In the sentence "TenMarks is awesome!", which of the following has a ratio of 10:7?
1 answer:
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A linear equation can be written as:
y = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:
The answers are:
a) y = (-12 L/min)*t + 9,000 L
b) 6,840 L
a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am
We know that at 6:42 am (at t = 42 mins) the tank has 8,496 liters.
And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.
Then we have two points of the line:
(42 mins, 8,496 liters)
(75 mins, 8,100 liters)
Then the slope is:
So the line will be something like:
y = (-12 L/min)*t + b
To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)
This means that if t = 75 mins, then we have y = 8,100 L
So we can replace these two on the above equation:
8,100 L = (-12 L/min)*75 mins + b
8,100L = -900L + b
8,100L + 900L = b = 9,000 L
Then the linear equation is:
y = (-12 L/min)*t + 9,000 L
b) Now we want to know how much water is in the tank at 9:00 am.
Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.
Then 9:00am is equivalent to t = 180 mins.
So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.
y = (-12 L/min)*180 mins + 9,000 L = 6,840 L
If you want to learn more, you can read:
Answer:
D=2.82
Step-by-step explanation:
Here we are given with two coordinates and asked to determine the distance between them.
Here we are going to use the distance formula, which is given as under
Where
Replacing these values in the distance formula
Hence the Distance is 2.82 units