Use Lagrange multiplier method to find the maximum and minimum values of (, , ) = − 2 + 5 On the sphere 2 + 2 + 2 = 30
Answers
Answer:
Please find the complete question in the attached file.
Step-by-step explanation:
Calculation with Lagrange multipliers of its optimum restricted places,
[tex]f_x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ g_x = 2x\\\\f_y = 1 \ \ \ \ \ \ \ \ \ \ \ \ \ g_y = 2y\\\\[/tex]
Set the multiplier formulas for Lagrange:
[tex]f_x = \lambda g_x \to 2 = \lambda 2x ............ (i)\\\\f-y = \lambda g_y \to 1 = \lambda 2y................ (ii)\\\\constraint: \\\\\to x^2 + y^2 = 5 .................... (iii)\\\\Taking \ (i)\ divides\ (ii), \ (assuming\ \lambda \neq 0)\\\\\frac{2}{1}=\frac{\lambda 2x}{\lambda 2y}=\frac{x}{y}\\\\\therefore \\\\2y = x\\\\Sub\ into\ (iii)\ to\ find\\\\4y^2 + y^2 = 5 \to y = \pm 1\\\\[/tex]
We get solutions (x,y)=(2,1) and (−2,−1) if combined with 2y = x. These are all the identical points we obtained in (c) and we know the f(2,1) is the max, whereas f(−2, −1) is a minimum.
Related Questions
4x+9/y+11=0 and 6/y -3x=8
Answers
9514 1404 393
Answer:
(x, y) = (-2 12/17, -51)
Step-by-step explanation:
Here is the answer to ...
[tex]4x+\dfrac{9}{y}+11=0\\\\\dfrac{6}{y}-3x=8[/tex]
If you mean something else, then parentheses are needed.
__
Let z = 1/y. Then the equations in general form are ...
[tex]4x+9z+11=0\\3x-6z+8=0[/tex]
The solution (cross multiplication method) is ...
x = (9·8 -(-6)·11)/(4(-6)-3·9) = 138/-51 = -2 12/17
z = (11·3 -8·4)/-51 = -1/51
y = 1/z = -51
The solution is (x, y) = (-2 12/17, -51).
What is the value of x?
Answers
Answer:
D. 30°
Step-by-step explanation:
By exterior angle theorem:
x° + 70° = 100°
x° = 100° - 70°
x° = 30°
x = 30
A house plan Is drawn to a scale 1cm to 2m. What is the length of a window 2.5cm long on the plan?
Answers
1cm = 2m
=> 1cm = 200cm
2.5cm = 2.5 × 200cm = 500 cm = 5m
So, the length of window is 500cm or 5m.
What is the system of equations shown in the graph
Answers
If you look at the graph the slopes and y intercepts match up
Answer:
D)
y = - x + 1
y = -1/4 +2
Step-by-step explanation:
The equation of a linear graph: y = mx + b
The red graph is going down, so it would mean the m value is negative (-). This cancels options A) and C). The red graph also moves one unit up the y-axis which means the b is one (1). So the equation would be y = - x + 1.
The blue graph is also going down, so it would mean the m value is negative (-). This means it could be options B) or D). But, the blue graph also moves two units up the y-axis, which means the b is two (2). So the equation would be y = - 1/4x + 2.
what is the ratio of Sin 45°?
Answers
Answer:
1/√2
Step-by-step explanation:
The value of sin 45 is 1/√2
Which of the following equations correctly represents the law of cosines?
Answers
Answer:
C
Step-by-step explanation:
In - ABC shown below, side AC is extended to point D with mZ DAB = (180 – 3x) °,
mZ B = (6x – 40) °, and m2 C = (x + 20).
