The length of the function y = 3x over the given interval [0, 2] is 3.2 units
For given question,
We have been given a function y = 3x
We need to find the length of the function on the interval x = 0 to x = 2.
Let f(x) = 3x where f(x) = y
We have f'(x) = 3, so [f'(x)]² = 9.
Then the arc length is given by,
This means, the arc length is 3.2 units.
Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units
Learn more about the arc length here:
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This problem can be solved using the Pythagorean Theorem.
<em>Note: the height of the telephone pole is unnecessary information.</em>
Convert the measurement in feet to inches.
The length from the base of the pole to the anchor point on the ground is inches. The distance from the base of the pole to the anchor point on the pole is
inches.
These are the two legs of a right triangle. The length of the stabilizing cable is the hypotenuse of the right triangle.
The Pythagorean Theorem is:
In this formula, and
are the legs and
is the hypotenuse.
Plug in the known values.
Swap the sides of the equation.
Evaluate the powers.
Simplify using addition.
Take the square root of both sides.
Separate the solutions.
Length and distance cannot be negative, so remove the negative solution.
Answer:
Step-by-step explanation:
The question lacks appropriate diagram. Find the diagram attached.
Slope is the change in coordinate of the y coordinate to the x coordinate.
Mathematically, slope m = ∆y/∆x
From the diagram ∆y is the same as 3 (along the vertical) while ∆x is the same as 1 (along the horizontal)
m = ∆y/∆x = 3/1
∆y/∆x = 3/1
y/x = 3/1
Cross multiply
y × 1 = 3 × x
y = 3x
Hence the slope of the line is y = 3x
