CPhill

We would write the domain as  (-∞,-4) U (-4, -2) U (-2,∞)

I'm not sure how to solve this algebraically, but WolframAlpha gives the answer as 27/5 = 5.4.....this males sense because (27/5)* floor(27/5)  = (27/5) *(5)  = 27

(Maybe another forum member can show a "mathematical" way to solve this....!!!)

Thank you, YourAssassin.....that answer was very helpful....!!!

1)hypotenuse is 12, an angle is 12 degrees, find the side opposite the angle

Use the sine here...the opposite side is ....   12*sin(12)

2) 2)hypotenuse is 32, an angle is 65 degrees, find the side adjacent to the angle

Here, we can use the cosine   ...... the adjacent side =   32*cos(65)

You should be able to take it from there....

Remember the exponent law that says  a^m * a^n  = a^(m + n)...so we have..

x^(2/7) * x^(3/14) = x ^(2/7 + 3/14) = x^(4/14 + 3/14) = x^(7/14) = x^(1/2)

This question makes no sense....

f(x) = 1 / √(9 - x^2)

Since the denominator can't  = 0 , x cannot be 3 or -3.  And since we can't take the square root of a negative number, any x values < -3 or > 3 make the square root non-real

So....the domain is  just (-3, 3)

The range is a little trickier.....as "small" as y can be is when x = 0 ...and this is 1/3....and as x approaches either -3 or 3 in the domain, y approaches infimity...so, the range is [1/3, ∞)

Here's one way...using the first 7 integers

(7^3 - 6^3) + (4^3 - 5^3) - (3 * 2 * 1)

(127) - (61) - (6) =

66 - 6   =

60

(I'm sure someone else will come up with something more elegant....!!!)

a)  We would have [ -4x + 4 ] / [x -3]