The value of t obtained is 4.76
Given,
Mean of group 1, [tex]M_{1}[/tex] = 10
Mean of group 2, [tex]M_{2}[/tex] = 12
[tex]SS_{1}[/tex] = 5
[tex]SS_{2}[/tex] = 8
Number of individuals per group, n = 6
The degrees of freedom are calculated as:
[tex]df = (n_{1} -1)+(n_{2} -1)[/tex] = ( 8-1) + (8-1) = 7 + 7 = 14
The difference between sample means [tex]M_{d}[/tex] is:
[tex]M_{d}[/tex] = [tex]M_{1} -M_{2}[/tex] = 10 - 12 = 2
Here n is equal for both groups which is = 8
Now,
The standard deviation of sample 1 :
[tex]s_{1} =\sqrt{\frac{SS_{1} }{n_{1} -1} } = \sqrt{\frac{5}{8-1} } = \sqrt{\frac{5}{7} } = 0.85[/tex]
The standard deviation of sample 2 :
[tex]s_{2}= \sqrt{\frac{SS_{2} }{n_{2}-1 } } = \sqrt{\frac{8}{8-1} } = \sqrt{\frac{8}{7} } = 1.07[/tex]
Now, we have to calculate the standard error for the difference of the means.
MSE = [tex]\frac{(n_{1}-1)s^{2} _{1}+(n_{2}-1)s^{2} _{2} }{(n_{1}-1)+(n_{2}-1) }[/tex]
= [tex]\frac{(8-1)(0.85^{2})+(8-1)(1.07^{2}) }{(8-1)+(8-1)}[/tex]
= [tex]\frac{10.1318}{14}[/tex]
MSE = 0.7237
Then, the standard error can be calculated as:
[tex]s_{M_{d} } = \sqrt{\frac{2MSE}{n} } = \sqrt{\frac{2 * 0.7237}{8} } = 0.42[/tex]
Now we can calculate t :
[tex]t=\frac{M_{d} }{s_{M_{d} } } = \frac{2}{0.42} = 4.76[/tex]
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I need help on this question please help me
Answer:
Step-by-step explanation:
6*[4-(42-63)]=
6*[4-(-21)]=
6*[4+21]=
6*25=150.
6*[4-9÷3]=
6*[4-27]=
6*(-23)=-138.
6*[4-3]=
6*1=6.
Which angle refers to the same angle as \angle BPF∠BPFangle, B, P, F?
A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.
ii. The value of x is [tex]47^{o}[/tex].
The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.
Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.
Thus from the given question, the angle that is the same as <PBD is <APC.
i.e <BPD ≅ <APC (vertically opposite property)
Also,
x + 133 = 180 (sum of angles on a straight line)
x = 180 - 133
= 47
x = [tex]47^{o}[/tex]
Therefore the value of x is [tex]47^{o}[/tex].
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The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube? 6 cubic feet 18 cubic feet 54 cubic feet 72 cubic feet
The volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron. It has six faces, twelve edges, and eight vertices.To find the volume of the cube that perfectly fits an 18 ft³ pyramid:
We have been provided that:
18 cubic feet is the volume of the pyramid.Now, in order for this pyramid to fit exactly into a cube, the base of the pyramid must be square, and the height of the pyramid must be equal to the height of the cube.We can conclude from this that the volume of a cube equals three times the volume of a pyramid.So, the volume of the cube = 3 × 18The volume of Cube = 54 ft³Therefore, the volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
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The correct question is given below:
The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube?
(A) 6 cubic feet
(B) 18 cubic feet
(C) 54 cubic feet
(D) 72 cubic feet
When does the rock hit the ground? the rock hits the ground between seconds and seconds after it is dropped.
Between 2 seconds and 2.5 seconds, the rock hits the ground after it is dropped.
What are distance and time?
A distance-time graph shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Distance is plotted on the Y-axis. Time is plotted on the X-axis.As you can see at 2s the height of the rock is 0.4m and at 2.5s it is -10.6m, which tells us that in between these values the height would have been 0m, as the movement of the rock is uniform in direction and hence, the rock will hit the ground between 2s and 2.5s.
The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped.
