Answer: The speed of the bird when it flies against the wind would be 8 meters per second
Answer:
= (-2,5)
Step-by-step explanation:
To Find:
Solution :
Referring the given graph
We can find the coordinates of 
and 
Coordinates of = (-7,1)
Coordinates of = (5,4)
Thus Coordinates of = (-7+5,1+4) = (-2,5)
Thus = (-2,5)
So, the point = (-2,5) is shown on the attached graph file
Answer:
Step-by-step explanation:
Geometric sequence
Each term in a geometric sequence can be computed as the previous term by a constant number called the common ratio. The formula to get the term n is
where 
is the first term of the sequence
The problem describes Georgie took 275 mg of the medicine for her cold in the first hour and that in each subsequent hour, the amount of medicine in her body is 91% (0.91) of the amount from the previous hour. It can be written as
amount in hour n = amount in hour n-1 * 0.91
a)
This information provides the necessary data to write the general term as
b)
In the 8th hour (n=8), the remaining medicine present is Georgie's body is
Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
