Answer:
f(-2,-1) = -8 is the minimum value of f(x,y)
f(2,1) = 8 is the maximum value of f(x,y)
Step-by-step explanation:
f(x,y) = 2x²y under the constraint 2x² + 4y² = 12
Let g(x,y) = 2x² + 4y² - 12
df/dx = 4xy, df/dy = 2x², dg/dx = 4x and dg/dy = 8y
Now, using the principle of Lagrange multipliers,
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
Substituting the values of the variables, we have
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
4xy + 4xλ = 0 (1) 2x² + 8λy = 0 (2)
xy + xλ = 0
x(y + λ) = 0
x = 0 or y + λ = 0
Since x ≠ 0, y = -λ
Substituting y = -λ into (2), we have
2x² + 8λy = 0
2x² + 8λ(-λ) = 0
2x² - 8λ² = 0
2x² = 8λ²
x² = 4λ²
x = ±2λ
Substituting the values of x and y into the constraint equation, we have
2x² + 4y² = 12
2(±2λ)² + 4(-λ)² = 12
2(4)λ² + 4λ² = 12
8λ² + 4λ² = 12
12λ² = 12
λ² = 1
λ = ±1
Substituting the value of λ into x and y, we have
x = ±2λ = ±2(±1) = ±2
y = -λ = -(±1) = ±1
The minimum values of x and y are -2 and -1 respectively. Substituting these int f(x,y), we have
f(-2,-1) = 2(-2)²(-1) = 2 × 4 × (-1) = -8
So f(-2,-1) = -8 is the minimum value of f(x,y)
The maximum values of x and y are 2 and 1 respectively. Substituting these int f(x,y), we have
f(2,1) = 2(2)²(1) = 2 × 4 × 1 = 8
So f(2,1) = 8 is the maximum value of f(x,y)
3. A polynomial or number that's left over after division is called the options: A) quotient. B) divisor. C) denominator. D) remainder.
Answer:
Remainder
Step-by-step explanation:
Remainder is a number that's left over after division.
For example:
11 divided by 2 is 5 remainder 1.17 leaves a remainder of 2 when divided by 3.Hope this helps ;) ❤❤❤
Answer:
[tex]\Large \boxed{\mathrm{D) \ remainder}}[/tex]
Step-by-step explanation:
The remainder is the amount left over after performing division.
For example when we divide 7 by 5:
7/5 = 1 and remainder 2. 2 is the amount left after dividing.
HELP PLEASE Find the value of Y given that M greater than KLM=134° and how did u get the answer
Answer:
5.44 = y
Step-by-step explanation:
KLM = KLN + NLK
134 = 47+ 16y
Subtract 47 from each side
134 - 47 = 47+16y - 47
87 = 16y
Divide each side by 16
87/16 = 16y/16
5.4375 = y
Round to two decimal places
5.44 = y
A 4% error is made in measuring
the radius of a sphere. Find the
Percentage error in the surface
area.
Answer:
8.51%
Step-by-step explanation:
Let us assume the radius of the sphere is r. The surface area of a sphere is:
Surface area = 4πr².
There is a 4% error in the measurement of the radius, therefore the radius being measured = (100% - 4%)r = (96%)r = 0.96r
The surface area as a result of error is:
Surface area after measurement = 4π(0.96r)² = 3.6864πr²
The percentage error is the ratio of the difference between the actual and measured value to the measured value. It is given as:
[tex]Percent\ error =\frac{Actual\ area-Measured\ area}{Measured \ area}*100\%\\ \\Percent\ error =\frac{4\pi r^2-3.6864\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =\frac{0.3136\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =0.0851*100\%\\\\Percent\ error =8.51\%[/tex]
The sum of two numbers is 52. The greater number is 4 more than the smaller number. Which equation can be used to solve for the smaller
number? (5 points)
a
XI- (x + 4) - 52
b
X + (x + 4) - 52
X(X + 4) - 52
x(x - 4) - 52
Answer:
x+(x+4)=52
Step-by-step explanation:
Let's name the smaller number x.
The greater number would then be (x+4).
The sum of two numbers means we are adding them together.
