CPhill

Let me add something to Melody's answer.....

And supplementary angles add to 180 degees

To remember the difference between the two...note that 90 comes before 180 and "c" comes before "s"

Well, we could write a linear equation for this...... Note, there might be other possibilties, as well.

Calling the two data points  (1, 125) and (.7, 325), the "slope" of this line is

(325 - 125) / (.7 - 1) =  (200) / (-.3) = -2000/3

So the equation becomes

y - 125 = (-2000/3) (x -1)

y = (-2000/3)x +(2000/3) + 125

y = (-2000/3)x + (2375/3)

And that's it ... 

Nice pic!!

The top surface area is given by (3/4)pi(8cm)²

The bottom is the same...so we have 2(3/4)pi(8cm)²  = (3/2)pi(8cm)²  = 96pi cm²

The curved surface area is given by (3/4)(2)(pi)(8cm)(6cm) = (3/2)pi(48)cm² = 72pi cm²

Then, we have two rectangles "inside" whose total area is 2(8cm)(6cm) = 96 cm²

So the total surface area = [96pi cm² + 72pi cm² + 96 cm² ] = [168pi + 96] cm²

And if we use 3.14 for pi, we have [168(3.14) + 96'] cm²  ≈ 623.52 cm²

It must be a matter of semantics.....in the US , we call this

(x+2) (x-1)  = x² + x - 2

"expanding" or an "expansion"

This

x² + x - 2  = (x+2) (x-1)

is called "factoring" an expression

You say, "to-ma-to,"   I say, "to-mah-to"

The general equation for any conic section is

Here, we have no "xy" term  (which would indicate a "rotated conic")

Look under the "Formulary" tab at the top of the page.....it will give you the formula and also has an app that will calculate it for you when you key in the radius

Condense the logarithmic expression ln5+3ln2

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We can write 3ln2 as ln(2)³ = ln(8)

And by another log property, we can write

ln(5) + ln(8)     as    ln(5*8) = ln40

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

Re: what is the distance between (0,6) and (5,-4)

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I could give you a long spiel about the "distance" formula, but here's a nice little trick to use when one of the points has a coordinate value of "0." Let's make, both of them "0."

Subtract 6 from the " y values" in both sets of points.

This gives us (0,0) and (5, -10)

Now, square both values in the second point and add them together...so we have

(5)² + (-10)² =  25 + 100 = 125

Now, take the square root of this

√(125) = √[(25)(5)] = √(25) * √(5) =  5√5... and there you go !!!

The "distance" formula would return the same thing, but here, we didn't have to remember any "formula."

(2/5) (2/5) = 4/25

Yep.......definitely 4/25

(3x^2)(6x^3) divided by 2x^4

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Simplifying the numerator, we have

18x⁶     so this gives us

[18x⁶ / 2x⁴]  or  (18 / 2) * (x⁶ / x⁴) = 9x²