Point J is located at (2,5)(2,5) and point K is located at (4,19)(4,19).
1 answer:
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Answer:
The function , where x is the depth in meters.
Step-by-step explanation:
As per the statement: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases.
Then, we have the two points i,e (0, 1) and (23, 3.3).
An equation of the line is in the form of y=mx+b where m is the slope or rate of the line and b is the y-intercept.
Let x represents the depth in meters and p(x)= y represents the pressure in atmosphere.
Calculate slope of the line:
Slope of line(m) is given by:
Substitute the given point we have;
Then, our equation of line become:
y = 0.1x + b .....[1]
To solve for b;
Substitute the point (0, 1) in [1];
Our equation for this line become: y = 0.1x +1
Now, we write this for x as a function of p,
i.e, p(x) = 0.1x + 1
Then, the function formula become;
where x is the depth in meters.
Answer:
y = 1.
Step-by-step explanation:
f(x) = x^2 + 1
We know that:
replacing the function, we get:
Now we can simplify this to:
and solving the quotient, we get:
then f'(x) = 2*x
And we want the equation for the tangent line at (0, 1)
The slope of that line will be:
f'(0) = 2*0 = 0
So this is a horizontal line, of the type y = a
And we know that this line must pass through the point (0, 1)
so we must have y = 1.
Then the equation of the tangent line to f(x) at the point (0, 1) is:
y = 1.