The equation we could then set up would be:
x+(x+4)=52
Now we can solve the equation to find the two numbers if needed.
Here is how:
x+x+4=52
Combine like terms.
2x+4=52
Subtract 4 from both sides.
2x=48
Divide both sides by 2
x=24
The smaller number is 24.
24+4=28
The larger number is 28.
To one-one functions g and h are defined as follows.
Answer:
9(x-8)/3-1Step-by-step explanation:
The inverse function for a set of ordered pairs can be found by swapping the x- and y-coordinates in each pair.
[tex]g^{-1}(-1)=9\qquad\text{from the $g(x)$ ordered pair $(9, -1)$}[/tex]
__
The inverse of a function expressed algebraically can be found by swapping the x- and y-variables and solving for y.
[tex]h^{-1}(x)\qquad\text{is found from }x=h(y)\\\\x=3y+8\\x-8=3y\\\\y=\dfrac{x-8}{3}\\\\\boxed{h^{-1}(x)=\dfrac{x-8}{3}}[/tex]
A function of its own inverse returns the original value:
[tex]\boxed{\left(h\circ h^{-1}\right)(-1)=-1}[/tex]
In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x?1 ? x?2 is normal if the
A. populations are normal.
B. population sizes are both greater than 30.
C. populations are nonnormal and the sample sizes are large.
D. sizes are both greater than 30.
Answer:
C. populations are non normal and the sample sizes are large.
Step-by-step explanation:
To test hypotheses about the difference between two populations means we deal with the following three cases.
1) both the populations are normal with known standard deviations.
2)both the populations are normal with unknown standard deviations.
3) both the populations are non normal in which case both the sample sizes are necessarily large.
So option C is the correct answer.
0.1 × 0.1 represent
Answer:
0.01
Step-by-step explanation:
0.1 x 0.1 = 0.01
HOPE IT HELPS YOU
Which of these expressions is equivalent to log(16 14)?
Answer:
log(16) + log(14)
Step-by-step explanation:
One ton equals 2,000 pounds. How many pounds are there in 2'/8 tons?
Answer:
There are 500 pounds in 2/8 tons.
Step-by-step explanation:
Let's first simplify 2/8. 2/8 is equal to 1/4 since 2 divided by 2 is 1 and 8 divided by 2 is 4. Now we have to divide 2000 by 1/4 which equals to 500 pounds. So there are 500 pounds in 2/8 tons.
We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/f t, the cost of the bottom is $2/f t and the cost of the top is $7/f t. If we have 700 determine the dimensions of the field that will maximize the enclosed area.
Answer:
Dimensions are 350/9 ft and 17.5 ft
Step-by-step explanation:
We are given the cost per ft of all the 4 sides. Let the horizontal be x and the vertical be y.
Now, we will set up the constraint and equation that we are being asked to maximize.
Thus;
700 = 10y + 10y + 7x + 2x
700 = 20y + 9x
Maiking y the subject, we have;
y = (700 - 9x)/20
y = 35 - 9x/20
Now,area of a rectangle is: A = xy
Thus, A = x(35 - 9x/20))
A = 35x - 9x²/20
We can get the critical points by finding the derivatives and Equating to zero
Thus;
dA/dx = 35 - 0.9x
At dA/dx = 0,we have; x = 350/9
At d²A/dx², we have;
d²A/dx² = -0.9
This is negative, thus we will disregard and use the one gotten from the first derivative.
Thus, we will use x = 350/9 ft
Plugging this into the equation y = 35 - 9x/20, we have;
y = 35 - ((9 × 350/9)/20)
y = 17.5 ft
The dimensions of the field that will maximize the enclosed area are 350/9 ft and 17.5 ft and this can be determined by forming the linear equation.
Given :
We are going to fence in a rectangular field. The cost of the vertical sides is $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft.Let 'x' be vertical, and 'y' be horizontal. So, the linear equation becomes:
700 = 10y + 10y + 7x + 2x
Simplify the above expression.
700 = 20y + 9x
Now, solve the above equation for 'y'.
