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Sometimes it helps to cancel units.  You can cancel units the same as you cancel numbers. 

Example:  1670 km/hour x 24 hour/1 =

I just put hour over 1 to make it obvious that hour is a numerator in that term.

Cancel the hour in the denominator of km/hour and the hour in the numerator:  km/hour x hour/1 = km/1 or simply km

And it's just arithmetic to multiply the numbers 1670 x 24

That's going to come to approximately 40,000 because 24 is almost (100 x 1/4) and (1/4 x 1670) is close to 400

You should multiply them on out formally and get the exact answer.

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Thanks a lot Melody & CPHill - you've got talent!...... & you have restored my sanity!

Could you help me graph the functions in desmos please? 

https://web2.0calc.com/questions/please-help_57149#r2

and hopefully you can graph the two fxns to find their points of intersection.......

116/15   =   7   11/15

Saturday    2 p/hr   requires  5 hrs   for 10 pcgs

Sunday      4 p/hre  requires 2 1/2 hrs for 10 pcgs

20 pcgs/7.5 hr  = 20 /7.5 = 2.6666666666666667  pcgs/hr    (2  2/3 packages/hr)

First

You take the first derivative and put it equal to 0

Have you done that?

What did you get?

Nicely answered HiylinLink    

Thanks Chris, I didn't realize there were 2 sets of solutions.     

Good 

-1/-1=1

I JUST KNEW

-1-0=-1

I Just Knew

\(x^2 - y^2 + x + y = 0\\ (x^2 + x) - (y^2 - y) = 0\\ \left(x^2 + x +\dfrac 1 4 - \dfrac 1 4 \right)- \left(y^2 - y +\dfrac 1 4 - \dfrac 1 4\right) = \\ \left(x+\dfrac 1 2\right)^2 - \dfrac 1 4 -\left(y-\dfrac 1 2 \right)^2 +\dfrac 1 4 = 0\\ \left(x+\dfrac 1 2\right)^2 -\left(y-\dfrac 1 2 \right)^2= 0\\ \left(x+\dfrac 1 2\right)^2 =\left(y-\dfrac 1 2 \right)^2\\ \left(x+\dfrac 1 2\right)=\pm \left(y-\dfrac 1 2 \right)\)

\(y = x+1,~y= -x - 1\\ \text{you can see that these two lines are perpendicular as }1 = -\left(\dfrac{1}{-1}\right) \)

1.Rachel draws three cards from a standard deck of cards, one at a time. How many different ways can she draw three cards? (The order of the cards matters.)

52 ways to select first card x 51 ways to select the 2nd card x 50 ways to select the last card  = 132,600 ways

2.Rachel draws three cards from a standard deck of cards, one at a time. However, this time, she puts each card she drew back into the deck. How many different ways can she draw three cards? (The order of the cards matters.)

There are  52 ways to select each card so.....52^3  = 140,608 ways

3.Joe wants to find all the four-letter words that begin and end with the same letter. How many combinations of letters must he examine? A word is any sequence of letters, such as MTHM, and does not have to be English.

If the middle two letters can be anything...then

He has 26^3  = 17576 possible "words"

26 ways to choose each of the first three letters ....the last letter is pre-determined by the first letter

4.There are 19 figure skaters in the Olympic women's competition, including 3 Americans. The gold medal goes to first place, silver to second, and bronze to third.
In how many ways can the medals be awarded to three of the 19 figure skaters?

We have a possibility of 19 first place competitors....then 18 possible second place competitors ...and 17 possible third place competitors....so

19 x 18 x 17  = 5814 ways

your the smartest person ive seen

You didn't specify the diameters but.....if memory serves from answering this problem before....I believe that the diameters were 2, 4, 6, 8 and 10

So....the radiuses are 1, 2, 3, 4 and 5

The inner red area  is easy  =  pi (1)^2  =  1pi

The   next red area  =   area of 3rd circle - area of second circle  =  pi (3^2 - 2^2) = pi (9 - 4)  = 5pi

The outer red area is =   area of 5th circle - area of 4th circle  = pi (5^2 - 4^2) = pi (25 - 16) = 9pi

So....the total of the red areas  = [ 1 + 5 + 9 ]  =  15 pi   [units^2 ]

If I see this answer on my exam you will not earn credit. Please learn the material in the course.

Ms. T

Nice solution,  Melody  !!!!!

To get the other solution, we have

sin(6x)  = cos(4x)

cos( pi/2 - 6x) = cos(4x)

pi/2 - 6x + 2pi * n   =  4x

pi/2 + 2pi * n =  10x

x = pi/20 + pi /5 *n

x = 9° + (36°) * n

Well......let's see if this has a solution....we have that

125^2x-1  = 25^{x + 4}

(5^3)^{2x- 1}  = (5^2)^{x + 4}

5^(6x - 3)  = 5^(2x + 8)        we have the bases the same...so....we can solve for the exponents

6x - 3  =  2x + 8

4x = 11

x = 11/4  = 2.75

The problem is probably that you didn't set the y scale high enough  in Desmos

We need it to be at least    25^(2.75 + 4)  ≈ 2,729,575,167   ≈ 2800000000

[ I set    the x scale for 0 to 3    and the y scale  for 0 to 2800000000  ...no commas !!!]

See the Desmos graph here : https://www.desmos.com/calculator/emuwj0rwgf

If I understand this correctly, JGA.....we have these series of moves  from the origin

East = x       North = y

  0                 10

  9                  8

  7                  6

  5                  4

  3                  2

  1                  0

Adding both columns.....she ends up  at the point  ( 25, 30)

So...the slope of the line  joining this point to (0, 10)  is found as  [ 30 - 10 ] / [ 25 - 0 ]  = 20/25  = 4/5

And the equation of the line joining these two points is given by :

y = (4/5)(x - 0) + 10

y = (4/5)x + 10         we want this in standard form, so.......multiply through by 5

5y = 4x + 50         subtract 5y from both sides

4x - 5y  + 50  = 0

4x - 5y = -50