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Sketch the graph of the following equation: y=-3x-5
Answer is below attached
Step by step. We know y = -3x -5
The first point on the graph is -5 on the y axis. It is your y intercept.
The second point is your slope, which is the number next to the x, stated as y/x, -3/1.
You will graph this from the y-intercept as shown in red.
Then you can connect the points, shown with the blue line.
HELP ASAP
Consider functions H and K
What is the value of (h o k)(2)?
and look at this graph and please tell me what the answers are
Answer:
-3
Step-by-step explanation:
(h o k)(2) means
h( k(2)).
Remember when you have a function like f(x) or g(x) or h(x) or k(x), whatever number (or expression) is inside of the parenthesis, they're telling you to use that in place of x.
What h( k(2) ) means is we're going to put k(2) into h.
Well, what's k(2)? We need to find that first. k(x) is given as the oval and arrows thing going on there. If we're looking for k(2) then 2 is being the x. Find 2 in the first oval, follow the arrow to the output which is k(2).
If x = 2, the k(2)= -2
So back to
(h o k)(2):
(h o k)(2)
= h( k(2) )
= h(-2)
Since h(x)= 3/x+1
and x is -2, we'll put -2 in place of x.
h(-2) = 3/-2+1
= 3/-1
= -3
How do you expressed the difference in the measures of center as a multiple of the measure of variation in a box plot when the IQ ours are different
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answer:
334 in^2.
Step-by-step explanation:
The surface area = area of the top prism + area of the bottom - 2 * area of the base of the top smaller prism
= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) - 2* 3*5
= 2* 39 + 2*143 - 30
= 334
Which of these is a simplified form of the equation 7p 4 = − p 9 2p 3p? 13p = 13 3p = 5 7 = 4 11 = 15
Answer:
[tex]\boxed{\sf{3p=5}}[/tex]Step-by-step explanation:
To find:
The value of pGiven:
7p + 4 = −p + 9 + 2p + 3p[tex]\sf{7p+4=-p+9+2p+3p}[/tex]
Isolate the term of p, from one side of the equation.
Combine like terms.
[tex]\rightarrow \sf{7p+4=-p+2p+3p+9}[/tex]
Add the numbers from left to right.
-p+2p+3p=4p
7p+4=4p+9
Then, you subtract by 4 from both sides.
[tex]\sf{7p+4-4=4p+9-4}[/tex]
Solve.
7p=4p+5
Subtract by 4p from both sides.
7p-4p=4p+5-4p
Solve.
[tex]\boxed{\sf{3p=5}}[/tex]
Divide by 3 from both sides.
3p/3=5/3
Solve.
p=5/3
Divide is another option.
5/3=1.6666
So, the final answer is 3p=5.
I hope this helps, let me know if you have any questions.
A high school principal reports that the average sat math score for last year’s graduating class is 520. a sample is taken of this year’s graduating class is taken and the average sat math score is reported to be 530. how would you compare the last two graduating classes?
Based on the average SAT Math score that the graduating classes got, the comparison is that this year's graduating class did better than last year's graduating class.
How can both classes be compared?The average score is used to show the general trend of scores that students were able to attain.
The average score of 530 that this year's graduating class attained is higher than the average of the previous graduating year which is 520.
This means that on average, this year's graduating class did better than that of last year because their general trend was higher.
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________ If an arc has measure 7π/4 radians, what is its measure in degrees?
________ What is 60° in radians?
If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
Given that arc has measure of 7π/4.
We are required to convert the measure from radian to degree measure.
Converting means chaning of units from one to another.
To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.
7π/4=7*180/4
=7*45
=315 degrees
Now we have to convert 60 degrees into radians.
60 degrees=60*π/180
=π/3
Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
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necesito la respuesta, urgente
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
What is the value of the function at f(-3/5) ?Given the function; f(x) = ( 8x² - 2x + 4 ) / 2
To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.
f(x) = ( 8x² - 2x + 4 ) / 2
f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2
Divide each term by 2
f(-3/5) = 4(-3/5)² - (-3/5) + 2
f(-3/5) = 4(9/25) - (-3/5) + 2
f(-3/5) = 36/25 +3/5 + 2
f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25
f(-3/5) = ( 36 + 15 + 50 ) / 25
f(-3/5) = 101/25
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
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Find all real numbers x such that x^2 < 4. Give your answer in interval notation.