[tex]\rm y = \dfrac{700-9x}{20}[/tex] --- (1)
Now, the formula of the area of the rectangle is:
A = xy
Now, substitute the value of 'y' in the above formula.
[tex]\rm A = x \times \dfrac{700-9x}{20}[/tex]
[tex]\rm A = 35x -\dfrac{9x^2}{20}[/tex]
Now, differentiate the above equation with respect to 'x' and then equate to 0.
[tex]\rm \dfrac{dA}{dx}=35-0.9x[/tex]
Now, equate the above equation to zero.
35 - 0.9x = 0
x = 350/9
Now, substitute the value of 'x' in equation (1).
[tex]\rm y = \dfrac{700-9\times \dfrac{350}{9}}{20}[/tex]
y = 17.5 ft
For more information, refer to the link given below:
https://brainly.com/question/1631786
The following is a list of 5 measurements. 19,30,20,10,17 Suppose that these 5 measurements are respectively labeled.
Answer:
79
Step-by-step explanation:
Σ is a summation symbol. It means you need to add all values of x1 through x5.
19 + 13 + 20 + 10 + 17 = 79
Find the slope of the line graphed below.
Answer: undefined
Step-by-step explanation:
#1 use the horizontal and vertical line concept
- when the line is horizontal, the slope is 0
- when the line is vertical, the slope is undefined
- Thus, in this case, the line is vertical, the slope is undefined.
-----------------------------------------------------------------------------------------
# use the slope formula
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- the two points are (1, 1) and (1, -4)
(-4-1)/(1-1)
=-5/0
= undefined (fractions with 0 base is undefined)
[tex] {e}^{y} + {x}^{3} {y}^{2} + ln(x) = 1[/tex]
and
[tex] \frac{dy}{dt} = 2 [/tex]
when x=1 and y=0.
Find
[tex] \frac{dx}{dt} [/tex]
when x=1 and y=0
Differentiate both sides implicitly:
[tex]\dfrac{\mathrm d}{\mathrm dt}[e^y+x^3y^2+\ln x]=\dfrac{\mathrm d[1]}{\mathrm dt}[/tex]
[tex]e^y\dfrac{\mathrm dy}{\mathrm dt}+3x^2y^2\dfrac{\mathrm dx}{\mathrm dt}+2x^3y\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm dx}{\mathrm dt}=0[/tex]
Solve for [tex]\frac{\mathrm dx}{\mathrm dt}[/tex]:
[tex]\left(3x^2y^2+\dfrac1x\right)\dfrac{\mathrm dx}{\mathrm dt}=-(e^y+2x^3y)\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{e^y+2x^3y}{3x^2y^2+\frac1x}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{xe^y+2x^4y}{3x^3y^2+1}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
Plug in [tex]x=1[/tex], [tex]y=0[/tex], and [tex]\frac{\mathrm dy}{\mathrm dt}=2[/tex]:
[tex]\dfrac{\mathrm dx}{\mathrm dt}=\boxed{-2}[/tex]
Tell whether x and y show direct variation. Explain your reasoning. x=y+2
Answer:
It does not show variation
Step-by-step explanation:
Given
[tex]x = y + 2[/tex]
Required
Determine if there's direct variation between x and y
The general form of direct variation is:
[tex]y = kx[/tex]
Make y the subject of formula in the given parameters;
[tex]x = y + 2[/tex]
[tex]y = x - 2[/tex]
Compare [tex]y = x - 2[/tex] to [tex]y = kx[/tex]
Since they are not of the same form, then the given equation do not show direct variation
find the missing number +(-3)=4
Answer:
the answer is 7
Step-by-step explanation:
7+(-3)=4
7-3=4
hence shown so missing number is 7
2x + 5x+3 combine like terms
Answer:
7x + 3
Step-by-step explanation:
Why is the mechanical advantage of using a single pulley always 1? Assume there’s no friction. A. The input force is in a different direction than the output force. B. The input force is less than the output force. C. The input force is greater than the output force. D. The input force is equal to the output force.
Answer:
D. The input force is equal to the output force
Step-by-step explanation:
A pulley changes the direction of the applied force, but does not change its magnitude. The mechanical advantage is the ratio of output force to input force, so must be 1 when the force magnitude does not change.
HELP ASAP ROCKY!!! will get branliest.
Answer :
One solutionStep by Step explanation :
Take the given equation :
⇒2 + x = 6
Now, start solving it
⇒x = 6 - 2
⇒x = 4
Hence, Solution of given equation is 4. And only one solution exists.
Answer:
one
Step-by-step explanation:
the answer is 4 and there is only one solution there
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec)
Frequency
60119
120179
180239
240299
300359
Answer:
Step-by-step explanation:
The total number of individuals included in this summary is the sum of the counts {119, 179, 239, 299, 359). That comes to 1195 individuals.
No, the info given here is insufficient to enable identifying the exact values of all the service times.
Simply the answer and write it as a mixed number.
Answer:
The answer is 1 4/7
Step-by-step explanation:
First you will want to take the mixed number and make it unmixed which will make it 11/3 divided by 7/3. Then you do the keep change flip method to divide fraction which makes it 11/3 times 3/7 then you multiply across and get 33/21 which as a mixed number is 1 12/21 but you can simplify it to be 1 4/7.
What are the subsets of 5564
Answer:
It will be in the total of 2 subsets.
Step-by-step explanation:
The only subsets of the set containing 5564 is the empty set and the set {5564}.
5564 belongs to the set of real numbers, the set of natural numbers, the set of integers, the set of whole numbers and the set of rational numbers.
Answer:
5564 belongs to the following subsets of real numbers:
real numbers
rational numbers
integers
whole numbers
natural numbers (counting numbers)
----
You can keep on going. You can even say this number belongs to the set of even integers.
Step-by-step explanation:
If you are looking for what subsets of the real numbers that 5564 belong to, then there is a lot of real number subsets to which this number can belong.
This number doesn't have an imaginary part so it's it a number.
We don't have to say it is complex (though it is), because we are looking at subsets of real numbers, not subsets of complex numbers (to which complex numbers are a subset of itself).
So the real numbers are divided into rational versus irrational.
The definition of rational numbers is any number that can be written as a fraction where the top and bottom are integers (of course the bottom integer cannot be 0). -(I will define integers in a second.)
Irrational numbers is any real number that isn't rational.
So since 5564 can be written as 5564/1, then it is rational.
A subset of rational numbers is integers (integers are in consequence also a subset of real numbers since rational numbers are a subset of real numbers).
Integers are numbers you count with, the opposite of those numbers you count with, or 0.
You can count to 5564 so 5564 can be further categorized as real rational integer.
Another subset of real numbers is whole numbers. The whole numbers is just the counting numbers and 0. Again since you count to 5564, then it is a whole number.
The natural numbers (counting numbers) is a subset of real numbers. Again, since 5564 can be counted to, it is a natural number.
Solve 14n2+32n=−34 by using the quadratic formula. Simplify any fractions. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.
Answer:
Step-by-step explanation:
Hello, first of all we can divide by 2.
[tex]7n^2+16n+17=0\\\\\Delta=b^2-4ac= 16^2-4*7*17=-220 < 0 \ \ !![/tex]
The discriminant is negative so there is no real solutions.
Thank you.
BRAINLIEST AND 50 POINTSThe domain of a relation is the output (y) values of the relation the input (x) values of the relation a set of points that pair input values with output values x and y values written in the form (x, y)
Answer:
the input (x) values of the relation
Step-by-step explanation:
The domain of a relation is the set of input values. On a graph, it is the horizontal extent of the graph. For a set of ordered pairs, the domain is the set of all first numbers in the pairs.
I need help on this like now. The answer has to be a fraction.
Speed = distance / time
Speed = 4/3 / 1/10
When dividing fractions flip the second fraction over and multiply:
Speed = 4/3 x 10/1 = (4 x 10)/(3 x1) = 40/3 miles per hour
Solve the equation and state the value of x
3x + 9 + 5x = 81
Answer:
x=9
Step-by-step explanation:
3x+9+5x=81
8x+9=81
-9 -9
8x=72
x=9
hope this help!
