Answers
Answer: The input is the x variable and the output is the y variable, so the equation is y=0 which is just a line on the x axis
**the thicker line in the picture is what the line should look like.
Related Questions
what does a researcher do with the mixed significance results he or she may have found in a multiple regression analysis?
Answers
The researcher will Eliminate the nonsignificant independence variable and rerun the regression.
Meaning of multiple regression analysis: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables. The objective of multiple regression analysis is to use the independent variables whose values are known to predict the value of the single dependent value.
When modeling the relationship between a single response variable and multiple regressor variables, multiple regression analysis is used.
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need help with this Drag the points to create graphs of linear relationships that have different y-intercepts and slopes of 1/5, 3/5, and 6/5.
Answers
Linear relationships that have different y-intercept and slope of 1/5 is y=1/5 x+25/6.
Given that, the slopes are 1/5, 3/5 and 6/5.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The coordinate points from the given figure are (6, 5), (5, 1) and (4, 3).
Substitute m=1/5 and (x, y)=(6, 5) in y=mx+c, we get
5=1/5 ×6+c
⇒ c=5- 5/6
⇒ c=25/6
Put m=1/5 and c=25/6 in y=mx+c, we get
y=1/5 x+25/6
Substitute m=3/5 and (x, y)=(5, 1) in y=mx+c, we get
1=3/5 ×5+c
⇒ c=-2
Put m=3/5 and c=-2 in y=mx+c, we get
y=3/5 x-2
Substitute m=6/5 and (x, y)=(4, 3) in y=mx+c, we get
3=6/5 ×4+c
⇒ c=3-24/5
⇒ c= -9/5
Put m=6/5 and c= -9/5 in y=mx+c, we get
y=6/5 x-9/5
Therefore, linear relationships that have different y-intercept and slope of 1/5 is y=1/5 x+25/6.
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[tex]2\frac{--80}{4} -14[/tex]
Answers
The value of the expression given as 2 - (80/4) - 14 when evaluated is -32
How to evaluate the expression?From the question, we have the following parameters that can be used in our computation:
2--80/4-14
To start with, we need to represent the expressions properly
This can be done with the use of brackets
So, we have the following representation
2 - (80/4) - 14
Solving further, we need to evaluate the expression in the bracket
This gives
2 - (80/4) - 14 = 2 - (20) - 14
Next, we remove the bracket
So, we have the following representation
2 - (80/4) - 14 = 2 - 20 - 14
Evaluate the difference
So, the expression becomes
2 - (80/4) - 14 = -18 - 14
Evaluate the last difference
So, the expression becomes
2 - (80/4) - 14 = -32
Hence, the solution is -32
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How many units are in a square?.
Answers
A unit square is a square with sides measuring 1 unit, while a square unit is a unit of measurement.
What are Square Units?
In geometry, a square unit can be defined as the metric unit used to measure area for example the area of this rectangle is measured in square units using unit squares.
Also, the square is an Imperial unit of area that is used in the construction industry, 1 square is equal to 100 square feet.
In the system of measurement, some commonly used square units can be square centimeter (cm²), square meter (m²), and square kilometer (km²).
Thus, a square unit is a unit of measurement where as a unit square is a square with sides measuring 1 unit.
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What type of number is the square root of 40?
Answers
Answer:
Irrational
Step-by-step explanation:
40 is not a perfect square.
Answer:
irrational
Step-by-step explanation:
40 isnt a perfect square where if you want to know weather it is or not you put the square root of any number on the calculator and if it's the same answer or in the answer there is a square root then it is an irrational number
The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that
the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses
are
a. H0: u < 40.1 Ha: u >= 40.1
b. H0: u => 40.1 Ha: u < 40.1
c. H0: u > 40.1 Ha: u <= 40.1
d. H0: u = 40.1 Ha: u =/= 40.1
b. H0: u => 40.1 Ha: u < 40.1
Answers
The null and alternative hypothesis are:
H₀ : µ = 40.1
Hₐ : µ < 40.1
If we want to test the claim that there is a reduction in the average work week, the null hypothesis should state:
- The alternative hypothesis should state the claim: there is a reduction in the average work week. This can be written as the true mean is less than 40.1
- The null hypothesis should state the oposite of the alternative hypothesis: that there is no significant reduction in the average work week. This can be written as the true mean is equal to 40.1.
