given that P = (4,1) and Q=(-4,4) find the component form and magnitude of the vector QP.
Answers
The magnitude of the vector QP is √73.
To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.
Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:
x-component of QP = x-coordinate of Q - x-coordinate of P
= (-4) - 4
= -8
y-component of QP = y-coordinate of Q - y-coordinate of P
= 4 - 1
= 3
Therefore, the component form of the vector QP is (-8, 3).
To find the magnitude of the vector QP, we can use the formula:
Magnitude of a vector = √(\(x^2 + y^2\))
Substituting the x-component and y-component of QP into the formula, we get:
Magnitude of QP = √((\(-8)^2 + 3^2\))
= √(64 + 9)
= √73
Therefore, the magnitude of the vector QP is √73.
In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.
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Related Questions
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of x. V = cm^3 (b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.) = ? (c) Find the length L , width W, and height H of the resulting box that maximizes the volume. (Assume that W < or = to L ) L= ?cm W= ?cm H= ? cm (d) The maximum volume of the box is ? cm^3.
Answers
(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x
(b) The domain of V in interval notation is 0<x<5,
(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773
(d) The maximum volume of the box is 192.421 cm^2.
In the given question,
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.
(a) We have to express the volume V of the box as a function of x.
If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.
So V = x(10-2x) (20-2x)
V = x(10(20-2x)-2x(20-2x))
V = x(200-20x-40x+4x^2)
V = x ( 200 - 60 x + 4x^2)
V = 4x^3-60x^2+200x
(b) Now we have to give the domain of V in interval notation.
Since the lengths must all be positive,
10-2x > 0 ≥ x < 5 and x> 0
So 0 < x < 5
(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.
We take the derivative of V:
V'(x) = 12x^2-120x+200
Taking V'(x)=0
0 = 4 (3x^2-30x+50)
3x^2-30x+50=0
Now using the quadratic formula:
x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
From the equationl a=3, b=-30, c=50
Putting the value
x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)
x= \(\frac{30\pm\sqrt{900-600}}{6}\)
x= \(\frac{30\pm\sqrt{300}}{6}\)
x= \(\frac{30\pm17.321}{6}\)
Since x<5,
So x= \(\frac{30-17.321}{6}\)
x= 2.113
So H = 2.113, W = 5.773, L= 15.773.
d) Now we have to find the maximum volume of the box.
V = HWL
V= 2.113*5.773*15.773
V = 192.421 cm^3
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How many significant figures should be included in the answer to the following calculation? (3.4876)/(4.11+1.2
Answers
The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.
First, let's analyze the number of significant figures in the given values:
- 3.4876 has five significant figures.
- 4.11 has three significant figures.
- 1.2 has two significant figures.
To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:
4.11 + 1.2 = 5.31
Now, we divide 3.4876 by 5.31:
3.4876 / 5.31 = 0.6567037...
Now, let's determine the number of significant figures in the result.
Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.
In this case, the value with the fewest significant figures is 5.31, which has three significant figures.
Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
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Which equations represent a linear function? Select two. a. y = x-1 b. y = – 4.5 C. 3x – 4y = 2 d. 5x2 = 10y e. y = 1/2x2 +6
Answers
Explanation
a linear function must have
dependent and independent variables, ( y and x in this case)and the exponent of the independent vairable must be 1, so
Step 1
Check
a)
\(a)\text{ y=x-1}\)this is a linear function
b)
\(y=4.5\)this is not a functin, this expression has not x
c)
\(3x-4y=2\)this functin has x and y, and the exponent of x is 1, so, this is a linear function
d)
\(5x^2=10y\)this function has x and y, but the exponent is 2, so this is not a linear function
e)
\(y=\frac{1}{2}x^2+6\)this function has x and y, but the exponent is 2, so this is not a linear function
i hope this helps you
a fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem
Answers
By using the concept of bell shaped curve of normal distribution, it can be concluded that
The histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is given by
f(x) = \(\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}\)
Where z = \(\frac{x - \mu}{\sigma}}\) where \(\mu\) is the mean and \(\sigma\) is the standard deviation
A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.
Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
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an economics class consists of 35 students. the mean and variance of recent test was 70% and 25(%)2, respectively. exam scores were negatively skewed. determine the number of students who scored less than 60 or more than 80.
Answers
The number of students who scored less than 60 or more than 80 is atmost 9.
What is mean and variance?A measurement of central dispersion is the mean and variance.
The average of a group of numbers is known as the mean.
The variance is calculated as the square root of the variance.
Chebyshev's rule is applicable for any distribution. If distribution is a normal distribution, then we can use empirical rule.
step: 2
Given mean is 70 and variance is 25.
We know standard deviation is square root of variance. So
σ = SD =√25
= 5
So the standard deviation is 5.
Here
60=70−2×5
80=70+2×5
So between 60 and 80 is within 2 standard deviation about mean.
So at least 75% are between 60 and 80.
Then percentage outside this is at most 25%.
Outside this means less than 60 more than 80.
So at most 25% of total data are less than 60 more than 80.
We have total 35 students.
25% of 35 students = 0.25*35
= 8.75
number of students who scored less than 60 or more than 80 is atmost 9
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\(\sqrt[4]{15} + \sqrt[4]{81}\) best answer will get branliest
Answers
\( \sf \purple{ \sqrt[4]{15} + \sqrt[4]{81} }\)
\( \sf \red{ \sqrt[4]{15} + 3}\)
\( \sf \pink{ 1.9 + 3}\)
\( \sf \orange{ \approx 4.9}\)
f(x, y, z) = y i (z − y) j x k s is the surface of the tetrahedron with vertices (0, 0, 0), (4, 0, 0), (0, 4, 0), and (0, 0, 4)
Answers
The surface integral ∬F · dS over the tetrahedron surface S is 128/3.
To evaluate the surface integral of the vector field F = yi - (z - y)j + xk over the tetrahedron surface S, we can use the surface integral formula:
∬F · dS = ∭div(F) dV,
where ∬ represents the surface integral, ∭ represents the volume integral, div(F) is the divergence of F, dS is the differential surface area vector, and dV is the differential volume.
To apply this formula, we need to find the divergence of F. The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by:
div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
In our case, P(x, y, z) = 0, Q(x, y, z) = y - (z - y), and R(x, y, z) = x. Let's calculate the divergence:
∂P/∂x = 0,
∂Q/∂y = 1 - (-1) = 2,
∂R/∂z = 0.
Therefore, div(F) = 0 + 2 + 0 = 2.
Since the divergence of F is constant, we can simplify the surface integral formula:
∬F · dS = ∭div(F) dV = 2 ∭dV.
Now, we need to set up the triple integral over the volume of the tetrahedron bounded by the given vertices. The tetrahedron has three sides lying on the coordinate planes, so we can use the limits of integration:
0 ≤ x ≤ 4,
0 ≤ y ≤ 4 - x,
0 ≤ z ≤ 4 - x.
Let's set up the triple integral and evaluate it:
∬F · dS = 2 ∭dV
= 2 ∫₀⁴ ∫₀⁴(4-x) ∫₀⁴(4-x) dz dy dx.
Integrating the innermost integral:
∫₀⁴(4-x) ∫₀⁴(4-x) dz dy = ∫₀⁴(4-x) (4-x) dy = (4-x)(4-x) = (4-x)².
Now integrating the next integral:
∫₀⁴ (4-x)² dx
= ∫₀⁴ (16 - 8x + x²) dx
= 16x - 4x² + (1/3)x³ ∣₀⁴
= (64 - 64 + 64/3)
= 64/3.
Therefore, the surface integral ∬F · dS over the tetrahedron surface S is equal to 2(64/3) = 128/3.
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XY has endpoints at X(2, -3) and
Y(-1, 2). What is the length of XY?
A. 2 units
B. 10 units
C. 34 units
Answers
Answer:
B.
Step-by-step explanation:
I did this, but I'm not 100% sure.
Please help! I will mark as brainliest IF answer is right. <3
Answers
Option A he would be paid:
$15 per session
Option B he would be paid:
$20 per session
Equations
A: Y = 15x + 17250
B: Y = 20x + 14000
When X = 650 the Y values of A and B are equal.
After 650 training sessions, they would be equal.
Answer:
P = 17250 + 15n
P = 14000 + 20n
The line y=kx+4 goes through the point (2,-2)
Sketch the graph the line
Please write it step by step
Answers
The line of the graph y= kx +4 goes through the point (2,-2) is given by
y = -3x +4.
As given in the question,
Equation of the line is given by y = kx + 4
Passing through the point (2, -2)
Substitute the value in equation we get,
-2= k(2) + 4
⇒2k = -2 -4
⇒k =-6 /2
⇒k =-3
Equation of the line y= -3x + 4 sketched on graph passing through (2,-2).
Therefore, the line of the graph y = kx +4 goes through the point (2,-2) is given by y = -3x +4.
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A variable is normally distributed with mean 9 and standard deviation 3.
a. Determine the quartiles of the variable.
b. Obtain and interpret the 90th percentile.
c. Find the value that 65% of all possible values of the variable exceed.
d. Find the two values that divide the area under the corresponding normal curve into a
middle area of 0.95 and two outside areas of 0.025. Interpret the answer.
a. Q1= Q2= Q3=
(Round to two decimal places as needed.)
b. The 90th percentile is __
(Round to two decimal places as needed.)
Choose the correct answer below.
A. The 90th percentile is the number that divides the bottom 90% of the data from the top 10% of the data.
B. The 90th percentile is the number that is 90% of the largest data value.
C. The 90th percentile is the number that occurs in the data 90% of the time.
D. The 90th percentile is the number that divides the bottom 10% of the data from the top 90% of the data.
c. The value that 65% of all possible values of the variable exceed is __
(Round to two decimal places as needed.)
d. The two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025 are__ and __
(Round to two decimal places as needed. Use ascending order.)
These values enclose the area of the normal curve that is within ____ standard deviations.
Answers
The two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025 are 2.12 and 15.88, respectively.
a) Determining the quartiles of the variable:
We use the formula:
Q1 = M – Z(σ/√n)
Q2 = Mean
Q3 = M + Z(σ/√n)
Given:
M = 9
σ = 3
n = 150
First, we find the value of Z for Q1 and Q3 using the standard normal distribution table:
Z for Q1 = 0.25 (as the first quartile is 25%)
Z for Q3 = 0.75 (as the third quartile is 75%)
Using the formulas, we can calculate:
Q1 = 9 - (0.67) = 8.33
Q2 = 9
Q3 = 9 + (0.67) = 9.67
Therefore, Q1 = 8.33, Q2 = 9, and Q3 = 9.67
b) Obtaining and interpreting the 90th percentile:
To calculate the 90th percentile, we use the formula:
X90 = Mean + Z(σ)
Given:
Mean = 9
σ = 3
Z = 1.28 (From the standard normal distribution table)
X90 = 9 + (1.28 × 3) = 12.84
The 90th percentile is the number below which 90% of the data falls.
c) Finding the value that 65% of all possible values of the variable exceed:
To find the value that 65% of all possible values exceed, we first find the Z value corresponding to 65% from the standard normal distribution table
Z for 65% = 0.39
Using the formula:
X = Mean + Z(σ)
Given:
Mean = 9
σ = 3
Z = 0.39 (from the standard normal distribution table)
X = 9 + (0.39 × 3) = 10.17
The value that 65% of all possible values of the variable exceed is 10.17.
d) Finding the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025:
To find the two values, we use the standard normal distribution table.
First, we find the Z-values corresponding to (1 - 0.95) / 2 = 0.025 from the standard normal distribution table.
Z for outside areas = 1.96
Using the formulas:
X1 = Mean - Z(σ)
X2 = Mean + Z(σ)
Given:
Mean = 9
σ = 3
Z = 1.96
X1 = 9 - (1.96 × 3) = 2.12
X2 = 9 + (1.96 × 3) = 15.88
Therefore, the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025 are 2.12 and 15.88, respectively.
These values enclose the area of the normal curve that is within 2 standard deviations.
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Factorise
p^2 + 8 - 8p - p
Answers
\( {p}^{2} + 8 - 8p - p \\ = {p}^{2} - p - 8p + 8 \\ = p(p - 1) - 8(p - 1) \\ = (p - 1)(p - 8)\)
Answer:\((p - 1)(p - 8)\)
Hope it helps..ray4918 here
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8 - 3/8=
F 8 3/8
G 5/8
H 7 1/2
J 7 5/8
K None
Answers
Answer:
Step-by-step explanation:
make the whole number into fraction, by copying the denominator of the fraction
so that will be 8 into 8/8
8/8- 3/8= since same of denominator , subtract the numerator , 8 minus 3 is 5 and copy the denominator since both denominator is same, so the answer will be 5/8
Given that f(x) = x^2 - 8x + 12 and g(x) = -6, find (f/g)(x) and express the result in standard form
Answers
We are given the following two functions
\(\begin{gathered} f(x)=x^2-8x+12 \\ g(x)=-6_{} \end{gathered}\)We are to find (f/g)(x)
(f/g)(x) is basically the division of function f(x) by function g(x)
\((\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x^2-8x+12}{-6}=\frac{x^2}{-6}-\frac{8x}{-6}+\frac{12}{-6}=-\frac{1}{6}x^2+\frac{2}{3}x-2\)Therefore, the function (f/g)(x) is
\((\frac{f}{g})(x)=-\frac{1}{6}x^2+\frac{2}{3}x-2\)Laura is thinking of a number such that the sum of the number and five times two more than the number is 26 more than four times the number. Determine the number Laura is thinking of.
Answers
Answer:
8
Step-by-step explanation:
Let x be the unknown number.
Then the equation is
x + 5*(x+2) = 4x + 26.
Solve it:
x + 5x + 10 = 4x + 26.
6x - 4x = 26 - 10,
2x = 16,
x = 16%2F2 = 8.
Z varies jointly with x, and y, and z=7 when x= 2, y= 2
pleasee I need an answer now!!
Answers
Answer:
(7/4)(2)(2)=7
Step-by-step explanation:
Answer:
z = 1.75xy
Step-by-step explanation:
Given z varies jointly as x and y then the equation relating them is
z = kxy ← k is the constant of variation
To find k use the condition z = 7 when x = 2 and y = 2, then
7 = k × 2 × 2 = 4k ( divide both sides by 4 )
1.75 = k
z = 1.75xy ← equation of variation
simplify the numerical expression.
12 +6 ÷ 2
Answers
Answer:
12+3
Step-by-step explanation:
12+6÷2
6÷2=3
12+3
pemdas
Answer:
15
Step-by-step explanation:
Start by dividing 6÷2 which is 3
Then add 3 by 12 which gives you 15
A wise man once said, "200 reduced by
twice my age is 60." What is his age?
Answers
Answer: 42 ?
Step-by-step explanation:
Answer:
70 years old
Step-by-step explanation:
Lets say this man’s age is x
200- 2x= 60
2x=140
x=70
what is the name of the length of the straight line drawn from an object’s initial position to the object’s final position?
Answers
Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position
The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.
If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.
The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.
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A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.
Is this a matched pairs design for this experiment?
Yes, the company used 24 different vehicles.
Yes, both types of tread were randomly assigned to each vehicle.
No, the vehicles were not put into groups of two.
No, the tires with the different types of tread were not randomly assigned to each vehicle.
Answers
This is a matched pairs design because both types of tread were randomly assigned to each vehicle.
What is matched pairs design?The term matched pairs design has to do with the situation in which participants are randomly assigned to an experiment or a control group. For each participant assigned to an experimental group, another is assigned to the control group.
Thus, this is a matched pairs design because both types of tread were randomly assigned to each vehicle.
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Mr. White is renting an oversized truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 325+100d to find how much he will pay for a 13-day rental. Each day = $100
Answers
Answer:
$1,625
Step-by-step explanation:
Given:
Total cost = 325 + 100d
Where,
325 = fixed cost
100 = cost per day
d = number of days
Find the total cost when d = 13 days
Total cost = 325 + 100d
= 325 + 100d
= 325 + 100(13)
= 325 + 1,300
= 1,625
Total cost = $1,625
Find
6\2(9) . Express your answer as a fraction in simplest form.
Answers
6/2(9)
6(9)=54
64/2=27
Solve the following three equations
Answers
Answer:
2 sq rt 33
Step-by-step explanation:
1st step: subtract one, each side
(radical 2/3)r = 22
2nd step: set up a proportion
(radical 2/3)r = 22
3rd step: cross-multiply
radical 2*r = 66
4th step: solve for 'r'
r = 66 / radical 2
5th step: rationalize the denominator
multiply numerator and denominator by radical 2
6th step: simplify
(66\(\sqrt{2}\)) / 2 = 33 \(\sqrt{2}\)
Write as an algebraic expression: the difference of 27 and 5
Answers
The algebraic expression of the statement given as the difference of 27 and 5 is 27 - 5
How to write the statement as an algebraic expression?The statement is given as:
the difference of 27 and 5
Difference means minus.
The minus sign is represented as -
This means that the statement given as: the difference of 27 and 5
Can be represented as
27 minus 5
So, have
27 - 5
Hence, the algebraic expression of the statement given as the difference of 27 and 5 is 27 - 5
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help meeeeeeeeee pleasee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)
Find the 13th term of the geometric sequence
3
,
−
15
,
75
,
.
.
.
3,−15,75,...
Answers
The \(13^{th}\) term of the geometric sequence is - 732421875.
A geometric sequence is given ; 3 , -15 , 75....
We have to find the \(13^{th}\) term of the geometric sequence.
What is the formula for calculation of nth term of geometric Sequence ?
The formula for calculation of nth term of geometric progression is \(a_{1} =a^{n} x (r)^{n-1}\)where r is the common ratio of geometric sequence.
Given geometric sequence is 3 , -15 , 75....
and
Common ratio is r.
i.e., r = -15 ÷ 3 = -5
∵ \({n}^t^h\) term of a geometric sequence is given by ;
\(a_{1} =a^{n} x (r)^{n-1}\)
where is the first term.
Hence,\(13^{th}\) term of the geometric sequence will be ;
\(a_{13}=3x(-5)^1^2\)
\(a^1^3\) = - 732421875
Thus , the term of the geometric sequence is - 732421875.
Please find <TQU in the question above
Answers
Answer:
<TQU = 72°
Step-by-step explanation:
<WQT = 60°
=> <WQT = <UYX (corresponding angles)
=> <UYX = <YUV (alternate angles)
=> <YUV = <UQR (corresponding angles)
So, <UQR = 60°
Now,
<PQT+<TQU+<UQR = 180° (angles on a straight line add up to 180°)
48° + <TQU + 60° = 180°
<TQU + 108 = 180
Subtracting 108 from both sides
<TQU = 180-108
<TQU = 72°
Please help me with this problem!!
Answers
Answer:
cn<fr
Step-by-step explanation:
trust me bro
Answer: Cr<Fr
Step-by-step explanation:
if you look at the angle it gives you, you can tell which inequality is bigger.
Three objective functions for linear programming problems are 7A+10B,6A+4B, and −4A+7B. Show the graph of each for objective function values equal to 420 .
Answers
Graph of each objective function using linear programming.
Here,
Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.
For example putting A=0 in 7A+10B=420 will yield (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.
Repeating thin step for each objective function and plotting the graph.
7A + 10B = 420 is labelled as a.
6A+4B = 420 is labelled as b.
-4A + 7B = 420 is labelled as c .
The graph of each function is attached below.
Know more about linear programming,
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If 45 men can construct a building in 48 days then how many days will 40 men take to constructthe same building
Answers
Answer: trick question
Step-by-step explanation: it depends on how strong and fast they are.
There are 43 days will 40 men take to constructed same building.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
There are 45 men can construct a building in 48 days.
Hence, By definition of proportion;
Number of days for 40 men take to constructed same building is,
⇒ x / 40 = 48 / 45
⇒ x = 43
Thus, There are 43 days will 40 men take to constructed same building.
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