Express the formula P=2L+2W in terms of the width,W. Use the formula to find the width when the perimeter is 70 and the length i
2 answers:
Answer:
<h2>The width is 13</h2>Step-by-step explanation:
From the question
P=2L+2W
where
L is the length
W is the width
To make W the subject move 2L to the left side of the equation
That's
2W = P - 2L
Divide both sides of 2 to make W stand alone
We have
when
P = 70
L = 22
W is
We have the final answer as
<h3>W = 13</h3>Hope this helps you
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The slope of tangent line at point(4, 2pi) is undefined.
For given question,
We have been given a polar equation r = 2 + 2cos(θ)
We need find dy/dx as well as the slope of tangent line at point(4, 2π).
We know that, for polar equation we use,
x = r cos(θ) and y = r sin(θ)
plug the given value of r into these equations we get:
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⇒ x = (2 + 2cos(θ) ) × cos(θ)
⇒ x = 2(cos(θ) + cos²(θ))
⇒ x = 2cos(θ) + 2cos²(θ)
Similarly,
⇒ y = r sin(θ)
⇒ y = (2 + 2cos(θ) ) × sin(θ)
⇒ y = 2(sin(θ) + sin(θ)cos(θ))
⇒ y = 2sin(θ) + 2sin(θ)cos(θ)
Now we find derivative of x and y with respect to theta.
.............(1)
Similarly,
..............(2)
Now we find dy/dx
⇒ dy/dx = (dy/dθ) / (dx/dθ)
From (1) and (2),
We know that The slope of tangent line is given by dy/dx.
So, the slope is:
Now we need to find the slope of tangent line at point(4, 2pi)
Substitute θ = 2π in above slope formula.
⇒ m = ∞
The slope of tangent line at point(4, 2pi) is not defined.
This means, the tangent line must be parallel to Y-axis.
Therefore, the slope of tangent line at point(4, 2pi) is undefined.
Learn more about the slope here:
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