CPhill

Not the "nearest" integer......but the "next"  integer

So    

1.35  rounds to   2

So...we need 2 bags

Yep....and then round up to the next integer [ since we can't buy "partial bags" ]

So....what's the correct answer  ???

2.)Isosceles triangle $OPQ$ has legs $OP = OQ$, base $PQ = 2$, and $\angle POQ = 45^\circ$. Find the distance from $O$ to $\overline{PQ}$.

Bisect base  PQ

Call the point of bisection M

Then angle OMQ  = 90

Angle MOQ = 22.5

MQ = 1

And angle OQM = 67.5

So....by the Law of Sines

OM/sin 67.5   =  1/sin (22.5)

OM =  sin 67.5 / sin 22.5 =   cos 22.5 / sin22.5  = cot 22.5  = ( 1 + cos 45) / sin 45 =

1 + √2/2              1                           2

  ______  =       ___     +   1   =      ___  + 1    =   √2  + 1

    √2/2              √2/2                       √2

5 + 5  = 10

5 * 5  = 25

1.)A regular hexagon has side length $6$. If the perimeter and area of the hexagon are $p$ and $A$, respectively, what is the value of $\frac{p^4}{A^2}$?

The perimeter  =  6*6  =  36

The area is composed of 6 equilateral triangles and is given by :

6 * (1/2) * (6)^2 * √3/2   =  

3√3 / 2 * 36 =

54√3

So

p^4              36^4              (36)(36)(36)(36)          (2)(2) (36) (36)     (4)(36)(36)   

___   =       _______  =    ______________  =    _____________=  ________ =

A^2             54^2 * 3          (54) (54) (3)                (3)(3)(3)                    27

(4)(4)(36)

________   =     16 * 12   =     192

      3

Remember, Nickolas....the area of a square  =  (side)^2

Calculate this.....(you got the triangle part correct....)

Add the two answers together to get the final answer....

Close....remember that  the area of  the triangle   =  (1/2) (3 *5)

Also...you need to calculate the area of the square on the left

Area of parallelogram  =   

(base) *( height)  =

( 2.5 + 6.5) * ( 6)  =   

(9) * (6)

Calculate this, Nickolas.....divide the answer by 40.....and round up to the next integer

What is the area of the square on the left  ???

What is the area of the triangle on the right???  [hint :  base = 3, height = 5]