Then, the null and alternative hypothesis are:
H₀ : µ = 40.1
Hₐ : µ < 40.1
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Apply the Gram-Schmidt orthonormalization process to transform the given basis for Rn into an orthonormal basis. Use the Euclidean inner product for Rn and use the vectors in the order in which they are given. B = {(0, 0, 7), (0, 1, 1), (1, 1, 1)}
Answers
To apply the Gram-Schmidt orthonormalization process, we first need to calculate the projection of the first vector onto the other two vectors.
What are vectors?Mathematics' version of a vector is an entity with both magnitude and direction. On a graph, they can be seen as arrows, with the length of the arrow denoting magnitude and the direction denoting direction. The movement or velocity of an item, as well as its acceleration or force, are frequently described by vectors in physics. They may also be used in geometry to represent how far an item has moved from one point to another. Vectors can be added and subtracted, as well as their magnitude multiplied or divided by a scalar. They are a crucial resource for comprehending and examining the motion of things in space.
How to solve?
p = (u * v) / (v * v) * v
For the first vector (0, 0, 7)
p1 = (0, 0, 7) * (0, 1, 1) / (0, 1, 1) * (0, 1, 1) * (0, 1, 1) = 0 * (0, 1, 1) = (0, 0, 0)
p2 = (0, 0, 7) * (1, 1, 1) / (1, 1, 1) * (1, 1, 1) * (1, 1, 1) = 0 * (1, 1, 1) = (0, 0, 0)
Therefore, the orthogonal component of the first vector is (0, 0, 7) - (0, 0, 0) - (0, 0, 0) = (0, 0, 7).
Next, p = (u * v) / (v * v) * v
For the second vector (0, 1, 1), we have:
p = (0, 1, 1) * (1, 1, 1) / (1, 1, 1) * (1, 1, 1) * (1, 1, 1) = 1 * (1, 1, 1) = (1, 1, 1)
Therefore, the orthogonal component of the second vector is (0, 1, 1) - (1, 1, 1) = (-1, 0, 0).
Finally, |u| = sqrt(u * u)
For the first vector (0, 0, 7), we have:
|(0, 0, 7)| = sqrt((0, 0, 7) * (0, 0, 7)) = sqrt(0 + 0 + 49) = 7
Therefore, the normalized vector is (0, 0, 1).
For the second vector (-1, 0, 0), we have:
|(-1, 0, 0)| = sqrt((-1, 0, 0) * (-1, 0, 0)) = sqrt(1 + 0 + 0) = 1
Therefore, the normalized vector is (-1, 0, 0).
Therefore, the orthonormal basis for R3 is {(0, 0, 1), (-1, 0, 0), (1, 1, 1)}.
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the graphical solution to a linear programming problem can only be used when there are two part 2 a. objective functions. b. constraints. c. available resources. d. decision variables.
Answers
The correct option d. decision variables; is used to find the the graphical solution to a linear programming problem.
Define the term decision variables?An uncertain in an optimization method is a choice variable. It has a domain, that is an condensed representation of the entire set of the variable's potential values.
The types of decision variables are references to objects, whose precise nature is determined by the model's underlying optimizer.The quantities which that decision makers need to know are described by decision variables. They are the variables in a model for mathematical programming. Usually, we will use an optimization technique to find the best values for them.These are the unknowables that the LPP solution is supposed to approximate as an output. All linear programming issues seek to maximize as well as minimize any numerical value that represents revenue, expenditure, output volume, etc.Thus, a linear programming problem's graphical solution is found using decision variables.
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two long parallel wires are a center-to-center distance of 4.80 cm apart and carry equal anti-parallel currents of 4.10 a. find the magnitude of the magnetic field at the point p which is equidistant from the wires.
