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David sat beside an empty artificial pond.  At 11:15 am, the pond began to fill up.     The water rose 12.5 cm every 30 minutes.  At what time will the water level reach     2.5 metres?  Show your work and explain your strategy.

2.5 meters  x  100 cm =250 cm

250 cm / 12.5 cm =20 30-minute periods to reach 2.5-meter level.

20 / 2 = 10 hours to reach 2.5-meter level.

11:15 am  +  10 hours =21.15 hours  - 12 hours =9:15 pm - when the pond level will reach 2.5 meters

The above typo should read: 54 minutes  and 32.727272......seconds.

There are ONLY 4 hypotenuses possible:13, 14, 15 and 16

The altitudes to the hypotenuse are as follows respectively: 4.615,  4.176,  3.538  and  2.583

Is it the right triangle??? 

2^2  x  5  x  7 =140 is the smallest 3-digit number.

Well, your "simplex method" didn't work very well !!!.

The cheapest deal is as follows: 35 Platter B  x  $20 =$700, which will give you: 70 burgers, 35 dogs and 280 C, wings.

                                                    20 Platters A x $16 =$320, which will give you: 20 burgers, 60 dogs and 100 C. wings.

                                                                   Total cost =$1020, which will give you: 90 burgers, 95 dogs &  380 C, wings.

 180=abs((30*4) - (5.5*M)), solve for M

M = 600 / 11 =54.545454......or 54 minutes, 32 minutes  and about 44 seconds.

That's a lot of trig.

This is a standard linear programming problem, where we can apply the simplex method.

Applying the simplex method, we obtain these results:

0 0 1 3 5 16
0 0 2 1 8 20
0 9 -2 0 6 34
0 12 -8 -3 0 44
16 0 0 -7 -24 50
9 0 7 0 -3 800
8 0 8 1 0 1210
2 7 0 0 15 1300
4 6 0 -1 0 1470
0 60 10 0 1160

So, the minimum cost is $1160, which is obtained for 60 of Platter A and 10 of Platter B.

Which is 2/3 of 9

In this problem because A - B = C + D, A has to be pretty big. So we start trying some cases in which A is big. First we try A = 10, so B has to equal 6. 10 -6 = 4. No 2 positive integers that multiply to 60 add up to 4. Next, we try 15 if A is 15 then B is 4，15 - 4 = 11 the smallest factor sum is 6 and 10 which adds up to 16 so that isn't right. Finally, we try A = 20 B = 3, 20 - 3 = 17. 12*5 = 20 and they add to 17 so we have found the answer. A = 20.

add 2, take a sqrt cube it and then expand

a # b  =  a + 2b + 3ab

For (a # a ) # a:

Working inside the parentheses first:

     a # a  =

    The second a takes the place of b in the formula:  a # b  =  a + 2b + 3ab

    so we have:  a # a  =  a + 2a + 3aa  =  3a + 3a²

Now we have:  (3a + 3a²) # a

    In this case, the expression "3a + 3a²" takes the place of the a

                        while a takes the place of b

   so we have:  a # a  =  (3a + 3a²) + 2a + 3(3a + 3a²)a

                                  =  3a + 3a² + 2a + 9a² + 9a³

                                  =  5a + 13a² + 9a³

This is the left-hand side. Can you do the right-hand side?

If you can, set the two sides equal to each other and solve ...

#3)  The ends create a circle whose radius is 0.4 m   --->   Area  =  pi·(0.4)²

        The rectangle   --->   Area  =  2 · 0.8

         Find the above area by adding the two answers together.

         To find the volume, multiply that answer times 2.8.

         Multiply the volume by 1000 to get the capacity in meters.

         To find the cost:

          --  you have the area of the bottom, so multiply that value times $40.00

          --  to find the area of the sides, find the circumference of the tank and multiply that number

              by the height:  there are two sides of 2 m each and now we need the circumference of

              the circle:  C  =  pi·diameter  =  pi·0.8  =  2.513

              The total circumference of the tank is 2 + 2 + 2.513  =  6.513.

              To get the area:  6.513 x 2.8  =  18.24

               Multiply this by $40.00 and add to the value above.

Seriously doubt that the distance to the 'hypothesis' is 14 .....longer than either of the legs...longer than the hypotenuse (13) .....

Because of the x² terms, there will be no negative values.

The smallest value will occur when x = 0   --->   (0² + 2)(2·0² + 1)  =  2·1  =  2

Posted yesterday or so...I think Geno answered it....try a search...

x+y+z=100

z=y+10

y=x+2-->z=x+12

x+x+2+x+12=100

3x+14=100

3x=86

x=86/3

z=122/3

pi/4 and 3pi/4

just use all students take calculus, and the unit circle

12 x 80 = 960 m²

960 m² / [( .3048 m/ft)(.3048 m/ft)] = 10333.35 ft²

10333.354 ft² / 200ft²/gal = 51.667 gal =~~52 gallons

There are two positive answers:  (6, 8)  and  (8, 6).

#4)  a)  rectangular area  =  3m x 12m  =  36 m²

            semi-circular area  =  ½·pi·5²  =  39.3 m²

            total  =  75.3 m²

       b)  $ 70 x 75.3  =  $5271.

       c)  100 mm  =  0.1 m

             volume  =  75.3 m² x 0.1 m  =  7.53 m³