Calculate the slope of the line on the graph
1 answer:
Answer:
3.5 (meters per second)
Step-by-step explanation:
To calculate the slope, we need two points. Let's see if we can select two points from the graph.
From the graph, we can pick out two possible points.
At the beginning, (0,2.5) is a valid candidate.
And at the end, with (5,20). Thus, let's use the slope formula to calculate the slope.
The slope formula is:
Let (0,2.5) be x₁ and y₁ and let (5,20) be x₂ and y₂. Thus:
Simplify:
Thus, the slope is 3.5 meters per second.
Further notes:
And the entire equation will be:
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Answer:
a. dy/dx = -2/3
b. dy/dx = -28
Step-by-step explanation:
One way to do this is to assume that x and y are functions of something else, say "t", then differentiate with respect to that. If we write dx/dt = x' and dy/dt = y', then the required derivative is y'/x' = dy/dx.
a. x'·y^3 +x·(3y^2·y') = 0
y'/x' = -y^3/(3xy^2) = -y/(3x)
For the given point, this is ...
dy/dx = -2/3
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b. 2x·x' +x^2·y' -2x'·y^3 -2x·(3y^2·y') + 0 = 2x' + 2y'
y'(x^2 -6xy^2 -2) = x'(2 -2x +2y^3)
y'/x' = 2(1 -x +y^3)/(x^2 +6xy^2 -2)
For the given point, this is ...
dy/dx = 2(1 -0 +27)/(0 +0 -2)
dy/dx = -28
_____
The attached graphs show these to be plausible values for the derivatives at the given points.
130 degrees see photo for steps
