ElectricPavlov

cos(x)^2 - sin(x)^2    =

cos^2    - ( 1-cos^2 )

2cos^2 -1                              cos ranges from -1 to 1      the range then becomes    -1  to 1

We are looking for k .....so put things in terms of k

b = 4k

k          

r = b - 296   =   4k - 296                 summed, they equal 1459

4k  + k   + ( 4k-296) = 1459

k = 195                                                 b = 780     r = 484

d = distance    rate * time

40x = d      and    30 (x + 28/60)  = d      equate the two       ( x = time in hours)

40x = 30x - 14

10x= 14

x = 1.4    hours                   40 * 1.4 hours = 56 miles

123% of 9     is    1.23 * 9 = ________

First....you should graph the two lines.....here is a graph :   https://www.desmos.com/calculator/xqbnu0g6mt

   now calculate the area of the larger triangle    ( remember area = 1/2 b h )

     and calculate the area of the smaller triangle

      prob  =  (larger - smaller) / larger

Because   6   saw   7  8   9      ( 7 ATE NINE)         

4 - 3x < - 2    add 3x and 2 to both sides to get

4+ 2 < 3x

6<3x              divide both sides by 2

2 < x               re-arrange

x > 2

First, find the height of the cylinder  to be   2 * sqrt(22.75) = 9.539 units       ( see image below)

Cylinder surface area = pi 2r h    + 2 * pi r^2        r = 1.5 for the cylinder      h = 9.539 units

Sphere surface  area    4 pi r^2          r = 5 for the sphere

    Add them together for your answer.............

Basically the same as Melody's answer:

Time on uphill  one way = time downhill coming back

'a'  distance uphill   is 'a'  distance  downhill on the way back

c downhill is             c uphill on the way back

b is flat    distance  = 2 b for the roundtrip

          total distance =  2 (a+b+c)

(a+c) / 100   + 2 b / (120) + (a+c)/ 150   =   time for round trip              common denominator 600

  [ (6)(a+c) + 10b  + 4 (a+c) ]  /  600   = time        <==simplify

time = 1/60 (a+b+c)                 remember distance/time = rate

            2 (a+b+c) / (1/60(a+b+c)   = 120 m/s

16 (x)  +   3 (12-x)   = 127        x = air time    12- x = sea time

x = 7 seconds       height = 16 m/s *  7 s = 112 meters

sea time = 5           depth =  3 m/s * 5 s =  15 meters