Answer:
The boat is 8.4m out of the sea
Step-by-step explanation:
Kindly find attached rough sketch of the problem.
From the sketch we can see that the observer from the cliff and the horizontal distance forms a right angle triangle
Let the horizontal distance be x
Let the angle of elevation from the boat be y
Applying sum of angles in a triangle
90+6+y= 180
96+y=180
y=180-96
y= 84°
Applying SOH CAH TOA
Using TOA
Tanθ= opposite /adjacent
Tan 84= 80/x
x= 80/tan 84
x= 80/9.51
x= 8.4m
To find the slope between two points, we need to find the rise over run. We can do this by using the slope formula. Between two points, (x, y) and (x₁, y₁), the slope is . Now we can substitute the values of our points and solve. The formula becomes:
Simplifying, we get:
2. That means that the slope between these two points is 2.
Answer: 2560 < 98415
Step-by-step explanation:
The number of cells increase in an exponential growth, which is, in general:
A(t) = A₀.
where;
A is the growth at a time "t"
A₀ is the initial amount of cells
k is rate of growth
t is time in minutes
To write an equation for the conditions described above, we have to find the rate k, knowing that at every 2 minutes, the number of cells increases by 50%, i.e., A₀*1.5:
A(2) = 2560
2560*1.5 = 2560
= 1.5
ln() = ln(1.5)
k = 0.2027
With the initial value, the rate and knowing that the number of cells has to be less than 98415:
2560 < 98415
<u>The inequality in terms of t is 2560</u><u> < 98415</u>