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)
Answer: dang that looks hard, are you actually gonna do that
Step-by-step explanation:
You want the (positive) distance when the height is 0, 0= -d^2 + 10d +5.
You would factor that out(You'd get radicals), and the final answer would be
<span>5±<span>30<span>−−</span>√</span></span><span>
You'd take the only positive one of the two, 5 + srt(30)
I hope I did that right :/</span>
Answer:
The greatest multiple of 14 and 21 is 7.
Step-by-step explanation:
1,2,<u>7</u>,14
1,3,<u>7</u>,21
Hope it helps!
You need the Law of Cosines here and you use it when you have 2 sides and an enclosed angle. The side across from the angle is the one we are looking for. The correct way to express the Law using what we have is the last choice above. Side RT is the unknown, and it is across from the angle that is enclosed between the 2 other sides.