Answers
the magnitude of the magnetic field at the point p which is equidistant from the wire is 170.833*10^-7
Given ,
Current = 4.10 I
Resistance = 4.80cm = 0.048m
Constant = 4π*10^-7 h/m
To determine magnetic field
B=μ*I / 2πR
= 4π*10^-7 * 4.10 / 2π * 0.048
=8.20*10^-7 / 0.048
= 170.833*10^-7
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The data for the number of hand-held gaming devices sold for the past 5 weeks are 15 units, 20 units, 25 units, 30 units, and 17 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three-period moving average forecast for week 6 is ________.a. 24 unitsb. 17 unitsc. 20 unitsd. 30 units
Answers
Setting k = 3, the three-period moving average forecast for week 6 is 24 (option A)
A moving average method is a time series average that moves through the series by replacing the last term of the previous averaged group and adding the next term in each consecutive average.
A moving average of an order n, k = n, is calculated as:
(x₁ + x₂ + ... + xₙ) / n
The given data is:
Week Number of units sold
1 15
2 20
3 25
4 30
5 17
Using k = 3 means the order of the moving average is 3, hence
forecast for week 6 = (25 + 30 + 17) / 3 = 24 (option A)
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There are 7 children that are taking turns using the swing on a playground. How many different ways are there in which they each can use the swing where everyone gets exactly one turn? roscoe has 15 books on his summer reading list. He wants to choose 6 books to read in order from first to last. In how many ways can he do this? the student council has 15 students. They need to choose a president, vice president, secretary and treasurer for student council. In how many ways can the 4 different positions be appointed from the 15 students? thomas is creating a 7 digit passcode using the digits 0 through 9. How many 7 digit passcodes are possible if the numbers cannot be repeated?
Answers
The number of different ways for all 4 conditions is 5040 ways, 3603600 ways, 32760 ways, and 604800 ways respectively.
What are permutation and combination?
A permutation is an orderly arrangement of objects or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
First condition,
The number of ways to take turns for 7 children is:
= Permutation of 8 children
= 7!
= 5040 ways
Second condition,
The number of ways to select 6 from 15 and in order is computed as the number of permutations of 15 books taken 6 at a time
= 15*14*13*12*11*10
= 3603600 ways
Third condition,
The number of ways to choose 4 different positions from 15 students is:
= Number of permutation of 15 students taken 4 at a time
= 15*14*13*12
= 32760 ways
Last condition,
The numbers cannot be repeated here, the number of permutations of 10 digits taken 7 at a time is:
= 10*9*8*7*6*5*4
= 604800 ways
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f(x) = 3x² + 6x - 5
g(x) = 4x³ - 5x² +6
Find (f + g)(x).
O A. (f+g)(x) = -4x³ + 8x² + 6x − 11
B. (f+g)(x) = 4x³ + 3x² + 11x + 1
O c. (f+g)(x) = 7x³ + x² + 1
O D. (f+g)(x) = 4x³ - 2x² + 6x +1
Answers
4x^3 -2x^2 + 6x +1
1, 5, 4, 7, 3, 7, 9, 2. if the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3. the correct answer is
Answers
The Correct answer is 27
Odd number are the numbers that are not multiple 2 and cannot be divided into two parts equally.
For examples: 3 , 5 , 7, 9,11 . . . . .
According to the question,
If the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3.
Sequence of the number is 1, 5, 4, 7, 3, 7, 9, 2
where 1 , 5 , 7 , 7 ,9 are odd numbers
The third odd number is 7 which is greater than 6
according to question we have to multiple 9 by 3
= 9 × 3
= 27
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slider owns a hamburger restaurant. slider's minimum average variable cost is $10 at a quantity of 100 hamburgers, and his minimum average total cost is $15 at a quantity of 200 hamburgers. his total fixed cost is $300 . use this information to answer the questions.
Answers
When he sells 200 hamburgers, the AVC is $13.5.
The average cost curve starts to rise when there are 250 hamburgers produced.
Given info,
Slider is the proprietor of a burger joint. For a quantity of 100 hamburgers, the slider's minimal average variable cost is $10, and for a quantity of 200 hamburgers, his minimum average total cost is $15. He has a $300 total fixed cost. Use his knowledge to respond to the questions.
