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You wrote that the shadow ws "14 feet inches".

Is it just feet, or just inches, or 14 feet and some number of inches?

If 14 feet, from the angle: the adjacent side is 14 feet and the height is the opposite side.

Since tan = opp / adj, use tangent:  tan(67)  =  x / 14   --->   x  =  14 · tan(67)  =  33.0 feet

0.6666667 is the answer

The next is 8

This site is for math

Grimm

The distance between two points is found by subtracting the beginning point from the ending point.

6.8 - -2.4  =  9.2

(3/5) of 9.2  =  (3/5) x 9.2  =  5.52

This distance must be added to the beginning piont:  -2.4 + 5.52  =  3.12  <--- 

I don't understand  ^6 + 2/2.

The distance formula is:  √[ (x2 - x1)² + (y2 - y1)² ]

o.6 i think or 0.66666666667

You can use the calculator at this site to find this answer.

If you multiply ½ x 2, the answer is 1

if you muliply 1 x 2, the answer is 2

if you multiply 2 x 2, the answer is 4

so, it seems that the next term in this sequaence is found by multiplying the preceding term by 2.

Knowing this, what is the next term?

If the problem is:  [x² + 4x + 4] / [x² + 6x + 8]

factor both the nmerator and the denominator:

[ (x + 2)(x + 2) ] / [ (x + 4)(x + 2) ]

Cancel the (x + 2) factor in the numerator with the (x + 2) factor in the denominator:

=  (x + 2) / (x + 4)

If you can only use real numbers, the answer is "no"

because real numbers only include 0, positive numbers and negative numbers

and, a positive times a positive is positive and a negtative times a negative is also a positive, so there is no way to get a negative for an answer.

However, if you use complex numbers the answer is "yes".

With complex numbers the  √(-1)  is usually written as just the letter 'i'. 

First, find the slope:  m  =  (y2 - y1) / (x2 - x1)

x1 = 1/4  y1 = -1/2  x2 = 3/4  y2 = 2     ---> 

m  =  (2 - -1/2) / (3/4 - 1/4)   =   (5/2) / (1/2)   =  5

Use the point-slope form for the equation of the line:    y - y1  =  m(x - x1)

y - -1/2  =  5(x - 1/4)     --->     y + 1/2  =  5x - 5/4     --->     y  =  5x -7/4

Distance  =  rate x time

Your rate is 55 mph and you are to represent the time traveled by the letter 'x':

Distance = 55 · x

y  =  55 · x

Now, find the y-values when x = 0, x = 5, and x = 10.

Since the cost for the gas is $4.98 times the number of gallons, the equation will be:  y  =  4.98x.

e^[2·ln(x)]

Since a multiplier times a log goes inside the log as an exponent:

= e^[ln(x²)]     

Sinc e^ln(z)  =  z,

= x²

If you are refering to a quadratic function (a parabloola), there are various ways:

1) graph the equation and read the values from the graph

2) complete the square and get the equation into the form:  y  = a(x - h)² + k; the vertex will be (h, k)

3) use the formulas:  x = -b/(2a)    y = (b² -4ac)/(4a) to find the x- and y-values of the vertex

 5784658365

+63675748475

We start at the right.  5+5=10.  Mark that column 0,  then carry the 1 a space to the left.

6+7+1=14.  Mark the column 4,  then carry the one to the left.

3+4+1=8.  There are no numbers to carry, so mark that column 8.

8+8=16.  Mark the column 6, and carry the one to the left.

5+4+1=10.  Mark the column 0,  then carry the 1 to the left.

6+7+1=14.  Mark the column 4,  then carry the one to the left.

4+5+1=10.  Mark the column 0,  then carry the one to the left.

8+7+1=16.  Mark the column 6,  and carry the one to the left.

7+6+1=14.  Mark the column 4,  then carry the one to the left.

5+3+1=9.  Mark the column 9,  there are no ones to carry.

There is one more 6 column.  Add it to the beginning of the answer.

6,946,040,680 is the answer,  and my work here is done

2 to the power 30 / 8 to the power 9

Note that 8 = 2^3

So we have

2^30 / (2 ^3)^9  =

2^30 / 2^27  =   2^(30 - 27)  = 2^3  = 8

ln (e)^sin(x   by a property of logs, we have

(sin x) * ln e      and lne = 1

So

(sin x) * 1   = sin x

You put ^4

2x+2=5x-3    Add 3 to both sides and subtract 2x from both sides

5 = 3x          Divide both sides by 3

5/3 = x

Notice that

2^n+1 - 2^n =

2^n(2 - 1) = 2^n(1) = 2^n

So

2^5000 - 2^4999 =

2^4999(2 -1) =  2^4999

That is a ridiculous question.  It's food.

Compound interest formula:      A  =  P(1 + r/n)^(n·t)

A = final amount              P = beginning amount = $5000.00               r = rate (as a decimal) = 0.03

n = number of times compounded each year = 1                                 t = number of years = 2

 A  =  P(1 + r/n)^(n·t)     --->      A  =  5000(1 + 0.03/1)^(1·2)      --->     $5304.50

A bad word

It is a gardening tool that people have turned into a bad word.  Happy?