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- ch 2/1
please help me...Consider the parabola y = 6x - x2.(a) Find the slope of the tangent line to theparabola at the point (1, 5).(b) Find an equation of the tangent line in part (a).y =

- COMPLEX NUMBERS
- combinatorics question
Using (1+x)1/2 = 1 + Σ(k>=1)(2k-2 choose k-1) *xkshow that:(1-4x)1/2 = 1- 2x Σ(k>=0) (2k choose k)*xk

- advanced calculus
\(H(x,r)=1/(1-2xr+r^2)^.5\) Expand H(x,r) to get P0, P1, ... , P4 in the power series.

- Flux integrals, advanced engineering mathematics third edition, 9.13 #29
This problem seems fairly straight-forward, but i keep getting 12, while the correct answer is 18. You end up evaluating the integral of 6yz with 0<z<2,0<y<sqrt(4-z^2), no?

- test treatment and factors
Sourcedfssms=ss/dfF=MS/MSE A32.250.755B10.950.956.333333333AB3(Adf*Bdf)0.90.32Error162.40.15(MSE) total236.5 Test to determine whether the treatment means differ,α=.10Test whether factors A and B interact using α =.10.

- differentials
If f and g are both differentiable at x=1 with f(1)=3, f'(1)=2, g(1)=3 and g'(1)=-5 and if h(x)=f(2f(x)+g(x)), determine the value of h'(1)

- Calculus III Vectors and the geometry of space
Write the equation r2 cos(2?) + z2= 1 in Cartesian form.

- help
Two particles, Alpha and Beta, race form the y-axis to thevertical line x = 6π. Alpha's position is given by theparametric equations xα= (3t -3sint),yα = (3 - 3cost)and Beta's position is givenbyxβ= (3t - 4sint), yβ =(3 - 4cost) for t>=0. Which sentence best describes therace and its outcome?[a] Alpha moves slower and loses.[b] Alpha takes a shorter path and wins.[c] Beta starts out in the wrong direction and loses.[d] Beta moves faster but loses.[e] Alpha and Beta tie.

- max and min of a triangle
the level sets of F(x, y) are equally spaced parallel lines and F(0, 1) = F(1, 0) andFx(0,0) = 3. Let T be a triangle with vertices at the points (0, 0), (0, 2), and (1, 0). determine the points on the triangle where F has a maximum or minimum.

- Homework problem on how to solve it
h(t)= t^3/4 -2t^1/4

- Polar Coordinates NEED HELP
Using Polar Coordinates, evaluate the double integral R ofsin(x2+y2)dAwhere Ris the region 4< x2+y2<81.I think i am going in the right direction but i cant seem to getthe correct answer.

- Really need help......urgent......anyone please
Suppose that and f,g arereal functions of a realvariable whose nth derivatives ,exist at a point a. Prove Leibniz'sgeneralization of the Product Rule:Can anyone give me a full examplequestion/ practice problemthat contain numbers to prove it? I cant get themeaning with all those

- Spring mass (laplace transform)
- real analysis (pointwise and uniform convergence)
Suppose is a sequence ofintegrable functions andthat is such that uniformly on [a, b]. Show that f isintegrable on [a, b]Please show your work carefully. Will rate lifesaver!!! Thanks

- Vector Functions and Space Curves
Show that the curve with parametric equations x = t cos t, y = tsin t, z = t lies on the cone z^2 = x^2 + y^2, and use this fact tohelp sketch the curve.

- precal44
show work pleaseGiven sin(x) = -5?7 with 180° < x < 270°. Find sin(2x).a) b) c) d) e)

- Hyphotesis Testing
A sports analyst claims that the mean batting average for teams in the American League is not equal to the mean batting average for teams in the National Leaguebecause a pitcher does not bat in the American League.The data listed below are from randomly selected teams in both leagues. At σ=0.05, test the sportsanalysis's claim.Assume the population varieances are equal.AmericanLeagueNational league0.2790.2740.2710.2680.2840.2670.2660.2630.2650.2540.2400.2610.2590.256

- geometry
Ray wants to prove the following theorem:If two angles are complementry to two congurent angles thenthen the original two angles r congurent.I the diagram which is thebest information?1. angle QMR is equal and congurent to angle UMT.2. angle QMR and angle RMSare complementry angles.angleUMT and angle TMS are comlementry angles.3.SM is perpendicular to QU and angle UMT and angle TMS arecomplementry angles.4. angle QMRis equal and congurent angle UMT, SMis perpendicular to QU.

- L7 #5
MUST SHOW YOUR WORK!!Evaluate