Let F(x, y, z) = (x, y, z) and let C consist of the line segment from (2,3,0) to (4,5,0) followed by the line segment from (4,5,0) to (0,0,7). (16 points) (a) Compute the line integral ∫ C F. dr. (b) Compute the line integral again, using a different method.
Answers
(a) The line integral ∫C F · dr is equal to 9.5.
(b) The line integral ∫C F · dr is equal to 8.
How to compute line integrals in two methods?(a) To compute the line integral ∫C F · dr, we need to evaluate the integral along each segment of C and then sum them up.
For the first segment of C from (2, 3, 0) to (4, 5, 0), we can parameterize the line as r(t) = (2 + 2t, 3 + 2t, 0) for t in [0, 1].
Now, we can calculate the line integral along this segment:
∫(C1) F · dr = ∫[0,1] F(r(t)) · r'(t) dt
= ∫[0,1] (2 + 2t, 3 + 2t, 0) · (2, 2, 0) dt
= ∫[0,1] (4 + 4t + 6 + 4t) dt
= ∫[0,1] (10 + 8t) dt
= [10t + 4t\(^2\)] evaluated from 0 to 1
= 10 + 4 - 0 - 0
= 14
For the second segment of C from (4, 5, 0) to (0, 0, 7), we can parameterize the line as r(t) = (4 - 4t, 5 - 5t, 7t) for t in [0, 1].
Now, we can calculate the line integral along this segment:
∫(C2) F · dr = ∫[0,1] F(r(t)) · r'(t) dt
= ∫[0,1] (4 - 4t, 5 - 5t, 7t) · (-4, -5, 7) dt
= ∫[0,1] (-16 + 20t - 35t) dt
= ∫[0,1] (-16 - 15t) dt
= [-16t - (15/2)t\(^2]\) evaluated from 0 to 1
= -16 - (15/2) - 0 + 0
= -31/2
Therefore, the line integral ∫C F · dr is the sum of the integrals along each segment:
∫C F · dr = ∫(C1) F · dr + ∫(C2) F · dr
= 14 + (-31/2)
= 9.5.
(b) To compute the line integral using a different method, we can break down the line integral into two separate line integrals along each segment of C.
First, we calculate the line integral along the first segment from (2, 3, 0) to (4, 5, 0):
∫(C1) F · dr = ∫(C1) (x, y, z) · (dx, dy, dz)
= ∫[2,4] (x, y, 0) · (dx, dy, 0)
= ∫[2,4] x dx + ∫[2,4] y dy + ∫[2,4] 0 dz
= [x^2/2] evaluated from 2 to 4 + [y\(^2\)/2] evaluated from 3 to 5 +0
= (16/2 - 4/2) + (25/2 - 9/2) + 0
= 8
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Related Questions
Suppose there are five processes, their arrival time and running time are listed as follows. Adopt FCFS and SJF, respectively, give the schedule order and average waiting time. (12) 1) Give the schedule order of FCFS. (3) 2) Compute the average waiting time of FCFS. (3) Give the schedule order of SJF. (3) 3) 4) Compute the average waiting time of SJF. (3) Process Arrival time Running time Pl 0 3 P2 3 10 P3 4 6 P4 5 1
Answers
Average waiting time for FCFS: 8.75
SJF schedule order: Pl -> P4 -> P3 -> P2Average waiting time for SJF: 4.75
To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:
Schedule order for FCFS:
The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:
Pl -> P2 -> P3 -> P4
Average waiting time for FCFS:
To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.
Process | Arrival Time | Running Time | Waiting Time
Pl | 0 | 3 | 0
P2 | 3 | 10 | 3
P3 | 4 | 6 | 13
P4 | 5 | 1 | 19
Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75
Therefore, the average waiting time for FCFS is 8.75.
Schedule order for SJF:
The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:
Pl -> P4 -> P3 -> P2
Average waiting time for SJF:
To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.
Process | Arrival Time | Running Time | Waiting Time
Pl | 0 | 3 | 0
P4 | 5 | 1 | 3
P3 | 4 | 6 | 6
P2 | 3 | 10 | 10
Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75
Therefore, the average waiting time for SJF is 4.75.
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Remove all perfect squares from inside the square root. √20 = urgent need help now first actual answer gets the thingy
Answers
Answer:
\(2\sqrt{5}\)
Step-by-step explanation:
\(\sqrt{20}\)
20 can be written as a product of 4 and 5.
