The setup for this problem is written as l(x,y)= f(x,y)+λg(x,y)
For example, a common economic problem is the consumer choice decision. Households are selecting consumption of various goods. However, consumers are not allowed to spend more than their income (otherwise they would buy infinite amounts of everything!!). Let’s set up the consumer’s problem:
Suppose that consumers are choosing between Apples (A) and Bananas (B). We have a utility function that describes levels of utility for every combination of Apples and Bananas.
11
A 2 B 2 = Well being from consuming (A) Apples and (B) Bananas.
Next, we need a set of prices. Suppose that Apples cost $4 apiece and Bananas cost $2 apiece. Further, assume that this consumer has $120 available to spend. The income constraint is
$2B+$4A≤$120
However, the problem requires that the constraint is in the form g(x, y)≥ 0. In
the above expression, subtract $2B and $4A from both sides. Now we have 0≤$120−$2B−$4A
g(A, B) Now, we can write out the lagrangian
11
l(A,B)= A2 B2 +λ(120−2B−4A)
f (A, B) g(A, B)
Step II: Take the partial derivative with respect to each variable We have a function of two variables that we wish to maximize.
Therefore, there will be two first-order conditions (two partial derivatives that are set equal to zero).
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What is 5 1/2 • 2 1/3
Answer:
77/6 or 12 5/6
Step-by-step explanation:
put it into improper fraction
then multiply 11/2 by 7/3
in the following triangle theta=60.Find the values of the angles of the angles B and B'
Answer:
A. B = 64.13° or B' = 115.87°
Step-by-step explanation:
The given angle is opposite the shortest of the given sides, so there are two possible solutions using the Law of Sines. Either way, we have ...
sin(B)/16 = sin(θ)/15.4
B = arcsin(16/15.4·sin(60°)) ≈ arcsin(0.899767)
B = 64.13° or B' = 180° -64.13° = 115.87°
what relationship do you see when comparing the equivalent decimal and percent
Answer:
decimal 0.25 percent 25
Step-by-step explanation:
Decimal -divide by 100%
Percent -multiply by 100
Select true or false to tell whether the following disjunctions are true or false. Use the truth table if needed.
5 · 3 = 15 or 7 + 5 = 20
True
False
Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3. A. Explain why the information Mary was given cannot be correct. B. If the given point (1, 3) and the given slope are correct, what is the equation for the line? C. Give the coordinates of another point on the line. D. If the given points are correct on the line, what is the slope? E. Write an equation for the line.
Answer:
Below in bold.
Step-by-step explanation:
A. We can calculate the slope using (y2 - y1) / (x2 - x1)
= (3 - (-2)) / (1 - 6)
= 5/-5
= -1.
So the given slope of 3 or one of the points is NOT correct.
B. If the point (1, 3 ) and the slope are correct then the equation for the line (using the point-slope form) is y - 3 = 3(x - 1)
C Another point on this line would be , when x = 0 , y = 3*-1 + 3 = 0
so it's (0, 0)
D. If the given points are correct the slope is ( as above) = -1.
E. The equation for this line is
y - 3 = -1(x - 1)
y = -x + 1 + 3
y = 4 - x.
Can somebody answer this????
Answer:
x ≥ 0
Step-by-step explanation:
The domain is the input values for the function
In this case it is what x can equal
In looking at the graph, x is greater than or equal to zero
x ≥ 0
will mark as bianlest plz plz hlpe asap The ____________ is the average distance of all the data values from the mean of the data. quartile interquartile range mean absolute deviation bias
Answer:
mean absolute deviation
What if f(0)? (The function f(x) is shown on the graph)
Answer:
35
Step-by-step explanation:
Answer:
please include the graph...
Step-by-step explanation:
A hemispherical tank is filled with water and has a diameter of 15 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
Answer:
55135 lbs
Step-by-step explanation:
Select all the situations where knowing the volume of an object would be more useful than knowing its surface area. *
A. Determining the amount of paint needed to paint a barn.
B. Determining the monetary value of a piece of gold jewelry.
C. Filling an aquarium with buckets of water.
D. Deciding how much wrapping paper a gift will need.
E. Packing a box with watermelons for shipping.
F. Charging a company for ad space on your race car.
G. Measuring the amount of gasoline left in the tank of a tractor.
Answer: C, E, G
Step-by-step explanation:
To measure the amount of gasoline left in the tank of a tractor we need to determine volume. Therefore, the correct options are C, E and G.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
A) Determining the amount of paint needed to paint a barn.
