Answer:
dh/dt = 0,07 ft/min
Step-by-step explanation:
The swimming pool has the shape of right circular cylinder, therefore its volume is
V(c) = π*x²*h
Where x is the radius of the base and h the height
We take differentiation on both sides of the equation to get:
dV/dt = π*x²*dh/dt
The rate of change in height of water in the pool, is independent of the height of the water, since the pool is a right crcular cylinder, and dV/dt is constant at 8 ft³/min.
Then:
8 = π*x²*dh/dt
dh/dt = 8 / π*x²
dh/dt = 8/113,04
dh/dt = 0,07 ft/min
Recipe is for 24 pieces, and required quantity is 16.
So the ratio is 16/24 = 2/3 means we need to reduce all ingredients to 2/3 of the given quantities. Not all recipes can be reduced prorata, but we will assume it can be done. A word of caution: the measurement of quantities will become awkward (like 3/8 of a teaspoon of salt, etc). The practical way is to make the full recipe, and invite friends to take home the remainder.
Here's the scaled recipe
Butter 1cup*3/4 = 3/4 cup
unsweetened chocolate = 4*3/4 = 3 squares
white sugar = 2 * 3/4 = 1 1/2 cups
eggs = 4 * 3/4 = 3 eggs
A.P. flour = 1 cup * 3/4 = 3/4 cups
vanilla extract = 1 * 3/4 = 3/4 teaspoons
salt = 1/2 * 3/4 = 3/8 teaspoons
chopped walnuts = 2 * 3/4 = 1 1/2 cups
For this reason, there is a trend to use weights (in grams) than volumes to make scaling recipes easier.
Answer:
s = 19.1
Step-by-step explanation:
Simplifying
25.3 = s + 6.2
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Solving
25.3 = 6.2 + s
Solving for variable 's'.
Move all terms containing s to the left, all other terms to the right.
Add '-1s' to each side of the equation.
25.3 + -1s = 6.2 + s + -1s
Combine like terms: s + -1s = 0
25.3 + -1s = 6.2 + 0
25.3 + -1s = 6.2
Add '-25.3' to each side of the equation.
25.3 + -25.3 + -1s = 6.2 + -25.3
Combine like terms: 25.3 + -25.3 = 0.0
0.0 + -1s = 6.2 + -25.3
-1s = 6.2 + -25.3
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Combine like terms: 6.2 + -25.3 = -19.1
-1s = -19.1
Divide each side by '-1'.
s = 19.1
Simplifying
s = 19.1
In a table it's EXAMPLE: Cars/Drivers the cars is x and the drivers is y(y-intercept). In an equation, EXAMPLE using y=mx+b the b is the y-int., and in a graph it is (x,y) the y being the y-int.
