Solve for n.--42 – 6n = -30
1 answer:
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For this case we have that by definition, the discriminant of a quadratic expression is given by:
If the discriminant is less than zero then the expression has two different complex roots.
In this case we have the following expression:
So we have to:
The discriminant is given by:
Then, if we want two complex roots it must be fulfilled that:
Thus, the expression has two complex roots for all values greater than 4.
ANswer:
The mass of the wire is found to be 40π√2 units.
<h3>How to find the mass?</h3>To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass =
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
Further simplifying;
Now, use integration to find the mass of the wire;
Therefore, the mass of the wire is estimated as 40π√2 units.
To know more about density function, here
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5