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Answers by Jim S.

Find Sum ... (answer)

the sum of the first N squared is N(N+1)(2N+1)/6   Jim

Eliminate the parameter (answer)

Daisy,           The idea is to solve one of the parametric equations for t in terms of x or y and then substitute that in the other equation giving a relationship between x and y.   1. t=(y-2)/3 and x=3-2((y-2)/3)=3-(2/3)y+4/3=(9/3)+(4/3)-(2/3)y=(13/3)-(2/3)y    ...

whats the name of a polygon that each side is 6 feet? (answer)

Hi        Regular polygons can have any number of equal length sides starting with 3. This is called a triangle, a 4 sided polygon is called a square, 5 sides pentagon, 6 sides hexagon to name a few.       Not sure if their is what you were aft...

Please find f(x)? (answer)

df/dx=-f, df/f=-dx, integrating both sides ln(f)=-x +c, at x=1 f(1)=1 so c=1, ln(f)=-x+1, and f(x)=e(1-x)   Jim

7x+2y=2, 6x-2y=4 (answer)

Adding the equations eliminates y and gives 13x=6 or x=6/13 substituting this in one of the two equations say 7(6/13) + 2y=2 solving for y gives y=-8/13.   So the solution is y=-8/13 and x=6/13. You should check this solution in both equations    Jim

Why do you multiply the two values? (answer)

Megan            Remember you are trying to make up 5 person committees so you can pick one of the 28 and for each one of those you have 56 two person committees so the total number is 28*56=1568. Another way to visualize it is if you Plot the male groups on...

Write the equation of the circle. (answer)

Hi Melyssa,                Does it help you to know that the center of the circle is located at (0,(7+3)/2) or (0,5) and the radius is (7-3)/2 or R= 2 and the equation of a circle with it's center at the point (h,k) is       ...

Differentiation (answer)

d/dx(f(x)g(x)h(x))=f(x)d/dx(g(x)h(x))+g(x)h(x)df/dx=f(gdh/dx +hdg/x)+ghdf/dx=fgdh/dx+fhdg/dx+ghdf/dx   The idea is to apply the product rule twice…the notation gets a little messy with a keyboard   Jim

Can you answer this calculus question? (answer)

Sun,        v(t)=<f'(t), -sin(f(t))f'(t)> you were given that at t=0 v(0)=<0,0>, and f'(t)=2t+C so C=0 and f'(t)=2t. So now f(t)=t2+b and you calculate b from the other initial condition at t=0 x=pi and y=-1   Jim

Can you please verify the correct answer? (Just check my work) (answer)

Sun,         The area is the area between two concentric circles larger one AL=π(2)2=4π and the smaller one AS=π The area between is 4π-π=3π   The indefinite integral of 3cos2(θ)dθ=3/2(θ+sin(θ)cos(θ)) if this is evaluated from 0 to π/2 you get 3π/4...

I need help finding optimal value, solution, slack/surplus. (answer)

Hi,       the optimal solution is x=0, y=250 and z=1125, these are the amounts of each product that will yield the maximum total profit  of 102,500 subject to the constraints given.   The slack values are 375 which is the amount in excess of 1000 that the optimal...