Answer:
(A) 125 scoops
(B) 31 scoops
Step-by-step explanation:
The volume of a cup in terms of radius and height is ...
V = (1/3)πr²h
The radius is half the diameter, so the volume in terms of diameter is ...
V = (1/3)π(d/2)²h = (π/12)d²h
The number of cups it takes to empty the sink will be the sink volume divided by the cup volume, so will be ...
n = (4000π/3)/((π/12)d²h)
n = 16000/(d²h)
__
(A) The number of cups required of diameter 4 and height 8 is ...
n = 16000/(4²·8) = 125
125 scoops are required to empty the sink
__
(B) The number of cups required of diameter 8 and height 8 is ...
n = 16000/(8²·8) = 31.25 ≈ 31
31 scoops are required to empty the sink
Answer:
(9 + r)/6
Step-by-step explanation:
Answer:
Step-by-step explanation:
The motion equations that describe the ball are, respectively:
![x = \left[\left(152\,\frac{ft}{s} \right)\cdot \cos 52^{\circ} \right] \cdot t](https://tex.z-dn.net/?f=x%20%3D%20%5Cleft%5B%5Cleft%28152%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%5Cright%29%5Ccdot%20%5Ccos%2052%5E%7B%5Ccirc%7D%20%5Cright%5D%20%5Ccdot%20t)
![y = 4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{ft}{s^{2}} \right) \cdot t^{2}](https://tex.z-dn.net/?f=y%20%3D%204.5%5C%2Cft%20%2B%20%5Cleft%5B%5Cleft%28152%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%5Cright%29%5Ccdot%20%5Csin%2052%5E%7B%5Ccirc%7D%20%5Cright%5D%20%5Ccdot%20t%20-%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%2832.174%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%20%5Ccdot%20t%5E%7B2%7D)
The time required for the ball to hit the ground is computed from the second equation. That is to say:
![4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{m}{s^{2}} \right) \cdot t^{2} = 0](https://tex.z-dn.net/?f=4.5%5C%2Cft%20%2B%20%5Cleft%5B%5Cleft%28152%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%5Cright%29%5Ccdot%20%5Csin%2052%5E%7B%5Ccirc%7D%20%5Cright%5D%20%5Ccdot%20t%20-%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%2832.174%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%20%5Ccdot%20t%5E%7B2%7D%20%3D%200)
Given that formula is a second-order polynomial, the roots of the equation are described below:
and 
Just the first root offers a realistic solution. Then, .
In this question, there are 3 conditions that need to be met
1. The number is 3-digit
2. Hundreds digit >7 (number that will fulfill it would be 8 or 9)
3. The tens is 1 more than hundred( since the hundred possibilities is 8 or 9, then 9 in hundreds can't be used since no number higher than 9)
4. The one digit <2( that mean 0, 1)
Using the list above, you can make your possible number:
890
891
Hello,
-2m^3+m²-m+1=(m+1)(-2m²+3m-4) +5
We must add -5 ; the remainder will be 5-5=0.
