Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60°, and from a second position L=20 feet farther along this path it is B=50° What is the height of the tree?

44.11 feets

Step-by-step explanation:

Using Pythagoras :

tan θ = opposite / Adjacent

Tan 60° = h / x

h = x tan 60 - - - (1)

tan 50° = h / (x + 20)

h = (x + 20) tan 50 - - - (2)

Equate (1) and (2)

x tan60 = (x + 20) tan 50

1.73205x = (x + 20) 1.19175

1.73205x = 1.19175x + 23.835

1.73205x - 1.19175x = 23.835

0.5403x = 23.835

x = 23.835 / 0.5403

x = 44.114380

Hence, height = 44.11 feets

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: