Answers
The Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
The function is given in the question as
m(x) = xcos(-x)
Taylor (Maclaurin) series of xcos(x) up to n=5
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) = xcos(x)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)
Evaluate the 2nd derivative at the given point: (f(0))′′=0
3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)
Evaluate the 3rd derivative at the given point: (f(0))′′′=−3
Now, use the calculated values to get a polynomial:
[tex]m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....[/tex]
[tex]m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
Thus, the Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
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Related Questions
In how many ways can 8 different pizza toppings be chosen from 21 available toppings?
Answers
NO LINKS!! What are the true converses for each theorem?
Answers
Answers:
If the alternate interior angles are congruent, then the lines are parallel.If the alternate exterior angles are congruent, then the lines are parallel.If the corresponding angles are congruent, then the lines are parallel.If the consecutive interior angles are supplementary, then the lines are parallel.If the consecutive exterior angles are supplementary, then the lines are parallel.=====================================================
Explanation:
A conditional statement is of the form "if..., then..."
For example, "If it rains, then the grass gets wet" is a conditional statement.
We can have a basic template of "If P, then Q" to represent any conditional. The P and Q are placeholders for logical statements.
The converse of that conditional is "If Q, then P". We swap P and Q.
------------
So let's say we had this original conditional:
"If the lines are parallel, then alternate interior angles are congruent"The converse would be:
"If the alternate interior angles are congruent, then the lines are parallel"Similar ideas apply for the other converses as well.
Answer:
If alternate interior angles are congruent, then lines are parallel.
If alternate exterior angles are congruent, then lines are parallel.
If corresponding angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
Step-by-step explanation:
Converse
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".-------------------------------------------------------------------------------------------------
Alternate InteriorGiven statement: If lines are parallel, then alternate interior angles are congruent.
Hypothesis: "lines are parallel"Conclusion: "alternate interior angles are congruent"Converse statement: If alternate interior angles are congruent, then lines are parallel.
Alternate ExteriorGiven statement: If lines are parallel, then alternate exterior angles are congruent.
Hypothesis: "lines are parallel"Conclusion: "alternate exterior angles are congruent"Converse statement: If alternate exterior angles are congruent, then lines are parallel.
CorrespondingGiven statement: If lines are parallel, then corresponding angles are congruent.
Hypothesis: "lines are parallel"Conclusion: "corresponding angles are congruent"Converse statement: If corresponding angles are congruent, then lines are parallel.
Consecutive InteriorGiven statement: If lines are parallel, then consecutive interior angles are supplementary.
Hypothesis: "lines are parallel"Conclusion: "consecutive interior angles are supplementary"Converse statement: If consecutive interior angles are supplementary, then lines are parallel.
Consecutive ExteriorGiven statement: If lines are parallel, then consecutive exterior angles are supplementary.
Hypothesis: "lines are parallel"Conclusion: "consecutive exterior angles are supplementary"Converse statement: If consecutive exterior angles are supplementary, then lines are parallel.
You have a carryover balance of $600 on a credit card that has a 18.99% annual percentage rate (APR). You have a recurring monthly purchase of $70 for your water bill and you make a payment of 7% of the ending balance is made each month. Complete the table below. Round each value to the nearest cent.
Answers
The completion of the credit card table is as follows:
Month Carryover Finance New Ending
Balance Charge Purchase Balance Payment
1 $600 $10.60 $70 $680.60 $47.64
2 $632.96 $11.12 $70 $714.08 $49.99
How are credit card finance charges computed?Credit card attracts finance charges.
The finance charges are the interest for using some credit to finance purchases.
Most finance charges are based on the annual percentage rate (APR), which may also be used to obtain the monthly percentage rate (MPR) by dividing the APR by 12.
The finance charge is applied to the unpaid balance at the end of the period, which may be daily, weekly, or monthly.
Carryover balance = $600
Annual percentage rate (APR) = 18.99%
Monthly percentage rate (MPR) = 1.5825% (18.99% ÷ 12)
Recurring monthly purchase = $70
Monthly payment = 7% of the ending balance
The finance charge for month 1 = $10.60 ($600 + $70 x 1.5825%)
Payment for month 1 = $47.64 ($680.60 x 7%)
Carryover balance for month 1 = $632.96 ($680.60 - $47.64)
The finance charge for month 2 = $11.12 ($632.96 + $70 x 1.5825%)
Payment for month 2 = $47.64 ($714.08 x 7%)
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Which expression represents "10 subtracted from the quotient of 3 and a number"?
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3}{n}[/tex] - 10.
The quotient of 3 and a number translates to [tex]\frac{3}{n}[/tex], then, all you have to do is subtract 10 from that value, giving the expression above.
a line with a slope of 7 passes through the point (-2,-9). what is its equation in slope-intercept form?
Answers
Answer: y=7x-5
Step-by-step explanation: Use the points to find the equation of y-(y1) = m (x- and x1)
The slope is 7. and x1 and y1 is (2,9)
Here is y-9=7 is (x-2). Then y-9=7 is (x-2)]
Multiply 7x-2, then you get y-9=7x-14 then now we got y=7x-5! :)
You eat ripe tomatoes on July 29. When did you plant the tomato seeds?
Answers
You planted the tomato seeds on the 10th of May
How to determine when you planted the seeds?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Number of days to ripe = 80 days
Date the tomato seed is eaten = July 29
The above parameters can be represented using the following subtraction equation:
The date you planted the seeds = Date the tomato seed is eaten - Number of days to ripe
Substitute the known values in the above equation, so, we have the following representation
The date you planted the seeds = July 29 - 80 days
Evaluate the difference
So, we have the following representation
The date you planted the seeds = May 10
Hence, the date you planted the seeds is May 10
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Complete question
It takes a tomato seed an average of 80 days to ripe. If you eat ripe tomatoes on July 29. When did you plant the tomato seeds?
A spinner with 10 equally sized slices has 4 yellow slices, 4 red slices, and 2 blue slice. Yolanda spun the dial 1000 times and got the following results. Answer the following. Round your answer to the nearest thousandth
Answers
Probability of landing on red 0.9%, when Yolanda spun the dial 1000 times.
What is probability?
The probability of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anywhere between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.
A spinner with 10 equally sized slices has 4 yellow slices, 4 red slices, and 2 blue slices.
Yolanda spun the dial 1000 times.
P( getting red) = 19/1000
From the chart, there are 19 red out of 1000
Experimental probability of landing on red
= Number of red outcomes / Total number of spins
= 9/1000
Experimental probability of landing on red 0.009.
Hence, Probability of landing on red 0.9%
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Write an equation of the line that passes through the pair of points. (5/12, −1), (−3/4, 1/6)
Answers
The equation of the line can be written as y = -x - (7/12).
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
Given that the line passes through (5/12, −1) and (−3/4, 1/6). Therefore, the slope of the line can be written as,
Slope of the line = [(1/6) - (-1)] / [(-3/4) - (5/12)]
= [(1/6) + 1] / [(-3/4) - (5/12)]
= (7/6) / [(-9-5)/12]
= (7/6) / (-14/12)
= -1
Now, the equation can be rewritten with slope and a point as,
y = mx + c
(1/6) = -1(-3/4) + C
(1/6) = (3/4) + C
C = (1/6) - (3/4)
C = (2/12) - (9/12)
C = (-7/12)
Therefore, the equation of the line can be written as,
y = mx + c
y = (-1)x + (-7/12)
y = -x - (7/12)
Hence, the equation of the line can be written as y = -x - (7/12).
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A 9-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
(Pls help)
Answers
Answer: 0.75 inches per hour
Step-by-step explanation:
9/12=0.75
0.75 x 12 = 9
0.75 inches per hour
Answer: 4.5 hours.
Step-by-step explanation:
Use a proportion.
3 3/8 = 3.375
9 inch is to 12 hours as 3.75 inches is to x hours.
9/12 = 3.375/x
3/4 = 3.375/x
3x = 4 * 3.375
x = 4 * 1.125
x = 4.5
Answer: 4.5 hours
Write an equation in slope-intercept form of the line given:
Answers
Answer: y=-x
Step-by-step explanation:
Choose 2 coordinates: (-2,2) and (2,-2)
Let us find the slope m:
[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=-2\ \ \ \ \ x_2=2\ \ \ \ \ y_1=2\ \ \ \ \ y_2=-2\\\\m=\frac{-2-2}{2-(-2)} \\\\m=\frac{-4}{2+2} \\\\m=\frac{-4}{4} \\\\m=-1\\[/tex]
Hence,
y=-x+b
To find the coefficient b, choose any coordinate belonging to the given line, for example (-2,2):
2=-(-2)+b
2=2+b
0=b
Hence, b=0
Thus, y=-x
If the point D (-6, 9) is reflected over the x-axis, the coordinates of D’ would be?
