17) replace the given number for "x" and evaluate
a) x² + 2x + 1 ; when x = 3
3² + 2(3) + 1
= 9 + 6 + 1
= 16
b) x² + 2x + 1 ; when x = -4
(-4)² + 2(-4) + 1
= 16 - 8 + 1
= 9
c) x² + 2x + 1 ; when x = 3
(-22.872)² + 2(-22.872) + 1
= 523.128384 - 45.744 + 1
= 478.384384
18) The dependent variable is affected by the other variable and is the "output" The independent variable is the input.
a) y = 3x - 5; "x" is the independent variable
b) the time of day is the independent variable (you would input the time of day to calculate the temperature).
19) Let the x-axis represent the length of the lumber cut off and the y-axis represent the length of the lumber remaining.
Answer:
53.08 ft
Step-by-step explanation:
The pressure at the bottom of the tank, P = ρgh where ρ = density of water = 1000 kg/m³, g = acceleration due to gravity = 9.8 m/s² and h = depth of water in tank.
Since the pressure at the bottom of the tank, P = ρgh, making h subject of the formula, we have
h = P/ρg
Since P = 23 psig = 23 × 1 psig = 23 × 6894.76 Pa = 158579.48 Pa
Substituting the values of the other variables into h, we have
h = P/ρg
h = 158579.48 Pa/(1000 kg/m³ × 9.8 m/s²)
h = 158579.48 Pa/(9800 kg/m²s²)
h = 16.18 m
h = 16.18 × 1 m
h = 16.18 × 3.28 ft
h = 53.08 ft
The total cost curve shows the cost of total shipment from the different
cities.
- a. Please find attached the graph of the total cost to quantity of shipment created with MS Excel.
- b. The city that provides the lowest overall cost is; <u>Salt Lake City</u>.
Reasons:
The given parameters are;
The number of shipment per = From 550,000 to 600,000 per year
The given table is presented as follows;
![\begin{tabular}{|l|c|c|c|}Location&Annual Fixed Costs&Variable Cost \\Denver&\$5,000,000&\$4.65 \\Santa Fe&\$4,200,000&\$6.25\\Salt Lake City&\$3,500,000&\$7.25\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%7B%7Cl%7Cc%7Cc%7Cc%7C%7DLocation%26Annual%20Fixed%20Costs%26Variable%20Cost%20%5C%5CDenver%26%5C%245%2C000%2C000%26%5C%244.65%20%5C%5CSanta%20Fe%26%5C%244%2C200%2C000%26%5C%246.25%5C%5CSalt%20Lake%20City%26%5C%243%2C500%2C000%26%5C%247.25%5Cend%7Barray%7D%5Cright%5D)
a. Required:
The plot total cost curve for the locations on a single graph.
Solution:
- Please find attached the graph of the total cost curves created with MS Excel
b. Required:
The city that provides the lowest overall cost.
Solution:
The two cities with the lowest overall costs are Denver and Salt Lake City.
- From the total cost curve, the area under the curves are;
Area under the curve for Denver;
(7557500 + 7790000) ÷ 2 × 50,000 = 383687500000
Area under the curve for Salt Lake City
(7487500 + 7850000) ÷ 2 × 50,000 = 383437500000
Therefore;
- <u>Salt Lake City provides the lowest overall costs</u>.
Learn more about total cost curves here:
brainly.com/question/4888738