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:
Step-by-step explanation:
Before adding we require the fractions to have a common denominator
The lowest common denominator of 2, 5 and 3 is 30, thus
+ 
+ 
= 
+ 
+ 
Add the numerators leaving the denominator
= 
=
In looking at it I would guess it is asking which of the points is on the line? To answer that you would have to take each point an plug it into the equation and see if it is true.
3x - 7 = y
A(9,20)
3(9) - 7 = 20
27 - 7 = 20
20 = 20 True - this point is on the line
B(5,0)
3(5) - 7 = 0
15 - 7 = 0
8 = 0 False - this point is not on the line
C(3,2)
3(3) - 7 = 2
9 - 7 = 2
2 = 2 True - this point is on the line
I hope this helps
Let's say that FH and EG intersection is O,
So we have the following:
OF = 2
OH = 5
Just because F and H are midpoints it means that EO = OG = x
And as it's given the area S=35
On the other hand
S = OF*OG/2 + OG*OH/2 + OH*OE/2 + OE*OF/2 = 2*x/2 + x*5/2 + 5*x/2 + x*2/2 = 2*x + 5*x = 7*x = 35
7x = 35 so x = 35/7 = 5
Answer: 5 units
Answer:
2>x
y>-1
Step-by-step explanation:
assume y=0 when finding x and vice versa
