We need to solve for the height of the tree given two angles and distance between the two observers. See attached drawing for a better understanding of the problem.
We derive to equations using SOH CAH TOA such as below:
sin30 = h / x
sin 45 = h / (100-x)
sin 45 (100-x) = xsin30
70.71 - 0.71x = 0.5x
70.71 = 1.21 x
x = 58.44
Solving for h, we have:
h = xsin30
h = 58.44 sin30
h = 29.22
The height of the tree is 29.22 feet.
Answer:
(x, y) = (-0.6, 0.8) or (1, 4)
Step-by-step explanation:
Use the second equation to substitute for y in the first.
(x -1)² +((2x +2) -2)² = 4
x -2x +1 + 4x² = 4 . . . . . . . eliminate parentheses
5x² -2x -3 = 0 . . . . . . . . . . subtract 4, collect terms
Now we can rearrange the middle term to ease factoring by grouping.
(5x² -5x) +(3x -3) = 0
5x(x -1) +3(x -1) = 0
(5x +3)(x -1) = 0
The values of x that make these factors zero are ...
x = -3/5, x = 1
The corresponding values of y are ...
y = 2(-3/5)+2 = 4/5 . . . . for x = -3/5
y = 2(1) +2 = 4 . . . . . . . . for x = 1
The solutions are: (x, y) = (-3/5, 4/5) or (1, 4).
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A graphing calculator verifies these solutions.
Answer:
A) The population in the year that she was born.
Step-by-step explanation:
The multiplier of an exponential function is the value that function has when the exponent is zero -- the initial value. The initial value of population in this context is the population in the year Adriana was born.
Ans5
Step-by-step explanation:
5
The tank WILL overflow.
60*30*40= 72000cm^3
<em>The max volume the fish tank can hold: 72000cm^3</em>
amount of L * 1000= cm^3
70L * 1000= 70000cm^3
<em>There is already 70000cm^3 of water in the tank</em>
70000cm^3 + 3000cm^3 = 73000cm^3
The tank can only hold 72000cm^3 and the water and rocks are 73000cm^3, so the tank will overflow.