Inequalities help us to compare two unequal expressions. For all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the inequality x²<4, whose solution can be calculated as shown below.
x² < 4
x² - 4 < 0
x² - 2² < 0
(x+2)(x-2)<0
x = (-2, 2)
Hence, for all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to tariqareesha2, tysm for the help!
Please help answer my questions like these I have many more quick algebra 1 questions that are all due in 2 days so it would be much appreciated if you check them out. Once again, tysm!
Answer:
its the 4th one i think
Step-by-step explanation:
What is the vertex of the graph of the function f(x)=x^2+8x-2 !?
Answer:
(-4, -18).
Step-by-step explanation:
f(x = x^2 + 8x - 2 Completing the square on x^2 + 8x:-
= (x + 4)^2 - 16 - 2
= (x + 4)^2 - 18
- which is the vertex form of f(x)
The vertex of
(x - h)^2 + k is at (h, k)
So the vertex of f(x) is at (-4, -18)
Graph the equation:
Y = 1/3x + 2
Please help!!
please explain in a way a middle schooler would understand!!
ty!
use substitution to solve the system 3x+8y = -56 2x-y = 7
Answer: x = 0 ; y = -7
Step-by-step explanation:
Given equation:
1) 3x + 8y = -56
2) 2x - y = 7
Subtract 2x on both sides of 2) equation to isolate y-value
2x - y - 2x = 7 -2x
-y = 7 - 2x
Divide -1 on both sides of 2) equation
-y / -1 = (7 - 2x) / -1
y = 2x - 7
Current system
1) 3x + 8y = -56
2) y = 2x - 7
Substitute 2) equation into the y-value of 1) equation
3x + 8 (2x - 7) = -56
Simplify by distributive property
3x + 8 × 2x - 8 × 7 = -56
3x + 16x - 56 = -56
Combine like terms
19x - 56 = -56
Add 56 on both sides
19x - 56 + 56 = -56 + 56
19x = 0
Divide 19 on both sides
19x / 19 = 0 / 19
[tex]\Large\boxed{x=0}[/tex]
Substitute the x-value into one of the equations to find the y-value
2x - y = 7
2 (0) - y = 7
0 - y = 7
-y = 7
[tex]\Large\boxed{y=-7}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Geometry: Complete these proofs, ASAP!!!
The complete proofs are:
Proof 1
a || b; c || d ⇒ Given∠5 is supplementary to ∠4 ⇒ ∠5 + ∠4 = 180∠2 = ∠4 ⇒ Definition of corresponding angles ∠5 + ∠2 = 180 ⇒ Substituting property of equality∠5 + ∠2 = 180 ⇒ Definition of supplementary anglesProof 2
BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given∠3 ≅ ∠4 ⇒ Definition of congruent angles∠1 ≅ ∠3 ⇒ Definition of corresponding angles ∠1 ≅ ∠4 ⇒ Definition of corresponding angles How to complete the proofs?Proof 1
Lines a & b and c and d are given as parallel lines.
So, we have
a || b; c || d ⇒ Given
From the question, we have:
∠5 is supplementary to ∠4
So, we have
∠5 + ∠4 = 180
This is so because supplementary angles add up to 180
Corresponding angles are equal.
So, we have:
∠2 = ∠4
By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have
∠5 + ∠2 = 180
Hence, angles ∠5 and ∠2 are supplementary angles
Proof 2
Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.
So, we have
BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given
From the question, we have:
∠3 ≅ ∠4 ⇒ Definition of congruent angles
∠1 ≅ ∠3 ⇒ Definition of corresponding angles
Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4
∠1 ≅ ∠4
Hence, the angles 1 and 4 are congruent
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HELP PLEASE !!!!!!!!!
The amount made per minute is $1.28 * 10^7
Ratio and proportionsFractions are written as a ratio of two numbers. For instance a/b is a fraction.
According to the question, a certain animated movie earned $1.1 * 10^9 every 9.1 * 10^1 minutes.
