thelizzybeth

I'm assuming you mean that it has crashed inside the forest, and the probablity that it has crashed in the lake. 

This is a case of geometric probability.

The total area of the entire forest is 4.5*9.

The area of the lake is 3*2.5

The probability therefore is \(\frac{2.5*3}{4.5*9}=\frac{5}{27}\)

If x and b are inversely proportional, the product is constant. 

From x=-3 when b=-6, 

xb=18

Sub in b=8

x=18/8=9/4

This is a right triangle.

The circumcircle of a right triangle has its diameter as the hypotenuse. The diameter is 26, therefore the radius is 13. The area of the circumcircle is 13^2pi.

The incircle's radius is 1/2(a+b-c), where a and b are the legs of the triangle and c is the hypotenuse. So the radius is 1/2(10+24-26)=4.

The area of the incircle is 4^2pi. 

169pi-16pi=153pi 

Assuming that EP's solution was right, b+c is -19 + 9 = -10, not -28. 

Let thhe distance between A and B be \(d\).

Since distance/speed=time, \(\frac{d}{36}+\frac{d}{48}=\frac{7}{2}\).

Multiplying both sides by 144, we get \(4d+3d=504\)

\(7d=504\)

\(d=72\)

They each need to have at least one object. There are \({6 \choose 2}=15\) different ways for this to happen. 

Now, we see the different cases for the remaining 4 objects.

Sri   Godfrey

4          0        = \({4 \choose 4}=1\)

0          4        = (same as above) = 1

3          1        = \({4 \choose 3}=4\)

1          3        = (same as above) = 4

2          2        = \({4 \choose 2}=6\)

Total Cases: 16

Now we multiply 15*16 = 240 ways

From the right triangle with hypotenuse 25 and base 15, we know the height of the trapezoid is 20, by the Pythagorean Theorem.

Another right triangle is with hypotenuse 52, height 20, and base x+15.

So (x+15)^2+400=52^2

This simplifies to x^2+30x-2079=0

Factorizing, we get (x-33)(x+63).

Since x=-63 makes the area negative, x=33. 

Plug x into your area equation to get your answer.