Answers
Answer:
D'(-6, -9)
Step-by-step explanation:
When a point is reflected over the x-axis, the x-coordinate remains the same. The reflected point is the same distance from the x-axis as the original point, but it's on the other side of the x-axis, so the y-coordinate changes sign.
In general, point (x, y) reflected over the x-axis becomes point (x, -y).
Here, point D(-6, 9) becomes point D'(-6, -9).
Teresa is maintaining a camp fire. She can keep the fire burning for 444 hours with 666 logs. She wants to know how many logs (y)(y)left parenthesis, y, right parenthesis she needs to keep the fire burning for 181818 hours. She assumes all logs are the same. How many logs does Teresa need to maintain the fire for 181818 hours?
Answers
Answer: 17 million
Step-by-step explanation: thank me later hehe
Answer: Teresa needs 27 logs to maintain the fire for 18 hours.
Step-by-step explanation:
We're dealing with a proportional relationship, so each ratio of logs to hours must be equivalent.
Hint #22 / 4
Here's one way to write the proportion:
18 hours = y logs
= 4 hours 6 logs
Hint #33 / 4
Now, solve the proportion for yyy:
18
y
yyy
=
4/6
=
2/3
=
2/3⋅18
=
2/3⋅18
=
1/2
3⋅18/9
=
1/3⋅9
= 1/27
=27
Which set of ordered pairs (x, y) could represent a linear function?
A = {(-6,9), (-3,6), (0,3), (4,0)}
B = {(1, 1), (2,3), (4,5), (5,7)}
C = {(-4,-4), (-2,-2), (1,0), (4,3)}
D = {(3,7), (5, 1), (6,-2), (7,-5)}
Answers
The frequency polygon to the right shows a distribution of IQ
scores. Determine if the following statement is true or false
according to the graph.
The graph is based on a sample of approximately 50 people.
of People (frequency)
Choose the correct answer below.
OA. The statement is false because the sum of the frequencies is greater than 50.
OB. The statement is false because there are less than 50 possible IQ scores.
OC. The statement is true because there are 50 possible IQ scores.
OD. The statement is true because the sum of the frequencies is 50,
Answers
The correct option is C. The statement is true because there are 50 possible IQ scores.
Explain the term frequency of the graph?A graph or data set that displays the number of occurrences of each potential result of a repeated event seen numerous times is called a frequency distribution in statistics. Election results and percentile lists of test scores are two straightforward examples. A histogram or pie chart can be used to represent a frequency distribution.For the given question-
The frequency for the total students are given on the graph.
The highest frequency is for 30 people.
The difference in the IQ score are ; 130 - 70 = 50
Thus, the statement that graph is based on a sample of approximately 50 people the is true because there are 50 possible IQ scores.
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Select all the equations that represent a line passing through the point (5,-2) with a slope of 4.
Answers
Answer:
y = 4x - 22
Step-by-step explanation:
y = 4x + b
-2 = 4(5) + b
-2 = 20 + b
b = -22
y = 4x - 22
What is the location of the y-intercept for the following exponential function? Give your answer in point form: (x,y) - 3 * (1/4) ^ x - 1 &
Answers
Answer:
Step-by-step explanation:
x=0
y=3(1/4)^x-1
y=3(1/4)^0-1
y=3(1)-1
y=2
y intercept is at (0,2)
50 POINTSS TO FILL THE WHOLE THING OUT!!
slide and its ladder form a right triangle with the ground, with the
slide representing the hypotenuse. The top of the ladder is 10 feet above
the ground, and the bottom of the ladder is 12 feet from the bottom of
the slide. What is the length of the slide to the nearest tenth of a foot?
1. Use the information in the problem to label the diagram.
Answers
Answer:
1. The problem involves finding the length of a slide about a ladder. The slide and the ladder form a right triangle, with the ground and the slide as the hypotenuse.
2. The top of the ladder is 10 feet above the ground, and the bottom of the ladder is 12 feet from the bottom of the slide.