$1.1 * 10^9 = 9.1 * 10^1
In order to determine the amount earned per minute;
x = 1minute
Divide both expressions
1.1 * 10^9/x = 9.1 * 10^1
x = 1.1 * 10^9 /9.1 * 10^1
Divide the result
x = 1.1 * 10^9 /9.1 * 10^1
x = 0.12 *10^8
x = $1.28 * 10^7
Hence the amount made per minute is $1.28 * 10^7
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find the value of n:
[tex]\frac{10}{n} = \frac{15}{6}[/tex]
Step-by-step explanation:
Greetings !
Given expression
[tex] \frac{10}{n} = \frac{15}{6} [/tex]
cross multiply
apply fraction cross multiply
[tex]if \: \: \frac{a}{b} = \frac{c}{d} \: \: then \: \: a.d = b.c[/tex]
10.6=n.15
simplify:
10.6=60Thus, 60=n.15
switch sides
[tex]n.15 = 60[/tex]
divide both sides by 15
[tex] \frac{n.15}{15} = \frac{60}{15} [/tex]
simplify
[tex]n = 4[/tex]
Hope it helps!
HELPPPPP: An ipod cost $200. Ivy is going to save money for the ipod by babysitting for $15 per week. Ivy already has $32 saved. Write an inequality that can be used to find the minimum number of weeks Ivy must babysit to earn enough to buy an ipod.
To form an equation from a word problem, we can recognize variables and operations from keywords.
Solving the QuestionLet the number of weeks be a.
We're given:
Goal amount is $200 at minimumMoney earned is $15aCurrent amount is $32Because $200 is the minimum account required, we know that the amount earned must be greater than or equal to 200.
[tex]200\leq[/tex]
Our current savings and money can be calculated by adding 15a and 32:
[tex]200\leq15a+32[/tex]
Answer[tex]200\leq15a+32[/tex]
Circle X is shown. Line segments W X and Y X are radii. Tangents W Z and Y Z intersect at point Z outside of the circle. Arc W Y is 109 degrees.
What is the measure of angle WZY?
54.5°
71°
125.5°
180°
From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°
How to find the angle from a circle tangent?The lines ZY and ZW are tangents to the attached circle which is centered at x.
From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.
From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.
Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;
∠WZY = 360° - (90° + 90° + 109°)
∠WZY = 360° - 289°
∠WZY = 71°
Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°
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Answer: B. 71°
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
I got it right!
pretty please what is g(x)
The value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x). This can be obtained by finding composite of (h ° g) (x) using the formula for composition.
Find the value of g(x):
Composition of a function : A composite function is created when one function is substituted into another.
f composite of g is denoted as (f ° g)
The formula to find the composite of a function,
(f ° g)(x) = f(g(x))For example,
f(x) = x + 2, and g(x) = 3x
(f ° g)(x) = f(g(x)) = g(x) + 2 = 3x +2 (g ° f)(x) = g(f(x)) = 3(f(x)) = 3(x+2) = 3x + 6
In the question,
Given that, f(x) = (8x³ - 1)³, h(x) = x³
f(x) = (h ° g) (x)
⇒ (8x³ - 1)³ = h(g(x))
⇒ (8x³ - 1)³ = (g(x))³
Taking cube roots on both sides,
⇒ ∛(8x³ - 1)³ = ∛(g(x))³
⇒ (8x³ - 1) = (g(x))
⇒ g(x) = 8x³ - 1
Hence the value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x).
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90 times 2.5 divided by 3 +200,000?
Answer:
200,075
Step-by-step explanation:
90 times 2.5 = 225
225 divided by 3 = 75
75 + 200,000 = 200,075
Answer: 200075
Step-by-step explanation:
90 * 2.5 = 225
225 / 3 = 75
75 + 200,000 = 200,075
Select the correct answer. What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1? A. -0.21 B. 0.74 C. 1.35 D. 1.97
Given the:
ln(x + 6) - ln(2x - 1) = 1
Using the logarithm rule:
ln a - ln b = ln (a/b)ln((x + 6) / (2x - 1)) = 1((x + 6) / (2x - 1)) = E ¹We know,
e1 = ²'⁷²((x + 6) / (2x - 1)) ≈ 2.72Simplifying we get,
(x + 6) = 2.72 (2x - 1)x + 6 = 2.72 (2x) - 2.72 (1)x + 6 = 5.44x - 2.728.72 = 4.44xBy cross multiplication we get,
x = 8.72 / 4.44x = 1.97Therefore, the value of x is 1.97.