Let,
Minimum average variable cost (AVC) = $10, when Q = 1 in00 hamburgers Minimum average cost (AC) = $15, when Q = 200 hamburgers
Fixed cost = $300
To compute the AVC when Q = 200 hamburgers, first compute Total cost (TC) as follows,
TC = AC * Q
= 15 * 200
= 3,000
Now, subtract fixed cost from TC that results variable cost (VC) as follows;
VC = TC - fixed cost
= 3,000 - 300
= 2,700
Now, compute the AVC when Q = 200 hamburgers as follows,
AVC = VC / Q
= 2,700 / 200
= 13.5
Hence, the AVC when he sells 200 hamburgers is $13.5
At a quantity of 250 hamburgers, the average cost curve is increasing.
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Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows:Game and Probability of Win Game 1 : 0.7 Game 2 : 0.45 Game 3 : 0.49 Game 4 : 0.55 Game 5 : 0.47 Game 6 : 0.45 Game 7 : 0.6Set up a spreadsheet simulation model for which whether Atlanta wins or loses each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.What is the average number of games played regardless of winner? If required, round your answer to one decimal place.
Answers
For each part of Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games, a detailed description has been provided down.
What do we understand by the term Probability?Probability is a way to gauge how likely something is to happen. Usually, it is stated as a number between 0 and 1, with 0 denoting impossibility and 1 showing certainty. Probability, which is founded on the idea of randomness, is frequently used in statistics, gaming, and other disciplines to forecast and evaluate the possibility of particular occurrences. The number of successful outcomes is divided by the total number of possible outcomes to determine probability. A coin flip, for instance, has a 50% chance of landing on heads. Probability is a crucial decision-making tool because it allows us to recognise and measure uncertainty in our surroundings.
How to solve?
To set up a spreadsheet simulation model for the World Series, we can create a table with columns for each game and the probability of Atlanta winning each game. We can then use the RAND function in Excel to generate random numbers between 0 and 1 for each game. If the random number generated is less than the probability of Atlanta winning the game, we can assume that Atlanta wins that game. We can then repeat this process for a large number of iterations to obtain the probability of Atlanta winning the World Series.
To calculate the probability that the Atlanta Braves win the World Series, we can sum the number of iterations in which Atlanta wins the World Series and divide it by the total number of iterations. For example, if we run the simulation 1000 times and Atlanta wins the World Series in 550 iterations, the probability that the Atlanta Braves win the World Series is 0.55.
To calculate the average number of games played regardless of the winner, we can sum the number of games played in each iteration and divide it by the total number of iterations. For example, if the simulation is run 1000 times and the number of games played in each iteration is as follows: 4, 5, 4, 6, 5, 4, 4, 6, 5, 4, the average number of games played is 4.7 (i.e. 47/10).
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from a point along a straight road, the angle of elevation to the top of a hill is . from farther down the road, the angle of elevation to the top of the hill is . how high is the hill? round to the nearest foot.
Answers
From a point along a straight road, the angle of elevation to the top of a hill is 33°. A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. The hill is 165.87 ft high.
Check the file attached below for a pictorial understanding of the question
[tex]tan[/tex]θ[tex]= \frac{opposite}{adjacent}[/tex]
From ΔABC..........(1)
[tex]tan33 = \frac{y}{x}[/tex]
From ΔABD............(2)
[tex]tan20 = \frac{y}{x+200}[/tex]
[tex]y = (x+200)tan20 ........(2)[/tex]
[tex]Equating (1) and (2)[/tex]
[tex]xtan33[/tex] [tex]= (x+200)tan20[/tex]
[tex]xtan33 = xtan20 + 200tan20[/tex]
[tex]0.649x = 0.364x + 72.794[/tex]
[tex]0.649x-0.364x = 72.794\\0.285x = 72.794\\x = \frac{72.794}{0.285} \\x = 255.42ft[/tex]
Substitute the value of x into equation (1)
[tex]y = 255.42tan33[/tex]
[tex]y = 165.87 ft[/tex]
The angle of elevation is an angle this is formed between the horizontal line and the road of sight. If the line of sight is upward from the horizontal line, then the angle fashioned is a perspective of elevation. A smooth-to-recollect equation for finding change in elevation as a decimal is “rise over run,” which means the upward push (the trade-in vertical distance) divided via the run (the change in horizontal distance).