\(\sqrt{4 \times 5}\)
4 is a perfect square.
\(\sqrt{4} \times \sqrt{5}\)
Square root of 4 is 2.
\(2 \times \sqrt{5}\)
A pair of shoes cost $50. You have a coupon for 20% off. What is the total cost of
the shoes after 5% sales tax is included?
Answers
Explanation:
20% off means you pay only 80%
80%*50$=0.8*=40$
5% tax:*40=0.05*40$=$2.00 tax
$40.00+$2.00=$42
Compute S_{4} (the 4th partial sum) of the following series. S=\sum_{n=1}^{\infty}\frac{1}{1 n^5} Answer: Estimate the error in using S_{4} as an approximation of the sum of the series. (i.e. use \int_{4}^{\infty} f(x)\, dx \geq R_{4} Answer: Use n = 4 and S_n + \int_{n+1}^{\infty} f(x)\, dx \leq S \leq S \leq S_n + \int_{n}^{\infty} f(x)dx to find a better estimate of the sum.Answer :
Answers
The series estimate of the sum is between 1.000020993 and 1.000031132.
Compute the 4th partial s4 given series is S = \(1/1^5 + 1/2^5 + 1/3^5\) + ...?The given series is S = \(1/1^5 + 1/2^5 + 1/3^5\) + ...
We need to compute the 4th partial sum S4.
S4 =\(1/1^5 + 1/2^5 + 1/3^5 + 1/4^5\)
Using a calculator, we get:
S4 ≈ 1.000015873
To estimate the error in using S4 as an approximation of the sum of the series, we can use the integral test. Let f(x) = 1/\(x^5\).
Then, ∫f(x) dx from 4 to ∞ = ∫(1/\(x^5\)) dx from 4 to ∞
= [-1/(\(4x^4\))] from 4 to ∞
= (1/\(4^4\)) - (1/∞)
= 1/256
Since f(x) is positive, decreasing, and continuous for x ≥ 1, the integral test applies and we have:
S - S4 = ∫f(x) dx from 4 to ∞
≥ 1/256
Therefore, the error in using S4 as an approximation of the sum of the series is at least 1/256.
To find a better estimate of the sum, we can use the following inequality:
S_n + ∫f(x) dx from n+1 to ∞ ≤ S ≤ S_n + ∫f(x) dx from n to ∞
where Sn is the nth partial sum of the series.
For n = 4, we have:
S4 + ∫f(x) dx from 5 to ∞ ≤ S ≤ S4 + ∫f(x) dx from 4 to ∞
Substituting the values, we get:
1.000015873 + ∫(1/\(x^5\)) dx from 5 to ∞ ≤ S ≤ 1.000015873 + ∫(1/\(x^5\)) dx from 4 to ∞
Simplifying the integral, we get:
1.000015873 + [(1/\(4^4\)) - (1/5^4)] ≤ S ≤ 1.000015873 + (1/\(4^4\))
Solving for the bounds, we get:
1.000015873 + 0.00000512 ≤ S ≤ 1.000015873 + 0.000015259
1.000020993 ≤ S ≤ 1.000031132
Therefore, a better estimate of the sum is between 1.000020993 and 1.000031132.
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Can someone help me out the first one, please! Also ignored what I wrote in the paper.
Answers
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have a nice day!
Homework due April 4th Round River is a town shaped like a circle with a diameter of 6 miles with a river flowing in a straight line through the center of town. The people of Round River prefer to live close to the river, so the population density at any point in town is given by the formula p(d) = 300(3 – d)2 people per square mile, where d is the distance to the river measured in miles. Find and evaluate an integral for the total population of Round River.
Answers
The total population of Round River is 5400π people
To find the total population of Round River:
We need to integrate the population density function over the entire town.
Since Round River is shaped like a circle, we can use the formula for the area of a circle to express the integral in terms of the diameter:
A = πr^2
A = π(3)^2
A = 9π
where r is the radius of the circle, which is half the diameter of 6 miles.
Now we can express the integral as follows:
Total Population = ∫p(d) dA
where dA is the differential element of area in terms of distance d.
For a circular region, dA = 2πr * dr, where dr is the differential element of distance.
Substituting for r and simplifying, we get:
Total Population = ∫p(d) 2π(3) * dr
Total Population = 6π ∫300(3 – d)^2 dr
Now we can integrate the function with respect to d, using the power rule:
Total Population = 6π * 300 ∫(9 – 6d + d^2) dr
Total Population = 6π * 300 [(9r – 3r^2 + (1/3)r^3) + C]
where C is the constant of integration.