Answers
Answer:
<BAC = 36degrees
Step-by-step explanation:
Find the diagram attached
The sum of the interior angle is equal to the exterior. Hence;
<B + <C = <DAB
6x+40 + x+20 = 180 - 3x
7x+60 = 180 - 3x
7x+3x = 180 - 60
10x = 120
x = 120/10
x = 12
Get <BAC
<BAC = 180 - (180-3x)
<BAC = 180-180+3x
<BAC = 3x
<BAC = 3(12)
<BAC = 36degrees
What is the perimeter of parallelogram WXYZ? StartRoot 5 EndRoot + StartRoot 17 EndRoot units 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units 16 units 22 units
Answers
Answer:
2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units
Step-by-step explanation:
The perimeter of the parallelogram is expressed as
Perimeter = WX + XY + YZ + WZ
Using the distance formula;
WX = √(0-(-1))²+(4-0)²
WX = √1²+4²
WX = √17
For XY:
XY = √(-2-(0))²+(3-4)²
XY = √(-2)²+(-1)²
XY = √4+1
XY = √5
For YZ:
YZ = √(-2+3))²+(3+1)²
YZ = √(1)²+(4)²
YZ = √1+16
YZ = √17
For WZ;
WZ = √(-3+1)²+(-1-0)²
WZ = √(-2)²+(-1)²
WZ = √4+1
WZ = √5
Perimeter = √17+√5+√17+√5
Perimeter = 2√17 + 2√5 units
Answer:
B
Step-by-step explanation:
pls answer if it is correct i will give brainlist
Answers
Answer:
1/ x = 22.5°
2/ x = 60°
Step-by-step explanation:
1/ We have: 3x + 2x + 3x = 180°
=> 8x = 180° => x = 22.5°
2/ We have: x + x + x = 3x = 180°
=> x = 60°
Answer:
1) x = 22.5
2) x = 60
Step-by-step explanation:
→ Add the angles together
1) 3x + 2x + 3x = 8x
2) x + x + x = 3x
→ Make it equal to 180
1) 8x = 180
2) 3x = 180
→ Divide both sides by 8 and 3
1) x = 22.5
2) x = 60
If x+y=15 and x-y=25, then what is the value of 2x^2 - y^2?
Answers
Answer:
775
Step-by-step explanation:
We are given two equations in which we can perform systems of equations by putting these two equations on top of each other then solving for one variable:
x+y=15
x-y=25
Here, we can cancel out the y variable and get:
2x=40
x=20
Then we can put the x variable into any of the equations to solve for y (in this case I will use the equation x+y=15 so 20+y=15
y=-5
Now, we can solve by plugging both variables into 2x^2 - y^2 :
2(20)^2 - (-5)^2
800-25 = 775
I hope this helps!
Answer:
775
Step-by-step explanation:
Hi there!
We are given the following system of equations:
x+y=15
x-y=25
and we need to find the value of 2x²-y²
First, let's find the value of x and y
Let's add the 2 equations together to clear y and solve for x (y-y=0)
2x=40
divide both sides by 2
x=20
Now substitute 20 as x into either one of the equations to solve for y
To do x-y=25 for instance,
20-y=25
subtract 20 from both sides
-y=5
multiply both sides by -1
y=-5
Now we know that x=20 and y=-5
Substitute those values into the expression (remember: y² is equal to y×y, or (y)²)
2(20)²-(-5)²
Raise to the second power
2(400)-(25)
multiply and open parenthesis
800-25
subtract
775
Hope this helps!
Write each as a percent. Use proportions.
7/25, 2/3, 3/8
Answers
Answer:
Step-by-step explanation:
[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]
The ages of Raju and Ravi are in the ratio 3:4 Four years from now the ratio of their ages will be 4:5 Find their present ages
Answers
Answer: Their present age is 12 and 16.
Step-by-step explanation:
Let the required age be 3x and 4x
so
(3x+4)/(4x+4) = 4/5
5(3x+4) = 4(4x+4)
or, 15x + 20 = 16x + 16
or, 15x - 16x = 16-20
or, -x = -4
so, x = 4
now,
3x = 3*4 = 12
4x = 4*4 = 16
Does anyone know this
Answers
The total width is shown as 12 ft. The width of the small square is 2 ft so the width of the larger square is 12-2 = 10 ft.
Area of each square: 10 x 10 = 100
2 x 2 = 4
Total area = 109 + 4 = 104 square ft.
