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|+| and then the equals is the upper and lower border.

edited by Melody :)

because it is interesting and can get you into colloge sike idk why lol

Mrs. B decided to have a treasure hunt with her math class. She takes her class out to the playground where she has marked out a 15-yard by 15-yard square region. She also gives her students a map that divides the playground into a coordinate plane. Somewhere within this region, she has buried a box full of prizes for her students, but they need to figure out the coordintes of the treasure's location. They are given 1-hour class time to find the treasure.

As the students begin searching they realize they are able to completely search about 5 square feet per minute. They realize at this pace they will not finish in the 1-hour time limit. At their current rate, how many more hours would they need to guarantee they find the treasure? Express your answer as a decimal to the nearest 100^th.

  1 yard    =  3 feet

15 yards  =  45 feet

45 feet * 45 feet  =  2025 square feet

They can search  5  sq ft per minute. How many minutes will it take to search  2025 sq ft?

5 sq ft per minute  *  x minutes  =  2025 sq ft

5x  =  2025

  x  =  405

It will take  405  minutes to search the entire area. That is  405 / 60  =  6.75 hours

The question asks how many more hours they need. So they need

6.75 - 1  =  5.75 more hours

Let's call the coordinates of the treasure  (x, y) .

The treasure is  10  yards away from  (0, 0) ,

and we know that the distance between any two points  = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the points  (x, y)  and  (0, 0)  and a distance of  10 , we have...

10  =  $\sqrt{(x-0)^2+(y-0)^2}\,=\,\sqrt{x^2+y^2}$                         →     100  =  x² + y²

The treasure is  10  yards from  (15, 0) . So we know that

10  =  $\sqrt{(x-15)^2+(y-0)^2}\,=\,\sqrt{(x-15)^2+y^2}$          →     100  =  (x - 15)² + y²

Now we have two equations and two variables.

They both equal 100, so we can set these equal.

x² + y²  =  (x - 15)² + y²

x²  =  (x - 15)²

x  =  ±(x - 15)

x  =  x - 15          or          x  =  -(x - 15)

0  =  -15                           x  =  -x + 15

 false                              2x  =  15

                                        x  =  15 / 2

Plug this value for  x  into  x² + y² = 100  to find the value of  y .

(15 / 2)² + y²  =  100

y²  =  100 -  (15 / 2)²

y   =  ±√[ 100 -  (15 / 2)² ]

y  ≈  6.6

Since there are only positive values of  y  on the map, the coordinates are  ≈  (7.5, 6.6)

20% means =20 / 100 =0.20

0.20 x 20 = 4

Here's the cross-section pic  :

The radius of the sphere  1.5  units

The volume of the cone is   pi (3)^2 *4 / 3   units^3  =  12pi  units^3

The volume of the sphere is (4/3)pi (1.5)^3  units^3 = 4.5 units^3

So   ratio  of the volume of the sphere to the cone is :

4.5 pi  / 12 pi  =    4.5 / 12  =      (9/2) / (24/2)  =  9 / 24  =  3 / 8

how would you excute this then 10^0.8? thanks  

If Caroline gets 1/9 of the money......the other two must receive 8/9 of it

And if Colin and Sarah share the rest in a 3:1 ratio.....Colin must receive 3/4 of the 8/9

So......Colin gets  (3/4) (8/9)  = (3/9)(8/4)  =  (1/3)(2)  =  2/3  of the money

thanks!

Given Degrees / 180  x      pi   =   radians

Example....convert 45 degrees to radians.....

45 / 180   x   pi   =     (1/4) pi   =   pi / 4   radians  

Because the absolute value of a number is really just the units it is away from the origin, or 0. Now lets simplify the equation.

lxl+3=5

lxl+3-3=5-3

lxl=-2 or +2.

-2 and 2 are the only two numbers that are 2 units away from 0, and so either of them could be the answer.

Thanks forthe comment Waffles :))

And how about responding to my first answer.

Sorry - I see you have :)))         

Waffles, you should have typed that one in.

If you cannot type well enought then you need the practice!

Nice detective work, Melody.........!!!!

the answer is FALSE. Unless the 51 is supposed to be 15.

yes you got the picture right

A litle hard to read....but....

15 yards  =  45 ft

So......[15 x 15 ]  sq yards  = [ 45  x 45 ] sq ft  =  2025 sq ft

At 5 square feet per minute....they can search  60 x 5  = 300 square feet in one hour

So....after one hour.....they have   2025 - 300  =   1725 square feet left to search

So.....it will take them     1725 / 5  =   345  more minutes  = 

345 min  x  1 hr / 60 min   =   5.75 hrs more

What about the first question. The one I already gave the address for.

It would  be nice if you at least commented,

I posted a new photo

Here is question 22.

The question, not the answer :))