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)
<u>Answer:</u>
<u>Step-by-step explanation:</u>
<u>Let's find 'a' using Pythagoras theorem.</u>
- => 4² = 2² + a²
- => 16 = 4 + a²
- => 12 = a²
- => a = √12
- => a = √2 x 2 x 3
- => a = 2√3
- => a = 2 x √3
- => a = 2 x 1.732
- => a = 3.464 = 3.5 (Estimated)
Hoped this helped.
Answer:
Step-by-step explanation:
Random
Answer:
5
Step-by-step explanation:
<span>216,000,000
</span><span>2.2 × 10 to the 3rd power = 2.2 * 10^3 = 2,200
</span>3.1 × 10 to the 7th power = 3.1 * 10^7 = 31,000,000
<span>310,000
Increasing order:
</span>2,200 , 310,000 , 216,000,000 , 31,000,000
So increasing order with original numbers:
2.2 × 10 to the 3rd power, 310,000, <span>216,000,000, 3.1 × 10 to the 7th power</span>