Describe the solution of h(x) shown in the graph.
a parabola opening up passing through negative 1 comma zero, zero comma negative 2, and 2 comma zero
A. All solutions that lie on h(x)
B. All real solutions
C. All whole number solutions
D. All positive solutions
Answers
Answer:
Step-by-step explanation:
This is a reading question. You have to know what all the terms mean.
B: is the first one you have to think about. All real solutions. Is that the answer, or do you have to think about it more. The key word is solutions. So that takes in A. So B is the answer.
A is the second best answer. Any solution has to be on the blue line. The blue line is the visual record of what works in B. Well, why not pick A? It is because B is more general, and it includes A.
C More than whole numbers solve this question. The line is continuous.
D There are negative solutions as well. Not the answer.
Answer:
the answer is A. All solutions that lie on h(x)
i took the test
Step-by-step explanation:
Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is
Look at image for reference
Answers
Answer:
(3)11
Step-by-step explanation:
We are given that
[tex](x^2-12x+35)(x^2+10x+24)=504[/tex]
We have to find the sum of positive roots of the equation.
[tex]x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504[/tex]
[tex]x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504[/tex]
[tex]x^4-2x^3-61x^2+62x+840-504=0[/tex]
[tex]x^4-2x^3-61x^2+62x+336=0[/tex]
Factor of 336
2,3,4,6,8,7,
Let x=2
[tex]2^4-2^4-61(2^2)+62(2)+336\neq0[/tex]
x=2 is not the root of equation
x=-2
[tex](-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0[/tex]
Hence x=-2 is the root of equation.
x+2 is a factor of equation.
x=3
[tex]3^4-2(3^3)-61(3^2)+62(3)+336=0[/tex]
Therefore, x=3 is the root of equation.
[tex](x+2)(x-3)(x^2-x-56)=0[/tex]
[tex](x+2)(x-3)(x^2-8x+7x-56)=0[/tex]
[tex](x+2)(x-3)(x(x-8)+7(x-8))=0[/tex]
[tex](x+2)(x-3)(x-8)(x+7)=0[/tex]
[tex]x-8=0\implies x=8[/tex]
[tex]x+7=0\implies x=-7[/tex]
Positive roots are 3 and 8
Sum of positive roots=3+8=11
Option (3) is true.
Help and explain pls and thankyouuu
Answers
Answer: (1, 8)
Step-by-step explanation:
Substitute y = 3x + 5 into the equation 2x + 3y = 26:
2x + 3(3x + 5) = 26
2x + 9x + 15 = 26
11x = 26 - 15
11x = 11
x = 1
Substitute the value of x into the equation y = 3x + 5:
y = 3(1) + 5 = 3 + 5 = 8
What are the coordinates of points E, F, and GS
A. E (2, 3), F (8,5), G (5,8)
B. E (3, 2), F (8,3), G (5,6)
C. E (3, 2), F (8,4), G (5,7)
D. E (3, 3), F (9, 4), G (6,7)
Answers
Answer:
its a i think
Step-by-step explanation:
What is the degree & leading coefficient?
h(t) = 0.2t^3 - 4t^2 +20t
Answers
Answer:
degree=3
coefficient=0.2
Mrs Nu paid $2083 for 2 smiler laptops and 3 similar earphones. Each laptop cost of each earphones?
Answers
Answer:
Step-by-step explanation:
The information given is incomplete :
Answer:
x = 1/2(2083 - 3y)
y = 1/3(2083 - 2x)
Step-by-step explanation:
Let
Laptop cost = x
Earpiece cost = y
Number of laptops= 2
Number of earpiece = 3
2x + 3y = $2083
The cost per laptop :
2x = 2083 - 3y
Divide both sides by 2
x = (2083 - 3y) / 2
x = 1/2(2083 - 3y)
Or
3y = 2083 - 2x
y = (2083 - 2x) / 3
y = 1/3(2083 - 2x)
A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Solution A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use
Answers
Answer:
The answer is "180".
Step-by-step explanation:
Please find the complete question in the attached file.
Let's
x = ounces solution of A
y = ounces solution of B
[tex]x + y = 180 \\\\y = 180 - x\\\\0.60x + 0.85y = 0.75(180)\\\\0.60x + 0.85y = 135\\\\[/tex]
Multiply both sides of the equation by 100 to remove the decimal points.