Need to determine the surface area barn.
B) Determining the monetary value of a piece of gold jewelry.
Need to determine the surface area of gold jewelry.
C) Filling an aquarium with buckets of water.
Need to determine the volume of aquarium and bucket.
D) Deciding how much wrapping paper a gift will need.
Need to determine the surface area of a paper.
E) Packing a box with watermelons for shipping.
Need to determine the volume of box and watermelon.
F) Charging a company for ad space on your race car.
Need to determine the surface area of ad space on your race car.
G) Measuring the amount of gasoline left in the tank of a tractor.
Need to determine the volume of the tank of a tractor.
Therefore, the correct options are C, E and G.
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Cole brought chocolate and vanilla cupcakes to school for his birthday. 40 students decided to take a cupcake, and 90% of them picked vanilla. How many people picked a vanilla cupcake?
PLEASE ANSWER DUE SOON
Answer:
36 people picked a vanilla cupcake
Step-by-step explanation:
40 * 90%
= 40 * 0.9
= 36
Answer:
36 = people picked a vanilla cupcake
= 40 * 0.9
= 36
Richard can mow the lawn three times as fast as Terri. Together, they finish mowing the lawn in 20 minutes. Which of the following equations would describe how many minutes it would take Richard to mow the lawn by himself? a. 1/x+1/3x=1/20 b. 1/x+1/3=1/20 c. 20 (1/x+1/3x)=1/20 d. x+3x=1
Answer:
d it adds the two up and only mutiplys terris amount.
The line represented by the equation 3x + 5y = 2 has a slope of - Which shows the graph of
y
..5
5
5
4.
4
4
3+
2
3
2
3
2
+
1
..
2
5
-2-4
1 2 3 4
-3-2-4
-2-
3
-5-4-3-2-14+ 1434
-2
--3-
14
L5
م ر بنه + کا
O
O
Answer:
Step-by-step explanation:
Solve the given 3x + 5y = 2 for y. This will automatically indicate the slope of the line.
Subtracting 3x from both sides of this equation, we get:
5y = -3x = -3x + 2.
Dividing both sides by 5 yields y = (-3/5)x + 2/5.
The slope of the given line is -3/5. The y-intercept of this line is (0, 2/5).
Next time, please share the answer choicess. Thank you.
Here is a table of values for y = f(x).
х
0 5 10 15 20 25 30 35 40
f(x) 5 6 7
8
9
10 11
12 13
Mark the statements that are true.
O A. f(15) = 8
B. The domain for f(x) is the set (5, 6, 7, 8, 10, 11, 12, 13},
C. The range for f(x) is all real numbers.
D. f(5) = 6
Answer:
D
Step-by-step explanation:
The population of algae in an experiment has been increasing by 5% each day. If there were 5p algae at the beginning of the experiment, predict the number of algae in 7 days. Help asap
Answer:
Number of algae in 7 days = 70.355
Step-by-step explanation:
Given:
Algae in beginning = 50
Rate of increasing = 5% per day = 0.05
Number of days = 7 days
Find:
Number of algae in 7 days.
Computation:
[tex]Number\ of\ algae\ in\ 7\ days = Algae\ in\ beginning(1+Rate\ of\ increasing)^{Number\ of\ days}\\\\Number\ of\ algae\ in\ 7\ days = 50(1+0.05)^7\\\\Number\ of\ algae\ in\ 7\ days = 70.355[/tex]
Number of algae in 7 days = 70.355
Answer:
70
Step-by-step explanation:
Acellus
Twice a number plus three times a second number is negative one. The first number plus four times the second number is two.
Answer:
Step-by-step explanation:
The first number is -2 and the second number is 1
Answer:
The first number is -2 and the second number is 1.
Step-by-step explanation:
2n + 3s = -1
(n + 4s = 2)-2 Multiply by -2 to cancel the n
2n + 3s = -1
-2n - 8s = -4 Add these equations together
-5s = -5 Divide both sides by -5
s = 1
Plug this into the first equation to find the value of n
2n + 3(1) = -1 Multiply
2n + 3 = -1
- 3 - 3 Subtract 3 from both sides
2n = -4 Divide both sides by 2
n = -2
what is the surface area of the given figure
Answer:
1,728cm square
Step-by-step explanation:
Surface area=sum of all faces of a polygon
Let's do the biggest ones: 32•20=640
32•16=512
Now the rest:
12•32=384
16•12=192 192÷2=96
16•12=192 192÷2=96
Now add it all up: 640+512+384+96+96=1,728cm square
Write an equation in standard form passing through the points (-2, 0) and (-3, -1). I know the answer to the question, but I do not know how to solve this question to get to the answer. I will give the title to whoever gives the most understandable explanation to the question and answer. I will be glad to answer to help you give to create an explanation. Thank you and good luck.
Answer:
[tex]y - x = 2[/tex]
Step-by-step explanation:
Given
Points (-2,0) and (-3,-1)
Required
Equation of Line
The first step is to determine the slope of the line; using the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]Where\ (x_1,y_1) = (-2,0)\ and\ (x_2,y_2) = (-3,-1)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{-1 -0}{-3 - (-2)}[/tex]
[tex]m = \frac{-1}{-3 +2}[/tex]
[tex]m = \frac{-1}{-1}[/tex]
[tex]m = 1[/tex]
The next is to determine the equation of the line using any of the points
The formula is as thus;
[tex]m = \frac{y - y_1}{x - x_1}\ or\ m = \frac{y - y_2}{x - x_2}[/tex]
Using [tex]m = \frac{y - y_1}{x - x_1}[/tex]
[tex]Where\ (x_1,y_1) = (-2,0)\ and\ m =1[/tex]
[tex]1 = \frac{y-0}{x - (-2)}[/tex]
[tex]1 = \frac{y-0}{x +2}[/tex]
[tex]1 = \frac{y}{x +2}[/tex]
Multiply both sides by x + 2
[tex](x+2)*1 = \frac{y}{x +2} * (x+2)[/tex]
[tex](x+2)*1 = y[/tex]
[tex]x+2 = y[/tex]
[tex]y = x + 2[/tex]
Subtract x from both sides
[tex]y - x = x - x +2[/tex]
[tex]y - x = 2[/tex]
Hence, the equation of the line in standard form is [tex]y - x = 2[/tex]
Solve the equation 25=7+r
Answer:
r = 18
Step-by-step explanation:
Subtract the seven from both sides
25 -7 = 7 - 7 + r
18 = r
Simple as that!
Hope this helps!
The solution of the given equation is 18.
The given equation is 25=7+r.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Transpose 7 to other side of the equation, we get
r=25-7
r=18
Therefore, the solution of the given equation is 18.
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You deposit $4300 in an account that earns 2% per year simple interest. The equation that represents this situation is: A(n) = 4300 + (n - 1)(0.02 • 4300) How much will you have in the account at the beginning of the 8th year? Round your answer to the nearest dollar. A. $10,320 B. $4988 C. $4902 D. $4386
Answer: $4902
Step-by-step explanation:
Amount = P (1 + rt)
= 4300 (1 + .02 * 7)
= 4300 (1 + .14)
= 4300 (1.14)
= 4902
3. Tanya needs to buy dirt for her children's playground.
The dirt costs $8 per ton, and there is a delivery cost
of $12 with each order.
If Tanya needs 5.5 tons, what will the cost be?
C=
A- A counter rotation of 270 around the origin
B- A counterclockwise rotation of 90 around the origin
C- A reflection over the x-axis
D- A translation down 5 units
Answer:
Step-by-step explanation:
how do u delete ur answer
Answer:
B- A counterclockwise rotation of 90 around the origin
Step-by-step explanation:
Have a great day!
Simplify the polynomial-
-3f²+4f-3+8f²+7f+1
Please help!!
I don't understand how to do this or anything with Polynomials really and I really need someone to explain in the easiest way possible!!
