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Answers by Kevin K.

x = amount invested at 6% y = amount invested at 9%   x+y = 25,000   interest income from 6% investment: .06x interest income from 9% investment: .09y   total interest income = 1,860 = .06x + .09y   two equations, two variables   x+y=25000...

(X-1)^-2=25 (answer)

(x-1)-2 = 25   (x-1)-2 is the same as 1/(x-1)2   1/(x-1)2=25   1=25(x-1)2   1/25 = (x-1)2   1/5 = √(x-1)2   + or - 1/5 = x-1   x-1 = 1/5 or x-1 = -1/5   x = 1 1/5 or x = 4/5

sin2x = sinx   use the identity: sin2x=2sinxcosx   2sinxcosx = sinx   2sinxcosx - sinx = 0   sinx(2cosx-1) = 0   sinx = 0  OR   2cosx-1=0   sin x = 0 when x is an integer multiple of pi, or x = npi (n = 0, +-1,...

We can factor 9-x on the bottom as (3-√x)(3+√x).   Then we can cancel out the 3-√x s. We are left with 1/(3+√x). Now if we plug in 9 for x. We get a value of 1/6, so it is continuous at x=9.

We can rewrite the term of the infinite series like this:   2 * (4/5)^n   Whenever you have a number raised to n like this [r^n], it's a geometric series.  A geometric series converges when the absolute value of the number being raised to a power is less than 1.  It...

To find max and min, we need the first derivative.   f(x) = xsqrt(x2+4) = x(x2+4)1/2   f ' (x) = x*1/2(x2+4)-1/2 * 2x + (x2+4)1/2 * 1 = x2/sqrt(x2+4) + sqrt(x^2+4)   = x2/sqrt(x2+4) + (x2+4)/sqrt(x2+4) =...

Formula for sum of geometric series:   Sum = a/(1-r)   where a is the first term and r is what we multiply by each time.   a = 32   To find r: -8/32 = -1/4; 2/-8 = -1/4.  So r = -1/4   Sum = 32/(1-(-1/4)) = 32/(1+1/4) = 32/(5/4)...

The problem discusses two conditions about the field: the area and the length of fencing.  First, the entire field has an area of 1,000,000 ft^2.  Since we don't know the dimensions yet, let's call those x and y.  Since it's a rectangle, the area equation would be:   1,000,000...

You're on the right track If you extend the height and slant height, we have a "missing" cone.  Let's call the missing cone's slant height x. So now we can think of a proportion: smaller missing cone to bigger overall cone (actual + missing) small radius/big radius...

Right and left behavior refer to what graph approaches as x goes to infinity (right) and negative infinity (left) if the function is 5 minus 7/(2x-3x^2), then when x gets big positive or big negative 7/(2x-3x^2) goes to 0 and we are just left with 5.  So the graph approaches y = 5 (as...

when you have a limit where the base and exponent both have a variable, we need to use a log, then L'hospitals Rule so first let's do ln of our limit to get x out of the exponent ln [lim x->oo (x/1+x)^x] = x * ln[lim x->oo x/1+x] = lim x->oo[x*ln(x/1+x)] then we...