[tex]60x + 85y = 13500\\\\60x + 85(180 - x) = 13500\\\\60x + 15300 - 85x = 13500\\\\-25x = -1800\\\\x = 72\ \ ounces\\\\y = 180 - 72 \\\\y = 108 \ \ ounces\\\\[/tex]
Is (-2,-4) a solution of the graphed inequality?
Choose 1 answer:
Yes
No
Answers
Answer:
Yes
General Formulas and Concepts:
Algebra I
Reading a coordinate graphCoordinates (x, y)Solving inequalitiesStep-by-step explanation:
When we plot (-2, -4) onto the graph, we can envision that the point is within the shaded region of the graphed line.
∴ (-2, -4) would be a solution.
What is the answer to this question
Answers
Answer:
4 is the answer to this question
What is the X and Y?
Answers
What is the circumference of D if the length of EF is 9 cm?
Answers
Answer:
It should be B, 180 cm
Step-by-step explanation:
x = circumference of circle D
18/360 = 9/x
9*360 = 18x
9*360/18 = x
x = 180
Solve for x.
3х - 4 = 13
Answers
[tex]\large\bold{\underline{\underline{ \: x = 5 \frac{2}{3} }}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3x - 4 = 13[/tex]
[tex]➺ \: 3x = 13 + 4[/tex]
[tex]➺ \: 3x = 17[/tex]
[tex]➺ \: x = \frac{ 17}{3} [/tex]
[tex]➺ \: x = 5 \frac{2}{3} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]➺ \: 3x - 4 = 13[/tex]
[tex]➺ \: 3 \times 5 \frac{2}{3} - 4 = 13[/tex]
[tex]➺ \: 3 \times \frac{17}{3} - 4 = 13[/tex]
[tex]➺ \: 17 - 4 = 13[/tex]
[tex]➺ \: 13 = 13[/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Hope it helps:)
7). Express 98 in base 2
Answers
ANSWER
1100010
EXPLANATION
converting 9810 to 2
The equation calculation formula for 98 base10 number to base 2 is like this below.
2|98|
2|49|0
2|24|1
2|12|0
2|6|0
2|3|0
2|1|1
2|1|1
Ans:1100010 base2
A Basket contains 3 types of fruits weighing 58/3 kg in all. If 73/9 kg of are apples,19/6 are oranges and the rest are pears. What is the weight of the pears in the basket?
Answers
Answer:
Step-by-step explanation:
233 322
PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?
A. (12, 8)
B. (3, 5)
C. (-3, 3)
D. (0, 4)
please don’t use this for points.
Answers
Answer:
A.............
Step-by-step explanation:
. ..........
Answer:
C. (3,3)
Step-by-step explanation:
When These equations are both graphed the solution for these equations when they intersect is (-3,3)
Rick has $8x and Helen has twice that amount. They save $3 each per week. What amount will be the sum of their money 4 weeks from now
Answers
Answer:
Savings total for both = 24x + 24
Step-by-step explanation:
Rick has 8x to start with
Let w = the number of weeks he will save.
Savings = 8x + 3*w
Let w = 4
Savings = 8x + 3*4
Savings = 8x + 12
Helen
Let w = the number of weeks she will save.
Savings = 16x + 3*w
Let w = 4
Savings = 16x + 12
Now we come to the question. It seems to want the total combining both of them.
Rick + Helen = 8x + 12 + 16x + 12 = 24x + 24
The only other possible answer is
Rick = 8x + 12
Helen = 16x + 12
if f(x) = 2x² +1 and g(x) = x² - 7 find (f+g) (x)
Help me find (f+g)(x) please!
Answers
Answer:
[tex](f+g)(x) = 3x^2 - 6[/tex]
Step-by-step explanation:
[tex]f(x) = 2x^2 + 1, \ g(x) = x^2 - 7\\\\(f +g)(x) = f(x) + g(x) \\\\(f+g)(x) = 2x^2 + 1 + x^2 - 7 \\\\(f+ g)(x) = 3x^2 - 6[/tex]
