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:
a) When x = 2, y = 0
and when x = 3, y = 4
b) curve C
c) 2 and -1
Step-by-step explanation:
Answer:
The answer is True.
Step-by-step explanation:
- <u>Estimate the Answer Before Solving Having a general idea of a ballpark answer .</u>
- <u>Or the problem lets students know if their actual answer is reasonable or not.</u>
Ok so
x - the smallest
The other 4 are : x+1, x+2, x+3, x+4
We know that sum is 120
So
x+x+1+x+2+x+3+x+4=120
Combine like terms
5x+10=120
Subtract 10 on both sides
5x=120-10
5x=110
Divide by 5 on both sides
X=22
The third number is x+2 = 22+2=24
Answer:
g=56
Step-by-step explanation:
In similar shapes, corresponding sides are always in the same ratio.
For example,
if the sides in triangle 1 were a and b, and triangle 2 had side lengths c and d, c and a had the same ratios, and b and d had the same ratios
and triangle 1 was similar to triangle 2, the ratio between the sides of the triangles would be
a/c, which is also equal to b/d
What that means is that in this situation, 8/5=g/35.
8/5=g/35
Cross multiply.
(8)*(35)=g*(5)
280=5g
g=56