The correct option in the exercise ln (x + 6) - ln (2x - 1) = 1 is alternative "D".
PLEASE HELP ASAP
18. A surveyor intends to create a bridge across a river. There is a tall tree on the other side of the river. He
measures a line down his side of the river for 125 feet. At each side of this line he uses his surveying
equipment to measure the angle to the tree on the other side of the river. At the beginning of the line, the
angle to the tree was 65°10', at the end of the line the angle to the tree is 60°10'. If he wants the bridge to go
from where he started his line to the tree, then how long will the bridge be?
The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.
Which rule can be used to find the length of the bridge?Given;
Location of the tree = The other side of the river from the surveyor
Length of the line measured along the river, L = 125 feet
Angle to the tree from the start of the line = 65°10'
1° = 60'
10' = ((1/60)×10)° = (1/6)°
65°10' = (65 + 10/60)° = (65 + 1/6)°
Angle measured at the end of the line, E = 60°10'
Similarly;
E = 60°10' = (60 + 1/6)°
The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;
Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)
S = (114+5/6)°
From the angle sum property of a triangle, angle formed at the tree, T, is therefore;
T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°
According to the rule of sines, we have;
l/(sin T) = b/(sin E)
Where;
b = The length of the bridge
Which gives;
124/(sin 5°) = b/(sin (60 + 1/6)°)
b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2
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Anne can make 6 headbands 3/5 from meters of cloth. Which expression shows the amount of cloth needed to make 1 headband? What is the solution to the expression?
The amount of cloth needed to make 1 headband is 10 meters.
Unit valueNumber of headbands Anne made = 6Total clothes used = 3/5 metersCloth needed to make 1 headband = Number of headbands Anne made / Total clothes used
= 6 ÷ 3/5
= 6 × 5/3
= (6 × 5) / 3
= 30/3
= 10 meters
Therefore, the amount of cloth needed to make 1 headband is 10 meters.
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help me pls like srsly
The time it will take the thermometer to hit the ground is 22 seconds
Calculating TimeFrom the question, we are to determine the how long it would take the thermometer to hit the ground
From the given information,
The equation for the height as a function of time is
h(t) = -16t² + initial height
From the given information,
The thermometer falls from a weather balloon at a height of 7744 ft
∴ Initial height = 7744 ft
When the thermometer hits the ground, h(t) = 0
Thus, we get
0 = -16t² + 7744
16t² = 7744
t² = 7744/16
t² = 484
t = √484
t = 22 seconds
Hence, the time it will take the thermometer to hit the ground is 22 seconds
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PLEASE HELP IM STUCK
Answer:
Step-by-step explanation:
As per the same approach I answered in a similar problem:
The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate theRise/Run:
RISE = (-11 - 9) = -20
RUN = (3 - (-2)) = 5
Rise/Run, or slope, is = -20/5 or -4
I graphed this line and the two points (attached).
Answer:
-20/5 or -4
Step-by-step explanation:
Answer:
Step-by-step explanation:
As per the same approach I answered in a similar problem:
The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate theRise/Run:
RISE = (-11 - 9) = -20
RUN = (3 - (-2)) = 5
Rise/Run, or slope, is = -20/5 or -4
Use lagrange multipliers to find the minimum distance between the origin and the plane 3x y 2z = 28
The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.
In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.
Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.
We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:
D = √(x² + y² + z²), which can also be shown as:
D² = x² + y² + z².
The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:
2x = 3λ, or, x = (3/2)λ,
2y = λ, or, y = λ/2, and,
2z = 2λ, or, z = λ.
Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:
3(3/2)λ + λ/2 + λ = 28,
or, 6λ = 28,
or, λ = 28/6 = 14/3.
Thus, we get:
x = (3/2)λ = 7,
y = λ/2 = 7/3, and,
z = λ = 14/3.
Substituting these in the distance formula, we get:
D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.
Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.
Learn more about the Lagrange Multipliers at
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