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:
1) 10.55%
2) 30.77%
Step-by-step explanation:
52/52•39/51•26/50•13/49 = 0.105498... ≈ 10.55%
100% chance you draw a unique card on the first draw
51 cards left of which 13(3) = 39 are unique suit for your second draw
50 cards left of which 13(2) = 26 are unique suit for your third draw
49 cards left of which 13(1) = 13 are unique suit for your forth draw.
Two balls are already green
Leaves 4 red balls in a field of 13 balls
4/13 = 0.307692... ≈ 30.77%
Answer:
Step-by-step explanation:
Multiply 2/3 and your number. If you have a whole number, convert it to a fraction by putting it over a denominator of 1. When multiplying fractions, calculate numerator times numerator, then denominator times denominator. For example, to find two-thirds of 18, multiply 2/3 x 18/1 to get 36/3.
Reduce the resulting fraction as needed by dividing it by the common denominator. For example, the common denominator of 36 and 3 is 3. Diving 36 and 3 by 3 gives you a fraction of 12/1, which is the same as 12. Thus, two-thirds of 18 is 12.
You know that we have to simplify the algebra equation, so first you have to combine x and 2x. X + 2x equals to 3x. Now that we combined x and 2x which makes 3x, we have to do 7 and -8. 7 + -8 which equals to -1. Therefore, the answer to this algebra equation is 3x + -1.