2(6)]²+[(-2)-(-9)²/4(6)] → 6[x+(

Can someone help me with this sum: 600 times 20=

Also what would the working out look like? thanks-Easy way to do this is: 6 times 2= 12 and there are three 0s so 12,000 Working it out looks like this: 600x20_____ +00012000 _______ 12,000-600

What is the value of 6x Squared when x = 1/3

x is squared... Im just looking on how you got the answer... Im confused can you explain please?-6(1/3)^2 6(1/9) 6/9 =2/3-6*((1/3)^2) = 6*(1/9) = 6/9 = 2/3

Find angles of sin(3x) = 0.5

This question is from Calculus II, polar curves etc. Please explain how to find all the angle of sin(3x) = 0.5, I can find the first one, which is pi/18. The question and solution is in the followin

What is the largest interval over which the reciprocal function decreases

in interval notation.-Hint: it decreases over any interval which does not contain 0

Solve this equation for x: Γ(x-1) + Γ(x) = Γ(x+1)

Γ(x-1) + Γ(x) = Γ(x+1) OR 1 + (x -- 1) = x(x -- 1) OR x^2 -- 2x = 0 giving x = 0, 2

Solve the Eqautions??????????

7x sqaured = -21x x sqauered - 2x = 0 Bonus:D Factor theese 400y sqaured -9 xsqaured + 6x + 9-1.) 7x² = -21x 7x²+21x = 0 7x(x+3) = 0 7x = 0 or x+3 = 0 x = 0 or x = -3 Solutions: x = -3 or x = 0

Calculus help for my final please

73) After a new firm starts in business, it finds that its rate of profits (in hundreds of dollars per year) after x years of operation is given by P(x) = 3x^2 + 6x + 6. Find the profit in year 6 of t

Let f:[0,1] to R be continuous function such that f(t) is greater or equal to 0 for all t in [0, 1].

Define g(x) = Integral f (t) dt(integrated between 0 to x)then 1. g is monotone and bounded 2.g is monotone but not bounded 3. g is bounded but not monotone 4. g is neither monotone nor bounded-If f(

Explain this factoring problem

First of all, I am only in 10th grade honors, so please dont make fun of me! Im a straight A student, but I wasnt here for the review of the homework, so I will greatly appreciate if anyone can explai

Need help with a math question please

What is the length of the arc of the circle that has a central angle of 2π/3 and a radius of 4.2cm? how would you go about solving this? thanks for your help. :)-the arc length of a full circle is th

Please help, calculus. The point P( 1/5 , 10 ) lies on the curve y = 2 / x .

The point P( 1/5 , 10 ) lies on the curve y = 2 / x . If Q is the point (x, 2 / x ) , find the slope of the secant line PQ for the following values of x . If x= 0.3 , the slope of PQ is: and if x= 0

F(x) = 2x^5 -3x^4 + x^3 - 6x + 20: x = 2

evaluate a.32 b.10 c.8 d.4-Just plug in the 2 on all x and solve it :) 32 is the answer-just plug in 2 wherever you see x and solve 2*2^5-3*2^4+2^3-6*2+20=32so, it is a-10-itll be a.32,funny quest