Answer:
Step-by-step explanation:
The first mathematician orders 1 beer, the second orders 1/2 a beer, the third orders 1/4 a beer, the fourth orders 1/8 a beer, the fifth orders 1/16 a beer. . .
- The Sequence is:
- On observation, the next term is derived through the division of the previous term by 2.
- 2 is the constant factor
- Therefore, the bartender says 'Fine, I’ll just pour you two beers.'
Therefore, if the first mathematician orders 6 beers, the second orders 2 beer, the third orders 2/3 a beer, and so on
- The sequence is
- On observation, the next term is derived through the division of the previous term by 3.
- 3 is the constant factor
- Therefore, the bartender should pour three beers.
Answer:
1. V = πr²h
2. dv/dt = πr²dh/dt
3. dv/dt = 113.04
Step-by-step explanation:
We have these information
Radius R = 3cm
Height = h
Volume = V
We have been given dh/dt = 4cm
1.
An equation relating V, r, h
Volume of cylinder = πr²h
2.
The related rates equation
dv/dt = πr²dh/dt
dv/dt = π3²dh/dt
3. Continuing from number 2 above, we have
dv/dt = π3²dh/dt
= π9x4
= 3.14x9x4
= 113.04
These are the answers to the questions
Answer:
D. tan(-π/6)
Step-by-step explanation:
The tangent function is periodic with a period of π, so ...
tan(5π/6) = tan(5π/6 ± kπ) . . . for any integer k
For k = -1, we have ...
tan(5π/6) = tan(5π/6 -π) = tan(-π/6)
Answer:
The principal amount was $23,393.45
Step-by-step explanation:
The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%
We will calculate Principal amount by this formula
Where A = amount (98,000)
P = Principal amount (P)
r = rate of interest 4.1% (0.041)
n = number of compounding interest monthly (12)
t = time (35 years)
98,000 = P(4.189386)
= 4.189386P = 98,000
P = 
P = 23,392.4494 ≈ $23,392.45
The principal amount was $23,393.45
Answer:
93 feet
Step-by-step explanation:
Let us first find the time it takes to reach the maximum height. We can do this by differentiating the height function to get velocity:
dh(t)/dt = v(t) = -32t + 72
The maximum height will occur when the velocity becomes 0. Therefore, the time it takes to reach maximum height is:
0 = -32t + 72
32t = 72
t = 72/32 = 2.25 seconds
Therefore, the maximum height of the pumpkin is:
h(2.25) = -16(2.25)^2 + 72(2.25) + 12
h(2.25) = -81 + 162 + 12
h = 93 feet
