CPhill

One diagonal bisects  the other

a  =  √ [ 15^2  - 9^2 ]  =  √ [225  - 81 ] =  √ 144   = 12

b =  √ [ 40^2  + 9^2 ]  =  √1681  = 41

c = 9

d = 15

e = b =  41

Here's 1

Angle  ABC  =  180  - 56 -  53  =  180  - 109  =  71°

Using the Law of Sines

11/  sin ABC  =  BC / sin BAC

11 / sin 71  =  BC  / sin 53      multiply both sides by sin 53

11 sin 53  / sin 71  = BC ≈   9.29

Triangle PST  is isosceles with PT  = ST

And in a triangle with equal sides, the angles opposite those sides are also equal

So  angle (PST)   = 62

And the sum of the interior angles in triangle PST   = 180

So......

angle (PST)  + angle ( SPT) + angle (PTS)  = 180

62     +     62   +   angle (PTS)  = 180

124   +  angle (PTS)  =  180      subtract 124 from both sides

angle (PTS)  =  56

The   ratio of the surface area  of the larger solid to the smaller  is   175 /112  = 25/16

Since we are talking about surface area, we need to take the square root of this to find the scale factor of the larger solid to the smaller

So   √[ 25 /16 ]  =    5/4

So....the corresponding side of the larger solid  is

(Side length of the smaller solid) *  (Scale Factor)  =

(20)   *  (5/4)  =

20 * 5   /  4  =

100 / 4  =

25 inches

Yep...just the same

You  want to isolate  y   so that we get the form    y   = mx + b

Where m  is the slope  and b is the y intercept

Call the rate of the boat in still water, R

And when the boat is traveling with the current, its rate is  (R + 6)  km/ hr

So...  Rate  * Time  = Total Distance

( R + 6 ) * 4   =  D    (1)

And Distance  / Rate    = Time  (in hours)

Note that when the boat goes against the current, that its rate   is being slowed by the current...so its rate  is (R - 6)...so we have

D / ( R - 6)  =  10     (2)

Sub  (1)  into  (2)

(R + 6) * 4  / (R - 6)   =  10    simplify

(R + 6) * 4  =  10 (R - 6)

4R + 24  =  10 R - 60        subtract 4R  from both sides, add 60 to both sides

84  =  6R      divide both sides by  6

14  =  R     ( the rate in still water is 14 km/hr)

To find the distance, plug 14  into  (1)

(14 + 6) * 4   =  D

20 * 4  =  80

So...the distance is 80 km  (one way)

3x  - 2y  =  - 16      subtract  3x  from both sides

-2y   =  -3x   -  16       divide everything by  - 2

y  =  (3/2)x  +  8

The slope is  (3/2)  and the y intercept  is  8

Very nice, hectictar.....!!!....this one had me stumped  !!!!

pi  * r^2  <   60 pi       .....divide out  pi

r^2  <  60

So.....the greatest possible  (integer) value for  r  is   7  (inches)