Since we are evaluating the integral over the entire circle, the limits of integration are 0 and 3:
Total Population = 6π * 300 [(9(3) – 3(3)^2 + (1/3)(3)^3) - (9(0) – 3(0)^2 + (1/3)(0)^3)]
Total Population = 6π * 300 [(27 – 27 + 3) - 0]
Total Population = 5400π
Therefore, the total population of Round River is 5400π people.
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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
Answers
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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Find the value of the variables in the table.
x
n
4
6
10
12
y
1
9
m
21
25
Answers
Answer:
n=0 , m= 13 A
Step-by-step explanation:
Suppose that shares of Walmart rose rapidly in price from $45 to $100 as a result of a doubling of corporate profits. Later, they fell to $60 at which point some investors will buy, figuring it must be a bargain (relative to the recent $100). Such investors are displaying which bias? a) Recency b) Anchoring c) Representativeness d) Confirmation Previous Page Next Page Page 3 of 6
Answers
The bias displayed by investors who consider the $60 price a bargain relative to the recent $100 price is: b) Anchoring
Anchoring bias refers to the tendency to rely heavily on the first piece of information encountered (the anchor) when making decisions or judgments. In this case, the initial anchor is the high price of $100, and investors are using that as a reference point to evaluate the $60 price as a bargain. They are "anchored" to the previous high price and are influenced by it when assessing the current value.
Anchoring bias is a cognitive bias that affects decision-making processes by giving disproportionate weight to the initial information or reference point. Once an anchor is established, subsequent judgments or decisions are made by adjusting away from that anchor, rather than starting from scratch or considering other relevant factors independently.
In the given scenario, the initial anchor is the high price of $100 per share for Walmart. When the price falls to $60 per share, some investors consider it a bargain relative to the previous high price. They are influenced by the anchor of $100 and perceive the $60 price as a significant discount or opportunity to buy.
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Take a look at the picture below and follow the rules using the STRATEGY, you need to draw the strategy to get the answer. brainliest will be given to the first person using this with the strategy it tells you to use in the picture.
Thank you
Answers
I would say (I am abbreviating square root to sqrt)
1. 4 sqrt(8488) = 4 sqrt(2x2x2122) = 8 sqrt(2122)
2. 3 sqrt(6936) = 3 sqrt(6x34x34) = 102 sqrt (6)
3. 2 sqrt(8648) = 2 sqrt(2x2x2162) = 4 sqrt(2162)
BioWare made 16 games in 8 years. How many games per year is BioWare able to make?
Answers
Answer:
1 every 2 years
Step-by-step explanation:
8x2=16 A game is made every other year
What is the side length of a square with the same area as the rectangle
Answers
Answer:
Down Below
Step-by-step explanation:
A rectangle and a square have the same area. The length of the rectangle is 48 meters more than two times its width. The length of a side of the square is 48 meters. The side of the square is 72 meters less than five times the width of the rectangle.
Answer:
wait what
Step-by-step explanation:
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet. a) what is the area of the parcel of land? area
Answers
The area of the parcel of land is 226934.799 square feet.
Given:
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet.
a).
Let a = 590 , b = 980, c = 1423 lengths
s = semi-perimeter
= 1/2(a+b+c)
= 1/2(590+980+1423)
= 1496.5
s-a = 1496.5-590
= 906.5
s-b = 1496.5-980
=516.5
s-c = 1496.5-1423
= 73.5
Heron's formula for area:
A = \(\sqrt{(s(s-a)(s-b)(s-c))}\)
= √1496.5(906.5)(516.5)(73.5)
= √51499402997.4
≈ 226934.799
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Anyone know the correct answer for the measure of angle B?
Answers
Answer:
∠B = 64.62°
Step-by-step explanation:
cos B = 3/7 = 0.4286
∠B = 64.62°
the accompanying observations are precipitation values during march over a 30-year period in minneapolis-st. paul. 0.31 0.48 0.51 0.58 0.78 0.82 0.82 0.89 0.97 1.17 1.19 1.21 1.32 1.36 1.44 1.52 1.61 1.73 1.86 1.88 1.96 2.04 2.11 2.19 2.49 2.82 2.99 3.08 3.36 4.76
Answers
Over the 30 year period, the values of Minneapolis and St. Paul's values will be: Mean 1.580666667 1.769333333 and Standard Deviation 0.890741799 1.123161779
Using the R software or any other graphing software and typing in the, we get the graphs.
