geno3141

power = work / time

K.E.  =  ½·m·v²

m  =  625,000 grams     

v  =  18.3 m/s

joules are in kg·m²/sec²

If you are going to translate it vertically 2 units, you will need to add 2 to the y.

If you are going to translate is horizonally -5 units, you will need to add -5 to the x.

(7 + 2, 2 + -5)  =  (9, -3)

a)  x  =  r·cos(theta)     --->   x  =  4·cos(5pi/3)  =  4·½  =  2

     y  =  r·sin(theta)     --->   x  =  4·sin(5pi/3)  =  4·-sqrt(3)/2  =  -2sqrt(3)

First:  let's factor the numerator:  xm - xn - 4m + 4n  

                                                     xm - xn - (4m - 4n)

                                                     x(m - n) - 4(m - n)

                                                     (m - n)(x - 4)

Then:  let's factor the denominator:  xm - xn + 4m - 4n

                                                         x(m - n) + 4(m - n)

                                                         (m - n)(x + 4)

Putting the two together:  [ (m - n)(x - 4) ] / [ (m - n)(x + 4) ]

(m - n)  is a common factor in both the numerator and the denominator; cancel it ...

leaving us with:  (x - 4) / (x + 4) 

The equation of any line parallel to  x + y  =  3

will be of the form:                            x + y  =  ??

To find  ??  replace the point (10, 10) into the equation:  x + y  =  ??

                                                                                        10 + 10  =  20  =  ??

So, the equation will be:  x + y  =  20

To place this into slope-intercept form:  x + y  =  20

                                                                     y  =  -x + 20
 

4sin(x) - 2  =  0

     4sin(x)  =  2

       sin(x)  =  2/4

       sin(x)  =  1/2

              x  =  sin^-1(1/2)

              x  =  pi/6     or  pi - pi/6  =  5pi/6

If the problem is:  [ 5 cis( 7pi/4) ]⁴

raise the constant to the fourth power

multiply the angle by 4.

There will be three answers:

First answer:        find the cube root of the constant and divide the angle by 3.

Second answer:  find the cube root of the constant and divide the angle by 3 and then add 2pi/3 to that angle.

Third answer:      find the cube root of the constant and divide the angle by 3 and then add 4p/3 to that angle.

List all the possibilities:

     H H H     *

     H H T     *

     H T H

     H T T      

     T H H     *

     T H T

     T T H

     T T T

3 out of the 8 possibilities will have at least 2 heads in a row.

So, the probability is 3/8.