Find the area of this triangle. Round to
the nearest tenth.l
Answer:
[tex]\boxed{109.3yd^2}[/tex]
Step-by-step explanation:
Hey there!
Well to find area we'll use the following formula.
[tex]\frac{b h_{b} }{2}[/tex]
Plug in the given info,
[tex]\frac{9.5*23}{2}[/tex]
Simplify
218.5/2
109.25 or 109.3 rounded to the nearest tenth
= 109.3yd²
Hope this helps :)
Area = 1/2 x side1 x side 2 x sin(angle)
= 1/2 x 9.5 x 23 x sin(85)
= 109.25 x sin(85)
= 108.8 square yards
6500000 is 100 as great as
Answer:
65000
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. is parallel to , and is perpendicular to . The number of 90° angles formed by the intersections of and the two parallel lines and is .
Answer:
The question is not complete, below is a complete question with the accompanying diagram:
Instructions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
AB is parallel to CD, and EF is perpendicular to AB
The number of 90° angles formed by the intersections of Ef and the two parallel lines AB and CD is ____
Answer:
The number of 90° angle formed = 8 angles
Step-by-step explanation:
From the question and attached diagram, the following information is given:
AB is parallel to CD
EF is perpendicular to AB
Required: number of 90° angles formed by the intersection of the perpendicular line and the parallel lines.
Note, the angle formed between a line and a perpendicular line = 90°
From the diagram:
Number of 90° angle formed by intersection of perpendicular line EF and line AB = ∠1, ∠2, ∠3 and ∠4 = 4 angles
Number of 90° angle formed by intersection of perpendicular line EF and line CD = ∠5, ∠6, ∠7 and ∠8 = 4 angles
Total 90° angles formed by perpendicular line with lines = ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 = 8 angles
Find the limit: [tex]\lim_{a x \to 0} \frac{(x + ax)^{2}-2(x + ax) + 1 - (x^{2} - 2x + 1)}{ax}[/tex]
I'll let h = ax, so the limit is
[tex]\displaystyle\lim_{h\to0}\frac{(x+h)^2-2(x+h)+1-(x^2-2x+1)}h[/tex]
i.e. the derivative of [tex]x^2-2x+1[/tex].
Expand the numerator to see several terms that get eliminated:
[tex](x+h)^2-2(x+h)+1-(x^2-2x+1)=x^2+2xh+h^2-2x-2h+1-x^2+2x-1=2xh+h^2-2h[/tex]
So we have
[tex]\displaystyle\lim_{h\to0}\frac{2xh+h^2-2h}h[/tex]
Since h ≠ 0 (because it is approaching 0 but never actually reaching 0), we can cancel the factor of h in both numerator and denominator, then plug in h = 0:
[tex]\displaystyle\lim_{h\to0}(2x+h-2)=\boxed{2x-2}[/tex]
Answer:
2x-2
Step-by-step explanation:
lim ax goes to 0 ( x+ ax)^2 -2 ( x+ax) +1 - ( x^2 -2x+1)
--------------------------------------------------
ax
Simplify the numerator by foiling the first term and distributing the minus signs
x^2+ 2ax^2 + a^2 x^2 -2x-2ax +1 - x^2 +2x-1
--------------------------------------------------
ax
Combine like terms
2ax^2 + a^2 x^2 -2ax
--------------------------------------------------
ax
Factor out ax
ax( 2x + ax -2)
----------------------
ax
Cancel ax
2x + ax -2
Now take the limit
lim ax goes to 0 ( 2x + ax -2)
2x +0-2
2x -2
The point K lies on the segment JL.
Find the coordinates of K so that JK is 3/7 of JL.
J= (-18, 17)
K=(?,?)
L= (3,-11)
Find the coordinates of K.
Answer:
( -9, 5)Step-by-step explanation:
We can observe that x coordinate increases on line segment JL from J and y coordinate decreases.
The difference in x:
-18 - 3 = -21The difference in y:
17 - (-11) = 28Point K is at 3/7 distance from J, so it's coordinates will be:
-18 -(-21*3/7) = -18 + 9 = -917 - (28*3/7) = 12- 7 = 5So K = ( -9, 5)