distance= rate ÷ time
time= rate ÷ distance
time= 200 km/hr ÷ 1400 km
time= 1/7 hr or 0.1428... hr
Answer:
8
Step-by-step explanation:
exponential growth
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)
Since one equation has a negative y and the other has a positive y, I'm going to use those since they cancel each other out. Before that, the two y's need to be equal to each other.
x+2y=6
x-y=3
Multiply the bottom equation by two so then you have:
x+2y=6
2x-2y=6
The y's now cancel out:
x=6
2x=6
Add them together
3x=12
Divide
x=4.
To find y, plug x into either equation (*don't have to do both, but I will)
(4)+2y=6
(4)-y=3
Subtract four
2y=2
-y=-1
Divide each
2y/2 = 2/2
y=1
-y/-1 = -1/-1
y=1
The answer is:
x=4
y=1
I hope that helps!
