geno3141

80 foot-pounds of force at 275º

Direction notation:  taking north to be 0º and moving in a clockwise direction, east is 90º, south is 180º, and west is 270º.

Putting directions on a graph, from the origin, the positive x-axis is 90º, the positive y-axis is 0º, the negative x-axis is 270º, and the negative y-axis is 180º.

So, in a trig sense, where the positive x-axis is 0º, the positive y-axis is 90º, the negative x-axis is 180º, and the negative y-axis is 270º, a direction of 275º becomes a trig direction of 175º.

To find the horizontal component, use r·cos(theta)     --->     80·cos(175º)  =  -79.7     (rounded)

To find the vertical component, use r·sin(175º)   --->   80·sin(175º)  =  7.0     (rounded)

A "foot-pound" is equivalent to lifting a weight of one pound one foot off the ground.

There are two answers: one if you take the direct distance between the two locations and the other if you walk along the streets.

The direct answer:  use the distance formua:  d  =  sqrt( (x₂ - x₁)² + (y₂ - y₁)₂ )

     with (x₁, y₁)  =  (17, 21)   --->   x₁ = 17  and  y₁ = 21

     and  (x₂, y₂)  =  (28, 13)   --->   x₂ = 28  and  y₂ = 13

--->   d  =  sqrt( (28 - 17)² + (13 - 21)² )   --->   d  =  sqrt( 11² + (-8)² )   --->   d  =  sqrt( 121 + 64 )  =  sqrt(185)

         which is a distance of about 13.6 blocks

The other answer by walking along the sidewalks:  going from 17 to 28  =  28 - 17  =  11 blocks

                                                                        and  going from 21 to 13  =  21 - 13  =  8 blocks

for a total of 11 + 8  =  19 blocks.

Try it:  do the sum of the squares of the two smaller numbers equal the square of the larger number?

Find:  176² + 73²   =

Then find:  192²     =

And compare the two answers; if they are equal, these three numbers form a Pythagorean Triple; if they aren't equal, they do not form a Pythagorean Triple.

0/0 has no specific answer; therefore, it's usually called "undefined".

If each cookie cost $1.20 each, a dozen cookies will cost  12 x $1.20  =  $14.40.

If you can buy a dozen cookies form $8.50, you will save  $14.40 - $8.50  =  $5.90.

To find the amount of discount divide the amount saved by the original amount and turn that answer into a percentage.

$5.90 / $14.40  =  0.4097  (approximately)  =  40.97%  or  41%  (approximately)

f(x)  =  ( 2x^3/2 - 3x^-3/2 )² + 5

f(x)  =  5                                             ===>     ( 2x^3/2 - 3x^-3/2 )² + 5  =  5    

Subtract 5 from both sides                 ===>     ( 2x^3/2 - 3x^-3/2 )²   =  0

Find the square root of both sides     ===>     2x^3/2 - 3x^-3/2   =  0

Add  3x^-3/2  to both sides                   ===>     2x^3/2  =  3x^-3/2   

Change the right side                        ===>     2x^3/2  =  3 / x^3/2   

Multiply both sides by x^3/2                  ===>     2x³  =  3                     (add exponents 3/2 + 3/2  =  6/2  =  3)

Divide both sides by 2                        ===>     x³  =  3/2

Take the cube root                             ===>     x  =  1.447...

x + yi              --->      -3 + 5i            --->      x  =  -3     and     y  =  5

rcis(theta)      --->     r  =  sqrt( x² + y² )     --->     r  =  sqrt( (-3)² + (5)² )     --->     r  =  sqrt( 34)

                      --->    theta  =  tan^-1( y/x )     ===>     theta  =  tan^-1( 5/-3 )     --->     theta  =  120.96^o 

sqrt(34) · cis ( 120.96^o )

Since it is a geometric progression, it has a common ratio:  r

Therefore:  x = 5·r

                   y  =  x·r  =  (5·r)·r  =  5r²

                   z  =  y·r  =  (5r²)·r  =  (5·r·r)·r  =  5r³ 

              405  =   z·r  =  (5r³)·r  =  (5·r·r·r)·r  =  5r⁴

Therefore  5·r⁴  =  405     --->     r⁴  =  81     --->     r  =  3     or     r  =  -3

There are 4 "steps" going from 5 to 405:  first step going from 5 to x; second step going from x to y; third step going from y to z; and fourth step going from z to 405.  These 4 "steps" give the exponent upon r.

The integral of  sec(x) dx  is:  ln| sec(x) + tan(x) |  +  a constant

If every person's salary goes up by $1000.00: 

The mean salary goes up by $1000.00.

The person who had the median salary before the raise will be the person who has the median salary after the raise and, since that person's salary went up by $1000.00, the median salary goes up by $1000.00

The person who had the lowest salary still has the lowest salary, but it is $1000.00 higher.

Similarly, the person who had the highest salary still has the highest salary, but it is also $1000.00 higher.

Finally, the quartiles of the salary distribution also increase by $1000.00.