Answer:
a) 25.15
b)
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c) (x,y) = (1, -2pi)
Step-by-step explanation:
a)
First lets calculate the velocity, that is, the derivative of c(t) with respect to t:
v(t) = (-sin(t), cos(t), 2t)
The velocity at t0=4pi is:
v(4pi) = (0, 1, 8pi)
And the speed will be:
s(4pi) = √(0^2+1^2+ (8pi)^2) = 25.15
b)
The tangent line to c(t) at t0 = 4pi has the parametric form:
(x,y,z) = c(4pi) + t*v(4pi)
Since
c(4pi) = (1, 0, (4pi)^2)
The tangent curve has the following components:
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c)
The intersection with the xy plane will occurr when z = 0
This happens at:
t1 = -2pi
Therefore, the intersection will occur at:
(x,y) = (1, -2pi)
The differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵
<h3>What is differentiation?</h3>
The method of determining the derivative, or rate of change, of a function in mathematics.is termed as the differentiation.
Given that:-
The derivative will be calculated as:-
Therefore the differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵
To know more about derivatives follow
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Since the 50 remains the same every time, is has no letters next to it in the equation. The 20, however, is multiplied by the amount of hours, and will therefore have an h next to.
20h + 50- the answer is a.
Answer:
Step-by-step explanation:
We are given:
And we want to find:
This is equivalent to:
So, we will evaluate g(-5) first, which yields:
So:
Then:
Therefore:
