geno3141

What's teh question?

To make the typing easier, I'm going to replace f(x) by y:

y  =  3/x + 1

To find its inverse, use this two-step process:

Step 1)  Exchange x and y:  x  =  3/y + 1

Step 2)  Solve for y:      

                  subtract 1 from both sides:  x - 1  =  3/y

                  multiply both sides by y:     (x - 1)y  =  3

                  divide both sides by x - 1:           y  =  3/(x - 1)

This final equation is the inverse. 

If you remember SSS, SAS, ASA, AAS, SSA (not legal in geometry, but legal in trig) from geometry:

if you have SSS or SAS, use Law of Cosines, otherwise use Law of Cosines.

This appears to be the coordinates of two points. Are you trying to find the slope or the equation?

Inverse tangent on this calculator is arctan (abbreviated as atan).

Press (2nd), then (atan), then enter the number.

If the number of branches is  4y² + y  and the number of leaves on each branch is  2y³+ 3y² + y,

then the total number of leaves is  4(2y³+ 3y² + y)² + (2y³+ 3y² + y).

As a composite function, it is b(l(y)).

1) One of the formulas for the area of a rhomus is:  A  = ½·d1·d2, where d1 and d2 are the lengths of the rhombus.    Area  =  ½·4.5·8  =  18

2) 2x - 3y  =  4                                --->  2x - 3y  =  4

      x + y  =  7   --->   multiply by 3   --->  3x + 3y  =  21

                                  add down:                     5x  =  25   --->   x  =  5   --->  y  =  2  

                                                                                                            --->  x - y  =  5 - 2  = 3

3)  B  =  (1/3)·C

     C  =  5000 + B         --->     C  =  5000 + (1/3)·C     --->  (2/3)·C  =  5000    --->  C  =  7500

4)  I don't have a neat way of doing this:

      10C  +  25D  +  30R  = 100                   seven ways:

      C = 10, D = 0, R = 1

      C = 7, D = 0, R = 1

      C = 5, D = 2, R = 0

      C = 4, D = 0, R = 2

      C = 2, D = 2, R = 1

      C = 1, D = 0, R = 3

      C = 0, D = 4, R = 0

5)  Let x be the number of questions after the first 20:

      This equations represents the number of correct answers:

      15 + (1/3)x  = (1/2)(x + 20)

      Multiply by 60:

       900 + 20x  =  30(x + 20)

       900 + 20x  =  30x + 600

            300  =  10x

               x  =  30  (extra questions)

       Total number of questions:  20 + 30  =  50

If you consider the core of the sun to be its center (actually, it isn't; but we'll handle that later), the speed of light would be determined by the distance it travels divided by the length of time:  

     696,000 km / 50,000 years  =  13.92 km/yr.

To compare this to the speed of light in a vacuum, we need to convert the above into m/s.

There are 1000 m in a km and approximately 31,500,000 seconds in a year.

--->  13.92 km/yr x (1000 m/1 km) x (1 yr/31,500,000 sec)  =  0.00044 m/s

This is very slow as compared to the speed in a vacuum because of the density of the sun. (Picture light as being a particle; it's being bounced around, therefore, it takes a long time to escape.)

Actually, the core of the sun is about 1/5th to 1/4th of the sun. Since light is not travelling from the center of the sun, the speed of light is still slower; reduce the speed by 1/5th or 1/4th. 

Since the ball is thrown horizontally, this does not change the amount of time the ball is in the air but it does determine where the ball lands.

Since we are only interested in the time in the air:  s  =  -4.9t² + 29.4

When the ball lands, s = 0:                        --->     0  =  -4.9t² + 29.4

                                                                    4.9t²  =  29.4

                                                                        t²  =  6

                                                                          t  =  2.5 seconds

√(a/x) · a     --->     √(a/x) · a  =  √a / √x · a

If you want, you can rationalize the denominator by multiplying both the numerator and denominator by √x:

--->      ( √a / √x · a )  · ( √x / √x )  =  √(ax) / x · a  =  a√(ax)/x