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Could that be the subject of your PhD dissertation in mathematics?

You need to know the other leg, or that the triangle is isosceles, or the size of one of the acute angles ...

Part b:  y = (1/3)x^3 + (1/2)x^2 + (1/4)x

            y'  =  3(1/3)x^2 + 2(1/2)x^1 + 1(1/4)x^0

            y'  =  x^2 + x + 1/4             The derivative of a constant is zero.

            y''  = 2x + 1

c)  s = -2t^-1 + 4t^-2                    (Write as negative exponents; it's easier.)

     x' = -1(-2t^-2) + -2(4t^-3)

     x' = 2t^-2 - 8t^-3

     x'' = -4t^-3 + 24t^-4

d)  r = 12θ^-1 - 4θ^-3 + θ^-4

     r' = -12θ^-2 + 12θ^-4 - 4θ^-5

     r'' = 24θ^-3 - 48θ^-5 + 20θ^-6 

e)  r  = 2θ^(-1/2) + 2θ^(1/2)              Easier to work if negative, fractional exponents.

     r'  = -θ^(-3/2) + θ^(-1/2)               Subtract 1 from each exponent

     r'' = (3/2)θ^(-5/2) - (1/2)θ^(-3/2)

f)  w = re^(-r)

     w' = -re^(-r)                           (Do you have exponentials?)

g)  y = x^(-3/5) + π^(3/2)            π^(3/2) is a constant, so its derivative is zero

     y' = (-3/5)x^(-8/5)                  Subtract 1 from the exponent               

It is usually easier to solve an equation if it has no denominators:

The denominators are  11, 3, and 6.  A common denominator is 66.

Multiply each term by 66:      66[(3/11)x] - 66(1/3)  =  66(5/6)

Simplify:                                                   18x - 22 = 55

Add 22:                                                           18x  =  77

Divide by 18:                                                        x  =  77/18

10^2 - 6^2  =  4^3

Did you forget part of the question?

(½)^11

You can get a decimal answer by using the calculator at this site.

Also:  (1/2)^11  =  (1)^11 / (2)^11  =  1 / 2048

In the top two graphs, the value of y depends upon the value of x.

The top graph looks close to:  y = -|x| + 2  so, as you put in various values for x, you get different values for y.

The middle graph looks like a modification of a y = sin(x) or  y = cos(x) graph. Again, as you put in different values for x, you get different values for y.

But, the last one:  The only number that you can put in for x is 1.5, but there are an infinite number of y-values that pair with this x-value.  Some examples are (1.5,0), (1.5,1), (1.5,-2), (1.5,653434). The value of y does not depend upon the value of x; it can be anything. So, this is not a function. Similarly, it does not pass the vertical line test; the vertical line that passes throught this vertical line hits this line, not in just 1 point, but in an infinite number of points.

Does this help or it is as clear as mud? 

WAIT THIS IS THE WRONG QUESTION!! THE QUESTION IS 

Decide whether the graph represents y as a function of x. Explain your reasoning.

Wait!  Two of these are functions!

so geno none of them are a function

The vertical line test:  when looking at a graph, if every vertical line that you can draw will intersect the graph in at most one point, then the graph is the graph of a function. 

So, two out of the three are function, but one of them isn't. Can you figure out which are functions?

Welcome!     If you have a specific question upon a problem, please ask.

A function is a relation such that each member of the domain is paired with only one member of the range. 

In a function the first number can never be paired with more than one second number; however, in a function the second number can be paired with more than one first number (but doesn't have to be).

If each member of the domain is matched with one and only one member of the range and each member of the range is matched with one and only one member of the domain, it is a one-to-one function. If each member of the domain is matched with one and only one member of the range but the same member of the range is used more than once, it is a many-to-one function.

{ (1,7), (1,-7) }   domain: {1}     range: {7,-7}  Not a function becase 1 is paired with both 7 and -7.

{ (2,8), (2,-8) }   domain: {2}     range: {8,-8}  Not a function because 2 is paired with both 8 and -8.

{ (3,2), (5,4), (7,4) }    domain: {3,5,7}     range: {2,4}  It is a many-to-one function.  I don't know quite what to do with the 6; I suppose that it could be put in the rangle but I wouldn't do that.

{ (0,-6), (2,-4), (4,-2), (6,0) }    domain:  {0,2,4,6}     range:  {-6,-4,-2,0}  It is a one-to-one function.

To find where 2376 belongs in the 8 times table, divide 2376 by 8.

To quote someone:  42

-1  to any even power has value  +1

-1  to any odd power has value  -1

To solve, remove the  7  from  7x.  Since the  7  and  x  are attached by multiplying, divide:

   7x / 7  =  t / 7

          x  =  t/7

You can use the calculator at this site...

If you start with  (x - 4)(x - 5) (x - 7) (x - 9)     and multiply by    x² + x (which is x(x + 1) )

and multiply by    1 - x

The roots will be the values that make the original factors zero; specifically,  4, 5, 7, 9, 0, -1, and 1.

If you have a common fraction such as 3/4, enter it that way; that is 3 / 4

1  =  (x - 4)²

Find the square root of both sides, use the symbol ± on either side:

√1 = ±1           √(x - 4)² = x - 4

±1  =  x - 4

Add 4 to both sides:  4 ± 1  =  x         --->      x = 4 + 1 = 5         x = 4 - 1  = 3

-y² + 9  =  9 - y²

This is the difference of two squares with the form:  a² - b²  =  9(a - b)(a + b)

So:  9 - y²  becomes  (3 - y)(3 + y)

How are taxes calculated in New York? What is the percentage rate (or rates)? Can federal taxes be subtracted before state taxes are calculated? Please give more information.

"25% of" means "0.25 times" so the problem reduces to:  .25 X 247  =