Elevations are probably organized for some of the motives, consisting of: As part of a survey of current buildings. To create a document of a construction. To discover and communicate indoor and outdoor design options. The elevation of an object is at its top above sea level. Altitude refers to the peak of an object above a given factor. Elevation refers to the peak of a place above the mean sea degree.
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Complete Question:
From a point along a straight road, the angle of elevation to the top of a hill is 33°. A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?
Can 5cm 9cm 3cm be sides of a triangle?.
Answers
Answer: It is not possible
Step-by-step explanation:
to have a triangle with sides 5 cm, 3 cm and 2 cm. Sum of any two sides of a triangle must be greater than the third side.
3 cm + 2 cm = 5 cm
If the margin of error decreases and the sample size remains the same, the level of confidence.
Answers
Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down
What is level of confidence?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.
We are given asked when the sample size is kept the same,
What will happen to the level of confidence if the margin of error decreases?we know that the margin of error is nothing but a statistic which tells us how many percentage points our results will differ from the real population value.we know that when a greater error is allowed, the more will be the confidence(fundamental concept of confidence intervals)
Let Margin of Error be represented by E and the confidence level by C hence the relationship goes like this,
E↑⇔C↑and E↓⇔C↓
Here we are asked when the sample size is kept the same, what will happen to the level of confidence if the margin of error decreases .
The answer is that Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down.
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Positive
Negative
No Correlation
Answers
Answer:
No Correlation
Step-by-step explanation:
The points are scattered randomly and there is no pattern so there is no correlation.
In estimating √60, the two perfect squares that provide the best two benchmarks to estimate
the answer can be represented by the numbers _____ and_______.
Write the smallest
perfect square in the first two boxes and the largest perfect square in the last two boxes.
Answers
Answer:
60 falls between two perfect squares: 49 (72), and 64 (82).
Step-by-step explanation:
In a room there are 40 people. 26 of these are women, the rest are men. What percentage of the people are men.
Answers
Answer:
35%
Step-by-step explanation:
Find the number of men:
40-26= 14
Find the ratio of men out of the 40 people
14/40 = 0.35
0.35 * 100% = 35%
What is the rule for multiplying by 6?.
Answers
Answer:
If you multiply 6 by an even number, it will end in the same digit. For example, 6 x 4 = 24, so 4 and the 4 in 24 are the same. The number in the tens place will be half the number in the ones place, so the 2 in 24 is half of 4
Which represents the explicit formula for the arithmetic sequence an = 15 5(n - 1) in function form?
Answers
The function the represents the explicit formula for the arithmetic sequence an = 15 + 5(n - 1) is f(n) = 10 + 5n
Nth term of the arithmetic sequence is given that
an = 15 + 5(n - 1)
Where 15 is the first term
5 is the common difference
Here we have to expand the given equation
f(n) = 15 + 5(n - 1)
Apply the distributive property in the equation
f(n) = 15 + 5n - 5
Add the like term of the equation
f(n) = 15 - 5 + 5n
f(n) = 10 + 5n
Hence, the function the represents the explicit formula for the arithmetic sequence an = 15 + 5(n - 1) is f(n) = 10 + 5n
The complete question is
Which represents the explicit formula for the arithmetic sequence an=15+5(n−1) in function form?
