W Write an equation of A-line that passes through the point (2,0) and is perpendicular to the line y= -1/2x + 3
1 answer:
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Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
( 1 , − 2 )
Equation Form:
x = 1 , y = − 2
Step-by-step explanation:
Graph.
y = 3 x − 1
y = x + 1
y = − x − 1
y = x + 1
Answer:
34.43
Step-by-step explanation:
A differential of length in terms of t will be ...
dL(t) = √(x'(t)^2 +y'(t)^2)
where ...
x'(t) = 4cos(4t)
y'(t) = 7cos(7t)
The length of c(t) will be the integral of this differential on the interval [0, 2π].
Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...
(π/5)(n -1/2), so the area of the piece will be ...
sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))
It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.
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The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.
The length of the curve is estimated to be 34.43.