Help me out please not the last one but last one
Answer:
d
Step-by-step explanation:
Pythagorean theorem
a^2 + b^2 = c^2
C = 10
a = 6
c^2 - a^2 = 100 - 36 = 64
sqrt. 64 = 8
hope this helps
Answer:
8
Step-by-step explanation:
Use pythagerom therom we know the hypotneusis 10 and the base is 6 so we do 100^2 - 6^2 and get 64 then we take the square root of 64 and get 8
I need help on this.
Answer:
The question itself is wrong .As u know curly brackets should be inside big brackets.So in other words the first step is wrong.
The correct solving would be
Step-by-step explanation:
Mistake first appears in step no.1
We have to use the BODMAS rule
B=Bracket
O=Of
D=Division
M=multiplication
A=Addition
S=Subtraction
Hope it helps..And the right answer of that expression is 116
Please see the attached picture for the full solution
Hope it helps...
Good luck on your assignment
Which graph represents the function below?
y=
2x if x> 3
-X+9, if x <3
Answer:
A
Step-by-step explanation
Answer:
You're only showing the first option...
On a coordinate plane, a square and a point are shown. The square has points R prime (negative 8, 1), S prime (negative 4, 1), T prime (negative 4, negative 3), and U prime (negative 8, negative 3). Point S is at (3, negative 5). Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU? (–5, –3) (3, –3) (–1, –6) (4, –9)
Answer:
(–1, –6)
Step-by-step explanation:
Given that S(3, –5) was translated to S'(–4, 1), the transformation rule is (x-7, y+6). Then, the coordinates of square RSTU are:
R'(–8, 1) -> (-8+7, 1-6) -> R(-1, -5)
S'(–4, 1) -> (-4+7, 1-6) -> S(3, -5)
T'(–4, –3) -> (-4+7, -3-6) -> T(3, -9)
U'(–8, –3) -> (-8+7, -3-6) -> U(-1, -9)
The point (–1, –6) lies on the segment RU
The point that lies on a side of the pre-image is mathematically given as
x=(-1,-6)
What is a Pre-Image?A pre-image is simply a the group of chosen elements from a mapped domain to give a given subset of the codomain.
What points can be found on the pre-image, square RSTU?Question Parameter(s):
which has vertices
R'(–8, 1),
S'(–4, 1),
T'(–4, –3),
U'(–8,
Generally, the equation for the transformation is mathematically given as
(x-7, y+6).
Therefore
R'(–8, 1) --> (-8+7, 1-6)
R'(–8, 1) --> R(-1, -5)
S'(–4, 1) -=> (-4+7, 1-6)
S'(–4, 1)-> S(3, -5)
T'(–4, –3) --> (-4+7, -3-6)
T'(–4, –3 -> T(3, -9)
U'(–8, –3) --> (-8+7, -3-6)
U'(–8, –3)-> U(-1, -9)
In conclusion, point S with coordinates of (3, –5) lies within RU
x=(-1,-6)
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As the result of experimental work, a student finds the density of a liquid to be 0.1369 g/㎤. The known density of that liquid is 0.1478 g/㎤. What is the percent error of this student's work? (Round final answer to the nearest tenth if necessary
Answer:
Percent error is [tex]7.4\%[/tex]
Step-by-step explanation:
Given:
As per the result of experimental work, density of a liquid is 0.1369 g/㎤
Known density of the liquid is 0.1478 g/㎤
To find: percent error
Solution:
The density of a substance is defined as mass per unit volume.
S.I. unit is Kilogram per cubic metre.
Error = Actual density - density as per the experiment = [tex]0.1478-0.1369=1.0109\,\,g/cm^3[/tex]
Percent error = ( error/Actual error ) × 100 = [tex]\frac{0.0109}{0.1478}\times 100=7.4\%[/tex]
which of the following is the proper name for the figure below
Answer:
d
Step-by-step explanation:
you name a triangle by its vertices so the only vertices are J,K and E. so the answer is JKE
Answer:
The answer is option 4.
Step-by-step explanation:
In the diagram, A, O and R are the lengths of the triangle. So the best way to identify the triangle using angles is ΔAKE.
(a) How could you calculate 23 x 4 on your calculator if the 4 button is broken? (b) How could you calculate 23 x 21 if the 2 button on your calculator is broken?
Answer:
You could add, subtract, multiply, and divide them to find the 21 or 4. then you just click the multiply and click 23.
