Write out the first few terms of the geometric series, Summation from n equals 0 to infinity (StartFraction x minus 4 Over 4 En
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Answer:
Step-by-step explanation:
the formula for density is:
where d is density, m is mass, and V is volume.
solving for m in the last equation:
so if we find the volume and multiply it by the density we will get the mass of the object.
The volume of a rectangular prism is given by:
where is length,
is width and
is height:
we substitute to find the volume:
since the density has units of we need the volume also in units of
, so we make the conversion using:
multiplying by 30:
and now we find the mass with the equation:
substituting d and V:
the nearest gram is:
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:
⇒ x = r cos(θ)
⇒ 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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