CPhill

What is the solution to (y(2-y))/(1-y)^2=1.7777e^(0.26(10))

So we have.... (2y  - y^2) / (1 -y)^2 = 1.7777e^(2.6)

This one would require some work to solve, so I'll take adantage of the calculator on this site to do the "heavy lifting."

We get two solutions (rounded)

y ≈ .799   and  y ≈ 1.2003

A parallelogram is a 4-sided shape formed by two pairs of lines. Opposite sides are equal in length and opposite angles are equal in measure. To find the area of a parallelogram, multiply the base by the height. The formula is:
where is the base, is the height, and · means multiply.
The base and height of a parallelogram must be . However, the lateral sides of a parallelogram are not perpendicular to the base. Thus, a dotted line is drawn to represent the height.

I believe this is what you needed.....

how can I prove that pi times radius squared is the area of a circle

Mmmmmm....this is an interesting one.

Let's start by inscribing a polygon of some "n" sides in a circle. It can be shown that, as the number of sides increase (to some "large" value), the perimeter of this polygon is almost the same as the circle's circumference ≈ 2*pi*r. And since we have n sides, the length of each side is just ≈ (2*pi*r) / (n)

Now, if from the center of the circle, we draw a radial line (r) to each vertex of the polygon, we will form "n" triangles. The base of each triangle is just the side length of the polygon (given in the previous paragraph). And we can also show that, as the number of sides of the polygon increase to some "large number," the height of each triangle aproaches "r" (the radius of the circle).

Therefore, the area of each triangle is (1/2)*(b)*(h) = (1/2)*[(2*pi*r) / (n)]*(r) =

pi*r^2 / (n).

And since we have n triangles, then the total area of all the triangles = (the number we have) * (the area of each one) =

(n)*(pi*r^2) / (n) =

(pi)*r^2........

A box has the shape of a rectangular prism with height 33 cm. If the height is increased by 0.7 cm, by how much does the surface area of the box increase?

The original surface area would be 2 [(W *33cm) + (L * 33cm)] = [2*33 (W + L)]cm^2 = [66 (W + L)]cm^2

Increasing the height by .7 cm, we have.. 2[(W * 33.7) + (L + 33.7)] =

[2*33.7 (W + L)]cm^2 = [67.4 (W + L)]cm^2

Since the (W +  L) is just a constant, we can just make their sum "C"

So, subtracting the "old" from the "new," we have

[67.4*C]cm^2 - [66*C]cm^2 = [67.4*C - 66*C]cm^2 = [1.4*C]cm^2 =

[1.4*(W + L)]cm^2

Tom bought a pair of shoes for $120.99 and a dress silk tie for $59.99. GST is 5% PST is 8%. How much did he pay for the tax in total

Canadian, eh ???

I don't know much about Canadian tax policy, but there are - from what I understand - two ways in which the Provincial Sales Tax (PST) is calculated, depending on the province. One is on the original sales price, and the other is applied on the combined sales price and GST (ouch!!).  I'll do it both ways.

Note that we spent ($120.99 + $59.99) = $189.98

The GST on this doesn't change, no matter the method....so we have

$189.98 x (.05) = $9.50

So, if we apply the PST strictly on the sales price, we get...$189.98 x (.08) = $15.20

And the combined amount we spend = $189.98 + $9.50 + $15.20 = $214.68

Now, if we calculate the PST on the combined sales price and the GST (= $199.48), we get

$199.48 x (.08) = $15.96

And, using this method, we spend $199.48 + $15.96 = $215.44

And that's it........

If we allow "leading" zeros.....note that there are 10 ways to "guess" each digit..(0-9)

So..... (10 ways) X (10 ways) X (10 ways) X (10 ways) = 10,000 ways

And, if we're only allowed one "guess,' than our probability of guessing correctly is just

1 / 10,0000

If we can't have a leading zero, then we just have

(9 ways) X (10 ways) X (10 ways) X (10 ways) = 9000 ways

And, if we're only allowed one "guess,' than our probability of guessing correctly is just

1 / 9,0000

Standard Form: the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

This eliminates A.... (2.5 isn't an integer) and B...("A" in the equation is negative).

C and D are correct.

Alan is correct......There is an interesting article by Isaac Asimov touching on this titled "T-Formation." He points out that  a "googleplex" CANNOT be "written out" because there isn't enough physical space in the Universe to do so, even if we made each zero extremely "small.' And even if we COULD make each zero extremely "small,' we wouldn't have the time to do so, anyway. If we lived 4 billion seconds (about 127 years), and we could write ONE TRILLION zeros per second, then we could only write about (4 x 10^21) zeros and that would be WAY short of a "googleplex" of them !!!

Re: what is the square root of 1,000,000

We can write 1,000,000 as 10^6

So, taking the square root of this is equal to (!0^6)^(1/2)

And, by a property of exponents, this is just (10^3)

Which is just 1000.....and that's the square root of a million.....

Thanks, Alan.......I knew there was only one more "real" solution (just no more "rational" ones). Any other possible real zeros would have been "out of bounds".......