Answer:
They are known as terms in algebraic expression
Step-by-step explanation:
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)
Volume = (l * w * h) or (11 * 3 * x) which will equal surface area. Volume is 33x for now
Surface Area = 2 (x * 11) + 2 (x * 3) + 2 (11 * 3)
Set Volume equal to surface area. I simplified SA already.
33x = 22x + 6x + 66
33x - 28x = 66
5x = 66
x = 66/5 or 13.2
Answer:
Part A: x0.50 + 3 = 18.50
Part B: x0.75 + 3 - x0.10 = 21
Part C: The equations from Part A and Part B differ because of the cost of plastic cup.
Step-by-step explanation:
Let x represent the number of cup of lemonade sold. Therefore, we have:
Part A:
This situation can be represented by the following equation:
x0.50 + 3 = 18.50
Part B:
This situation can be represented by the following equation:
x0.75 + 3 - x0.10 = 21
Part C:
The equations from Part A and Part B differ because of the cost of plastic cup.
For equation from Part A, revenue is the same as profit as Sydney does incur any cost to buy plastic cup before selling her lemonade.
For equation from Part B, revenue is different from profit because Daria has to incur the cost of plastic cup which $0.10 per cup of lemonade before selling her lemonade.
