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

what is the positive difference between Ronald's height and the mean height? (answer)

The difference is (68-71.4)=-3.4" Below the mean. or -3.4/2.6=-1.31 standard deviations below the mean.   Jim

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...

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

how do you do this step by step? (answer)

g(f(x))=3((7x+6)2=3(49x2+84x+36)=147x2+252x+108   Jim

Marrisa hike at a pace of 2 miles per hour. If she hikes for 6 and 1/3 hours, how many miles did she hike? (answer)

Distance =rate x time    rate=2 mi/hr,  time=6.3333 hours   Distance =2*6.333=12.666 miles or if you want to convert 6 1/3 hrs to 19/3 hrs then distance =38/3 miles =12 2/3 miles.   Jim

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

A dealership sets car prices so that there is a 40% profit. If the dealership paid \$5300 for a car how much would the sell it for? (answer)

Josh       If we let: P=  selling price of the car C= cost of the car to the dealer   Then the profit is P-C and the percent profit is 100*(P-C)/P and this is 40% so we have to solve   (P-C)=.4P so .6P=C or P=C/.6 we know C=5300 so P=8,833...

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       ...

Can anyone help me answer these two trigonometry math word problems and show all my work for both? (answer)

Raymond,               We want to find the value of x that makes P(x) = 3,800,000. So we have    3,800,000=x2-4000x+7,800,000, subtracting 3,800,000 from both sides   x2-4000x+4,000,000 = 0 The solution of this quadratic...

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

HOW DOES THE LAW OF CONSERVATION OF ANGULAR MOMENTUM CONTROL A FIGURE - SKATERS RATE OF SPIN. (answer)

Conservation means once established the vector does not change, in the absence of external forces. Ω=Iω is a constant. The figure skater, by changing his  moment of inertia,I, will rotate (spin) faster or slower so that Iω remains constant. The moment of inertia is very sensitive...

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

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...

a \$100 suit is on sale for 30% 0ff. You present a coupon for an additonal 20% off . (answer)

Olivia,           the price of the suit = \$100(1-.3)*(1-.2) = \$100*.7*.8=\$56.00. Notice that the total % (56)is a little larger than the sum of the percents off (30+20=50).   Jim

can someone help me integrate the following? (answer)

Allison,             recall that sec(x)=1/cos(x) so the integrand is now sec2(θ) and you should know that ∫sec2(θ)dθ = tan(θ) +c.   Jim

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...

How do you find the axis of symmetry when the vertex are (4, 0)? (answer)

Alicia The vertex is on the axis of symmetry  at x=-b/2a=-4/-1=4 sub this in the original quadratic and you get h(4)=0 so the coordinates are (4,0)   Jim