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)
23. Kim and Jay leave at the same time to travel 25 miles going to the beach.
Kim drives 9 miles in 12 minutes
Jay drives 10 miles in 15 minutes.
Question: who will arrive first?
Unit rate of Kim
=> 9 miles in 12 minutes
=> 0.75 miles / minutes
=> 25 / 0.75
It will take 33.33 minutes for Kim to arrive
Unit rate of Jay
10 miles in 15 minutes.
=> 10 miles /15 minutes
=> 0.67 miles /minute
=> 25 / 0.67
It will take Jay 37.31 minutes to arrive at the beach.
SO Kim will arrive first
Answer:
The correct answer is
(x + 2) (x + 1) (x - 3)
Step-by-step explanation:
Answer:
33.
Step-by-step explanation:
8x + 4y = 44
4(2x + y) = 44
2x + y = 44/4 = 11.
6x + 3y
= 3(2x + y)
= 3 * 11
= 33.
Answer:
They are dependent events. Event A is choosing one musician while Event B is choosing another musician. THey are ALL musicians, no matter what instrument they play, we just know that there are 7 musicians in total. Therefore, the events are dependent because after choosing one musician, you would have 6 musicians left, instead of 7.
Step-by-step explanation: