When writing an expression that represents some quantity, we’ll often turn that expression into an equation (or formula, if you like) by using a letter to represent the value of the expression. How do we know so much about the snow cone business? Because one of us used to own one! The total cost of selling snow cones is the sum of the variable cost for supplies (which you just found) and the fixed costs: These are costs that aren’t affected by the number of snow cones sold, like rent, insurance, licensing, etc. Look back at the table to find the fixed costs for this business, then use that to write an equation of the form C = _______ that represents the total cost based on x , the number of snow cones sold.
When writing an expression that represents some quantity, we’ll often turn that expression into an equation (or formula, if you like) by using a letter to represent the value of the expression. How do we know so much about the snow cone business? Because one of us used to own one! The total cost of selling snow cones is the sum of the variable cost for supplies (which you just found) and the fixed costs: These are costs that aren’t affected by the number of snow cones sold, like rent, insurance, licensing, etc. Look back at the table to find the fixed costs for this business, then use that to write an equation of the form C = _______ that represents the total cost based on x , the number of snow cones sold.
Solution Summary: The author calculates the total cost of snow cones sold by adding total combined supply costs and fixed cost.
When writing an expression that represents some quantity, we’ll often turn that expression into an equation (or formula, if you like) by using a letter to represent the value of the expression.
How do we know so much about the snow cone business? Because one of us used to own one!
The total cost of selling snow cones is the sum of the variable cost for supplies (which you just found) and the fixed costs: These are costs that aren’t affected by the number of snow cones sold, like rent, insurance, licensing, etc. Look back at the table to find the fixed costs for this business, then use that to write an equation of the form C = _______ that represents the total cost based on x, the number of snow cones sold.
Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
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