Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Step-by-step explanation:
Since we have given that
Height = 9 inches
Diameter = 6 inches
Radius = 3 inches
So, 
Volume of cone is given by
By differentiating with respect to time t, we get that
Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie 
and h = 2 inches deep.
Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Answer:
x = 3/2 or x = -5/4
Step-by-step explanation:
Solve for x over the real numbers:
8 x^2 - 2 x - 15 = 0
Using the quadratic formula, solve for x.
x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:
x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16
Simplify radicals.
sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:
x = (2 + 22)/16 or x = (2 - 22)/16
Evaluate (2 + 22)/16.
(2 + 22)/16 = 24/16 = 3/2:
x = 3/2 or x = (2 - 22)/16
Evaluate (2 - 22)/16.
(2 - 22)/16 = -20/16 = -5/4:
Answer: x = 3/2 or x = -5/4
Part A: The probability is 1/6. This is because there are six options in total, and only one of those options is 6.
Part B: The probability is 6/6, or alternatively 100%. This is because that the probability of rolling a 6 is 1/6, and the probability of rolling any of the other options is 5/6. Adding them together gives a probability of 6/6.
Part C: The probability is 5/6. This is because there are six options, and of those, five of them are not 6.
Answer:
4x + 28.4 in.
Step-by-step explanation:
perimeter = sum of lengths of sides
perimeter = x + 2 + x + 2 + x + 2 + x + 2 + 10.2 + 10.2
perimeter = 4x + 28.4