3. In order to solve this problem, a diagram can be used to represent the scenario.
4. Label the bottom of the slide as point A, the bottom of the ladder as point B, and the top of the ladder as point C.
5. Draw a straight line from point A to point B and label it 12 feet.
6. Draw a straight line from point B to point C and label it 10 feet.
7. Draw a straight line from point A to point C, which is the hypotenuse of the triangle.
8. Use the Pythagorean Theorem to find the length of the hypotenuse.
9. The Pythagorean Theorem states that a2 + b2 = c2, where a and b are the sides of the triangle and c is the hypotenuse.
10. In this problem, a is 12 feet, and b is 10 feet. Plugging these values into the equation, we get 122 + 102 = c2. Solving for c, we get that the length of the slide is 14.04 feet to the nearest tenth of a foot.
Step-by-step explanation:
6 * 10x^{-3}/8*10x^{-6}
Answers
The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4 × 10³
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6 × 10⁻³ / 8 × 10⁻⁶
Simplifying the expression
6 × 10⁻³ / 8 × 10⁻⁶
This can be written as
6/8 × 10⁻³/10⁻⁶
Reduce the fraction
3/4 × 10⁻³/10⁻⁶
Apply the division law of indices
3/4 × 10⁻³ ⁻ ⁽⁻⁶⁾
3/4 × 10⁻³ ⁺ ⁶
3/4 × 10³
Hence, the value is 3/4 × 10³
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4. For the following write the converse , inverse, contrapositive and biconditional.
If studying helps your grade, then studying also hurts your grade.
Is the conditional true or false?
Is the converse true or false?
Is the bi-conditional true or false?
Answers
The converse, inverse, contrapositive and biconditional for the given sentences has been written down for a better understanding.
What are inverse statements?Two assertions that are logically opposed to one another are referred to be inverse statements. An inverted statement would be "It is raining" and "It is not raining."Biconditional statements can be both true and untrue depending on the veracity or falsity of each of its component elements. For instance, "If it is raining, then the ground is wet" is a biconditional statement because if it is raining, the ground will be wet, and if it is not raining, the ground won't be wet. In other words, the truth or falsehood of the first part (it is raining) determines the truth or falsehood of the second part.
How to solve?
Converse: If studying hurts your grade, then studying also helps your grade.
Inverse: If studying does not help your grade, then studying does not hurt your grade.
Contrapositive: If studying does not hurt your grade, then studying does not help your grade.
Bi-conditional: Studying helps your grade if and only if studying also hurts your grade.
The conditional is false.
The converse is false.
The bi-conditional is false.
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y-5x 7x + xy x = 0 and y = 4
Answers
Answer:
x(7y)x(7y)
Step-by-step explanation:
The given expression: 7(xy)7(xy)
i.e. a product of 7 and xy.
The operation used here: Multiplication.
Commutative property of multiplication :-
a\times b=b\times aa×b=b×a for any numbers a and b.
Associative property of multiplication :-
a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.
Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]
=(x7)y=(x7)y [Commutative property of multiplication]
=x(7y)=x(7y) [Associative property of multiplication]
Evaluate 25 - 4x when x = 2 and when x = 3. Which gives you the larger value and
what is that value?
O x = 2 will give you the larger value of 17.
O x = 3 will give you the larger value of 63.
O x = 2 will give you the larger value of 42.
O x = 3 will give you the larger value of 13.
Answers
Answer:17
Step-by-step explanation:
Substitute: 25-4x2
Calculate the product or quotient: 25-8
Calculate the sum or difference: 17
Answer: 17
Isaiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. The equation P=0.025x+85P=0.025x+85 represents Isaiah's total pay on a day on which he sells xx dollars worth of computers. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?
Answers
Answer:
$85
Step-by-step explanation:
x=0 p= 85 => (0,85) {y-intercept}
p=0 x= -3400 => (-3400,0) {x-intercept}
y-intercept means Isaiah sells $0, then the company will pay him $85.
If Malik has 4 times as many nickels as quarters and they have a combined value of 315 cents, how many of each coin does he have?
Answers
Set up your equation
4q + q = 315 Add (q = amount of quarters)
5q = 315 Divide
q = 63
Therefore he has 63 quarters.
