Y=Acos(p)+m, A=amplitude, p=period, m=midline, in this case:
A=1/2, p=360(t/12)=30t, m=(10-9)/2+9=9.5 so
h(t)=(1/2)cos(30t)+9.5
The equation of the line is y = 
x + 9
Step-by-step explanation:
The equation of a line in slope-intercept form is y = m x + b, where
- m is the slope of the line
- b is the y-intercept ⇒ the value of y when x = 0
∵ The line has a slope
∴ m =
∵ The y-intercept is 9
∴ b = 9
- Substitute the values of m and b in the form of the equation below
∵ y = m x + b
∴ y = x + 9
The equation of the line is y = x + 9
Learn more:
You can learn more about the linear equations in brainly.com/question/12941985
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Answer: 1/2
When looking at a graph, you need to follow the formula rise/run. This means that between two points, you need to find the distance up and down/left and right.
Looking at points (0,2) and (2,3), I see that the second point is 1 point higher. Let’s add that in for rise.
Rise/run
1/run
Now for run. The second point is 2 points to the right of the first one. Let’s add that in.
1/2
This is your answer! Hope this helps comment below for more questions :)
Opposite
additive inverse
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