a) f(n)=5n+15
b) f(n)=n+20
c) f(n)=5n+10
d) f(n)=n+10
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The total cheese production in 2006 is 7.7 billion pounds and the total cheese production in 2014 is 9.7 billion pounds
The total cheese production in 2006From the question, we have the following function that can be used in our computation:
y = 7(1.03)ˣ
Such that
x = Number of years after 2003
In the year 2006, the value of x is calculated as
x = Current year - 2003
So, we have
x = 2006 - 2003
Evaluate
x = 3
Substitute x = 3 in the equation y = 7(1.03)ˣ
y = 7(1.03)³
Evaluate
y = 7.7
The total cheese production in 2014In the year 2014, the value of x is calculated as
x = Current year - 2003
So, we have
x = 2014 - 2003
Evaluate
x = 11
Substitute x = 11 in the equation y = 7(1.03)ˣ
y = 7(1.03)¹¹
Evaluate
y = 9.7
Hence, the amount of cheese is 9.7 billion pounds
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A spinner with 7 equal parts labeled g, a, b, c, d, e, f. a point is chosen in the circle at random. determine which of the statements are true. check all that apply. it is unlikely the point is in region a. it is likely the point is in region c. it is likely the point is in region g. it is impossible for the point to be in region h. it is certain that the point will land in a lettered region.
Answers
Answer:
Step-by-step explanation:
Subtract 4 from any element's value that is greater than maxval. Ex: if maxval = 10, then datapoints = {2, 12, 9, 20} becomes {2, 8, 9, 16}.
Answers
Answer:
Step-by-step explanation:
for (i = 0; i < dataPoints.size(); ++i) {
if (dataPoints.at(i) > maxVal) {
dataPoints.at(i) = dataPoints.at(i) - 4;
}
}
The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club. Each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell. Which equation represents this situation?72 = 3x + 6 (6)
72 = 3x + 6
72 = 6x + 3
72 = 6x + 3 (6)
Answers
72 = 3x + 6 equation represents if each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell.
Define equation.In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated proposition that has been mathematically quantified. There are numerous possible equation types. To equate two expressions, we employ equations.
Given,
The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club.
Each pie was then cut into six pieces and sold.
There were a total of 72 pieces to sell.
Equation representing this equation is:
72 = 3x + 6
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Find all zeroes of the polynomial: 9x^3-36x^2+2x-8
Answers
x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given polynomial is 9x³-36x²+2x-8
We have to find roots or zeroes of polynomial.
Nine times of x cube minus thirty six x square plus two times of x minus eight.
(((9(x³)) - (2²3²x²)) + 2x) - 8 = 0
((3²x³ - (2²3²x²)) + 2x) - 8 = 0
9x³-36x²+2x-8 is not a perfect cube
9x³-36x²+2x-8
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x-8= 2(x-4)
Group 2: -36x²+9x³=9x²(x-4)
Add up the two groups :
(x-4) (9x²+2)
x=4
x=0.0000-0.4714i
x=0.0000+0.4714i
Hence x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8
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A poster whose area is 180 square inches, has 1 inch margin at bottom and on sides 2 inch margin at the top. What are its dimensions for which printed area is maximized?
Answers
The dimensions for which the printed area is maximized are 16.432 × 10.954 in².
let the height of the poster = x inches
area of the poster = 180 in²
thus, its width is 180/x inches.
The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.
The sides have a margin of 1 inch, so the width of the printed area is:
180/x - 2
the area of printed area A is given by the formula of a rectangle,
A = height × width
A = (x-3)(180/x - 2)
A = 180 - 2x - 540/x + 6
the maximized area is when dA/dx = 0
dA/dx = - 2 - 540(- 1/x²) = 0
540/x² = 2
x = √270
hence height = √270 = 16.432 inches,
and width = 180/√270 = 10.954 inches.
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it shows also that the barn will be used as part of the fencing on one side. find the largest area that can be enclosed if 88 feet of fencing material is available
Answers
The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².
Given, a barn has a perimeter of 88 feet.
Now, the perimeter of the rectangle i.e. Barn is 88 feet.
Perimeter = 2(l + b)
88 = 2(l + b)
l + b = 44
b = 44 - l
Now, area = l × b
Area = l × (44 - l)
Area = 44l - l²
On differentiating both the sides, we get
A' = 44 - 2l
On putting A' = 0
44 - 2l = 0
l = 22
Now, for l = 22 the area will be the largest.
if l = 22
then, 22 + b = 44
b = 22
So, the largest area will be 22×22 = 484
Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².
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