The commands were
qqnorm(c(0.32,0.52,0.77,0.81,0.96,1.2,1.31,1.43,1.62,1.87,1.95,2.1,2.48,3,3.37)) and qqnorm(c(0.47,0.59,0.81,0.9,1.18,1.2,1.35,1.51,1.74,1.89,2.05,2.2,2.81,3.09,4.75))
We see there's a slight difference between the two graphs.
For Minneapolis, the curve goes upwards to 0.4
and the for St. Paul the curve goes downwards to 0.4
The term "mean" refers to the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of means that can be computed. By adding all of the numbers in a set and dividing by the total number of numbers in the set, the arithmetic mean is determined. The standard deviation is a measurement of how widely distributed or how much a group of data differ. A low standard deviation indicates that the values typically tend to be close to the set mean, while a high standard deviation suggests that the values are dispersed over a wider range.
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Let R be a relation on the set of all integers such that aRb if and only if 3a - 5b is even. 1) Is R reflexive? If yes, justify your answer; if no, give a counterexample. 2) Is R symmetric? If yes, justify your answer; if no, give a counterexample. Hint: 3b - 5a = 3a - 5b + 86-8a 3) Is R anti-symmetric? If yes, justify your answer, if no, give a counterexample. 4) Is R transitive? If yes, justify your answer, if no, give a counterexample. 5) Is R an equivalence relation? Is R a partial order? Justify your answer
Answers
R is not reflexive. To show this, we need to find an integer a such that a is not related to itself under R. Let a = 1, then 3a - 5a = -2, which is not even. Therefore, 1R1 is not true, and R is not reflexive.
R is not symmetric. To show this, we need to find integers a and b such that aRb but bRa is not true. Let a = 1 and b = 2, then 3a - 5b = -13, which is odd. Therefore, 1R2 is false. However, 3b - 5a = 1, which is also odd, so 2Ra is false. Therefore, R is not symmetric.
R is anti-symmetric. To show this, we need to show that if aRb and bRa, then a = b. Suppose 3a - 5b and 3b - 5a are both even. Then we can write 3a - 5b = 2k and 3b - 5a = 2m for some integers k and m. Adding these equations gives 2a - 2b = 2(k + m), or a - b = k + m, which is even. Therefore, aRb and bRa implies that a = b, and R is anti-symmetric.
R is transitive. To show this, suppose aRb and bRc, then 3a - 5b and 3b - 5c are both even. We can write 3a - 5b = 2k and 3b - 5c = 2m for some integers k and m. Substituting the first equation into the second gives 3a - 5c = 3b - 5b - 5c = -2b - 5c + 10b = 8b - 5c = 2(4b - 5c/2) = 2n for some integer n. Therefore, aRc, and R is transitive.
R is not an equivalence relation because it is not reflexive and not symmetric. However, R is a partial order because it is anti-symmetric and transitive.
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Write an equation for a function using..
Sine curve with a period of 8π
Amplitude of 3
Left phase shift of π/4
Vertical translation down 2 units.
f(x) =
Answers
Equation for a function f(x) = 8π.
The function of a sine curve with the period of 8π, amplitude of 3, left phase shift of π/4, and vertical translation down 2 units can be represented by the following equation:
f(x) = -3sin [ (π/4) - (2π/8π) (x) ] - 2 where, f(x) is the function-3 is the amplitude of the function-2 is the vertical translation π/4 is the left phase shift
The period of the function can be calculated as:
T = 2π/b = 2π/[(2π/8π)] = 8
Therefore, the period of the function is 8π.
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not sure how to work this out pleaseeee help!!:
A child who weighs 14kg needs to be given 15mg of paracetamol for every 2kg of body weight.
Every 10mL of a particular medicine contains 120mg of paracetamol.
What is the correct dosage?
Answers
14/2 = 7
7 x 15 mg = 105mg
120mg divided by 10mL = 12mg (per 1mL)
105 divided by 12 = 8.75mL
Answer is 8.75 mL
A class is divided into teams for small group work. There are six tearns and each has five students. Use the equation (s)/(5)=6 to find the total number of students in the class. A 11 students B 25 students C 30 students D 3 students
Answers
The correct answer is C) 30 students i.e the total number of students in the class is 30.
