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1. Find the pair of integers (a,b) for which 2^a+1 + 2^a = 3^b+2 -3^b. Please show your steps and explain clearly!!!?

...equal 3^b, so b = 1 That's the only way to get 8 as a factor of the LHS and 3 as a factor of the RHS. This is the same way everyone...

4 Answers · Science & Mathematics · 22/01/2018

2. Prove identity: cosx + cos2x + cos3x = cos2x(1+2cosx)?

To prove : cosx + cos2x + cos3x = cos2x(1 + cos2x) LHS = cosx + cos2x + ( cos(2x + x) = cosx + cos2x + cos2x* cosx - sin2x*sinx = cosx + cos2x + cos2x...

2 Answers · Science & Mathematics · 02/01/2018

3. Math help?

... = (a + b)(a² - ab + b²) Let a = sinx, b = cosx : ∴ LHS = sin³x + cos³x = a³ + b³ = (a + b)(a² - ab...

2 Answers · Science & Mathematics · 11/12/2017

4. Moving a box, how is there an equal and opposite reaction?

... = 100 N But note that the two forces on the LHS are parts of two different action/reaction pairs. As for...

2 Answers · Science & Mathematics · 08/12/2017

5. Prove this?

RHS = (tanx-1)(cotx+1) = 1+tanx-1/tanx-1 = tanx - 1/tanx = tanx - cotx = LHS

4 Answers · Science & Mathematics · 06/12/2017

6. NEED help asap with the shear and moment diagrams of this beam !!!!! thanks :)?

.../m * 1.5m * (0.5m + 2.5m) = 27 kN·m The moment due to the LHS of the load is 6kN/m * 1.5m * 0.5m = 4.5 kN·m and so ...

1 Answers · Science & Mathematics · 10/11/2017

7. How do I explain why after multiplying 2x < 4 by the inequality "<" swaps?

...from both sides -4 < -2x step 3 rewrite with the -2x term on the LHS -2x > -4 Which shows if you multiply the original inequality by -1...

2 Answers · Science & Mathematics · 04/11/2017

8. Calculus question!?

...500 let u = tanθ du/dθ = sec²θ let v = x/500 dv/dx = 1/500 differentiate LHS WRT t using the chain rule du/dt = du/dθ dθ/dt = sec²θ...

5 Answers · Science & Mathematics · 09/04/2017

9. Math trigonometric identities proving?

LHS = (1+cosx)/sinx = [ 1 + (2cos^2(x/2) - 1)]/2sin(x/2)cos(x/2) = 2cos^2(x/2)/2sin(x/2)cos(x/2) = cos(x/2)/cos(x/2) * cos(x/2)/sin(x/2) = 1 * cos(x/2)/sin(x/2) = cot(x/2) = RHS

2 Answers · Science & Mathematics · 30/11/2016

10. How to prove this? I tried multiply in etc but couldn't get any further...?

...there exist x,y > 0 such that (x+y) (1/x + 1/y) < 4 simplify the LHS and we get (x+y)^2/(xy) < 4 (x+y)^2/(xy) - 4 < 0...

2 Answers · Science & Mathematics · 02/11/2016