To find the amount of nickels, multiply 4 and 63
4 x 63 = 252
Therefore he has 63 quarters and 252 nickels.
I hope this helps! :)
pls answer the top one need a naswer fast
Answers
The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft
what is a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.
Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28
Perimeter = (3x^2 +3x -148)ft
when x = 10
Perimeter = 3(10)^2 +3(10) -148 = 182ft
In conclusion the expression (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft
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A line has a slope of one and passes through the point (0, -10). What is is equation in slope intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form
Answers
Slope intercept form has the general form of y = mx + b, where m is the slope and b is the y-intercept.
You are given the y-intercept with the point (0, -10). Thus, the y-intercept is -10.
You are also given the slope of 1.
Next, just plug your numbers in!
y = 1x - 10
y = x - 10
Hope this helped!
Three years ago, Jerry purchased a condo. This year his monthly maintenance fee is $1,397. Twenty percent of this fee is for Jerry’s property taxes. How much will Jerry pay this year in property taxes?
Answers
Answer: $279.40
Step-by-step explanation:
To find how much he is paying in property taxes, you have to multiply the maintenance fee by the percentage you are given, so
1,397×20%=279.40
Answer:
$3,352.80
Step-by-step explanation:
This is the correct answer
PQTU and PRSU are rectangles.
PU = 11 cm
PQ = 4 cm
QR = 3 cm
Work out
perimeter PQTU: perimeter PRSU
Give your answer in its simplest form
Answers
The value of the ratio of the perimeters of the rectangles PQTU and PRSU is 30:36, that is 5:6.
Define Perimeter.The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Equation for perimeter of a rectangle (P) =2 (l + w), where l is the length and w is the width.
In the question, length of rectangle PQTU= 11cm
Width of rectangle PQTU= 4 cm
Perimeter of rectangle PQTU= 2( 11+4)
= 2 x 15
= 30 cm
The length of the rectangle PRSU= 11cm
The width of the rectangle PRSU= PQ + QR
= 4+3 = 7
The perimeter of the rectangle PRSU= 2(11+7)
= 36 cm
Therefore, perimeter of PQTU: perimeter of PRSU = 30:36
Dividing by 6 on both= 30/6 :36/6 = 5:6
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What’s 3/5 equal to ?
Answers
Answer:
0.6
Step-by-step explanation:
3/5 is equal to 0.6
Answer:
3/5 could be equal to many things. I will just give a list of all the possibilities:
3/5 = 3/5
3/5 = [tex]\frac{3}{5}[/tex]
3/5 = 3:5
3/5 = 0.6
3/5 = 60%
Step-by-step explanation:
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Using the simplex tableau solve for the LPP.
Objective function z=x1+2x2
Constraints
2x1 + x2<8
X1 + x2 <5
X1,x2>0
Answers
The values of the objective function obtained for the given set of equation is 7.
Define the term LPP?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.For the stated question-
Objective function z = x1+2x2
Constraints
2x1 + x2<8 ....eq 1x1 + x2 <5 ....eq 2x1, x2>0 .....eq 3Subtract equation 2 from 1.
x1 = 8 - 5
x1 = 3
Put value if x1 in eq 2
x1 + x2 = 5
x2 = 5 - 3
x2 = 2
Put the values of x1 and x2 in Objective function
z = x1 + 2x2
z = 3 + 2x2
z = 7
Thus, the values of the objective function obtained for the given set of equation is 7.
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what is the equation for a line that passes through (3.4) and 4,9
Answers
The equation of the line in slope-intercept form that passes through (3, 4) and (4, 9) is: y = 5x - 11.
How to Find the Equation of a Line?The equation of a line can be written in point-slope form as y - b = m(x - a), if we know the slope (m) and a point (a, b) on the line. It can be rewritten to the slope-intercept form as y = mx + b.
Given the points on a line:
(3, 4) and (4, 9)
Slope of the line (m) = change in y / change in x = (9 - 4)/(4 - 3)
Slope of the line (m) = 5/1
m = 5
To write the equation of the line, substitute m = 5 and (a, b) = (3, 4) into y - b = m(x - a):
y - 4 = 5(x - 3)
Rewrite in slope-intercept form:
y - 4 = 5x - 15
y = 5x - 15 + 4
y = 5x - 11 [equation of the line]
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