To find the total number of students in the class, we can solve the equation (s) / 5 = 6, where (s) represents the total number of students.
Multiplying both sides of the equation by 5, we get:
s = 5 * 6
s = 30
Therefore, the total number of students in the class is 30.
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A ribbon measures
4.5 meters. Express this length in millimeters.
Answers
Answer:
4500 meters.
Step-by-step explanation:
1 meter = 1000 millimeters so just do the number of meters (in this case 4.5) times 1000.
Help me please. I need to find the length of jk and jp and compare the lengths
Answers
d = √(x2-x1)^2 + (y2-y1)^2 where d is distance and (x1, y1) and (x2, y2) are coordinates of the beginning and end of a line segment.
To find the distance of segment JL, plug the coordinates (1, -1) and (2, 4) into the distance formula:
d = √(2-1)^2 +(4+1)^2
d = √1+25
d = √26 = 5.099 units
To find the distance of segment JK, plug the coordinates (2,4) and (7,8) into the distance formula.
d = √(7-2)^2+(8-4)^2
d = √25+16
d = √41 = 6.403 units
The length of segment JK is 6.403 units. The links of segment JL is 5.099 units. Segment JK is longer than segment JL.
Graph.
y > x2 + 2x-9
Please help!!
Answers
Answer:
I can't see all the pics properly but the graph looks like this:
Step-by-step explanation:
First, find the length of each edge of the cube one side is 3
Answers
Therefore, the length of each edge of the cube is 3 units
Somebody help me please with this question!!
Answers
Make W the subject of the formula.
y-aw=2w-1
Please help.
Answers
Answer:
w=(y+1)/(2+a)
Step-by-step explanation:
Answer:
w=(y+1)/(2+a)
first you isolate w because u have to make 'w' the subject and bring all the value with w to one side of the equation and start eliminating those values then u will end with w as the subject
Plzzz help me 10 min left
Answers
Answer:
D
Step-by-step explanation:
The opposite of negative is positive therefore,
the opposite of -2 is positive 2.
2 is locaded at D.
Find the diameter of each circle.
Answers
Answer:
Diameter Length: ( About ) 5.4 km; Option B
Step-by-step explanation:
~ Let us apply the Area of the Circle formula πr^2, where r ⇒ radius of the circle ~
1. We are given that the area of the circle is 22.9 km^2, so let us substitute that value into the area of the circle formula, solving for r ( radius ) ⇒ 22.9 = π * r^2 ⇒ r^2 = 22.9/π ⇒ r^2 = 7.28929639361.... ⇒
radius = ( About ) 2.7
2. The diameter would thus be 2 times that of the radius by definition, and thus is: 2.7 * 2 ⇒ ( About ) 5.4 km
Diameter Length: ( About ) 5.4 km
how to write -9/14 in simplest form
Answers
Answer:
Step-by-step explanation:
-9/14=3*3/2*7
so, there are no common factors. -9/14 is the simplest form.
Write the mathematical model and use Solver to answer the following question:
A farm co-op has 6,000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,501 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $75 for corn and $40 for soybeans. Round your answer to the nearest cent if necessary.
a. $210,000.00
b. $393,750.00
c. $371,255.83
d. $180,004.44
e. $318,744.17
Answers
The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.
To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.
Let x be the number of acres of corn and y be the number of acres of soybeans.
1. Total acre constraint: x + y ≤ 6,000
2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501
3. Labor constraint: 0.75x + y ≤ 5,250
The objective function to maximize is the profit function: P(x,y) = 75x + 40y
Now, we will use the Solver to find the maximum profit:
Step 1: Set up a spreadsheet with the constraints and the objective function.
Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.
Step 3: Set the objective function by selecting the cell with the profit function.
Step 4: Choose "Max" for the objective.
Step 5: Add the constraints by selecting the corresponding cells.
Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.
After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83
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n C (x) = 0.6x² − 168x+17,507. What is the minimum unit cost?
-
Answers
Step-by-step explanation:
Answer:
Minimum Unit Cost = $14,362
Step-by-step explanation:
The standard form of a quadratic is given by:
ax^2 + bx + c
So for our function, we can say,
a = 0.6
b = -108
c = 19,222
We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a
So,
-(-108)/2(0.6) = 108/1.2 = 90
Plugging this value into original function would give us the minimum (unit cost):