Calculus
e^x = 1+x+x^2/2! + ... Looks like the series is e^5 Since cos(x) = 1 - x^2/2! + ... Looks like the series is cos(2)
Math
#1. No idea what "pattern" we are looking for. 'Splain? #2. TRUE #3. yes, if base 10 #4. D is correct. The more often compounded, the better return.
Calculus
for velocity, just take the derivative: v(t) = -3e^(-2t) (2sin 3πt - 3πcos 3πt)
Precalculus
You know that for the parabola y = ax^2 + bx + c the vertex (maximum in this case) is at x = -b/2a So, plug and chug.
Calculus
assuming the fenced area is rectangular, Let steel side be x, wood side be y xy = 917, so y = 917/x The cost of the fence is thus c(x) = 5x + 2*7(917/x) Then find where c'(x) = 0
Calculus
find f(3) and f(6) find where f'(x) = 0 for local extrma in the interval pick largest/smallest of those values
Calculus
f' = 7-3/t^2 f'=0 when t=±√(3/7) f" = 6/t^3 f" > 0 when t>0 so min at t=√(3/7) f" < 0 when t<0 so max at t=-√(3/7)
Physics
The vertical component of the velocity is Vy = V cos 44.6 = .712V The height of the ball in feet is given by h(t) = (.712V)t - 16t^2 So, if h(t) = 0 when t=3.6, .712V*3.6 - 16*3.6^2 = 0 V = 80.9 ft/s Guy's a pretty decent kicker, since the average kickoff speed is about 50...
Algebra
Well, if you mean 1/2 (√x)^(-1/2) √(2x+9) There's not much to do. If you make it all a 4th-root, then you have 1/2 ∜((2x+9)^2 / x) I still don't think that's what you meant, but ...
Algebra
eh? Do you mean 1/2 (√x)^(-1/2) ----------------- √(2x+9) Kind of odd, having a root of a root
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