Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
A. multiplication is your answer.
Decimal: Divide 16 by 25: 0.64
Percent: move the decimal 2 places to the left: 64, then add a percent sign: 64%
Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Differentiate</u>
- [Function] Derivative Rule [Product Rule]:
- Rewrite [Derivative Property - Multiplied Constant]:
- Basic Power Rule:
- Arctrig Derivative:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Write an inequality to describe the region is x < 0 < 3
Inequalities in three dimensions:
When an inequality representing a region in three dimensions contains only one of the three variables, then the other two variables have no restrictions. We use inequalities to describe solid regions in three dimensions.
Answers and Explanation:
The y z - plane is represented by the equation x = 0
As the region is between this plane and the vertical plane x = 3, we will get the inequality 0 < 0 < 3
Thus, the desired inequality is
0 < 0 < 3.
Learn more about inequalities at:
brainly.com/question/14408811
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