If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.
Compute the gradients and evaluate them at the given point.
[tex]f(x,y)=xy+\frac1x +\frac1y[/tex][tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]
[tex]f(x,y) = x^2+2x[/tex][tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]
[tex]f(x,y)=xy-y^2[/tex][tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]
[tex]f(x,y) = xy-\frac1x-\frac1y[/tex][tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]
The first and third functions drop out.
The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].
[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]
This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,
[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]
for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.
For the fourth function, check the sign of the Hessian determinant at (-1, 1).
[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]
The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.
The correct choice is the fourth function.
what is 4.685 in expanded form
Answer:
4*1/1000+6*100+8*10+5*1
Step-by-step explanation:
Enter the letter for the function graphed
below.
1
a) y = √x - 5
b) y = √√√x-5
c)y=5-√√x
d) y = √x +
e) y = √√√x +
Answer:
e) y = √(x) +5
Step-by-step explanation:
The graph shown is the graph of the square root function shifted upward 5 units. There is no translation left or right.
Translated functionA function can be translated h units right and k units up by the following:
g(x) = f(x -h) +k
Translated square rootWhen the function is f(x) = √x, and it is translated 5 units up, but none left or right, we have ...
g(x) = f(x-0) +5
y = √(x) +5 . . . . . . matches choice e
Kelsey is looking for a job cutting hair. One option is self-employment at The Oakland Salon, where she would pay $400 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Kelsey pay?
she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
How to find the amount paid to either salon that is equal?she would pay $400 per month to rent a station and keep all of her earnings.
Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.
Therefore,
let
x = number of haircut
Hence,
4x = 400
divide both sides by 4
4x / 4 = 400 / 4
x = 100
Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
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Find the value of x
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 35°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]
[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]
[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]
[tex]\qquad❖ \: \sf \:x = 35[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 35°will give brainliest
The possible rational roots of the given equation are 1 and -3
Solving polynomial equationsFrom the question, we are to determine all the possible rational roots of the given equation
The given equation is
x⁴ -2x³ -6x² +22x -15 = 0
To determine the rational roots, we will test for values that make the equation equal to zero
Test for -1(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15
1 + 2 - 6 - 22 -15
= -40
∴ -1 is not a root of the equation
Test for 1(1)⁴ -2(1)³ -6(1)² +22(1) -15
1 - 2 - 6 + 22 -15
= 0
∴ 1 is one of the roots of the equation
Test for -2(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15
16 + 16 - 24 - 44 -15
= -51
∴ -2 is not a root of the equation
Test for 2(2)⁴ -2(2)³ -6(2)² +22(2) -15
16 - 16 - 24 + 44 -15
= 5
∴ 2 is not a root of the equation
Test for -3(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15
81 + 54 - 54 -66 -15
= 0
∴ -3 is one of the roots of the equation
Test for 3(3)⁴ -2(3)³ -6(3)² +22(3) -15
81 - 54 - 54 + 66 -15
= 24
∴ 3 is not a root of the equation
The other roots of the equation are irrational roots.
Hence, the possible rational roots of the given equation are 1 and -3
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5. Compound Interest - Single Payment: $5000 was invested at 5.2%, compounded semi-annually, for 3 years. What was the investment worth at its maturity? (3)
Answer:
78000
Step-by-step explanation:
5000/1 times 52/10 times 3)1
Fill in the blank with the correct response.
Twenty-one is 20% of
Answer: 105
Step-by-step explanation:
105 * .2 = 21 :)
David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.
Select the expression that will help him to determine the total cost.
The expression that will help him to determine the total cost is as follows:
y = 60 + 4x
How to construct an expression?He signed up to provide snacks for his daughter and her school group's camping trip.
He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.
He also wanted to buy some boxes of fruit snacks, which were $4 each.
The number to buy and the total cost can be expressed as follows:
let
y = total cost
x = number of boxes of fruit juice.
Therefore, the expression that will help him to determine the total cost is as follows:
y = 60 + 4x
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If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
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Study the spinner below. If wedges 2 and 5 are each twice the area of one of
the other wedges, what is the likelihood of landing on 2 or 3?
Using the probability concept, the likelihood of landing on 2 or 3 is given by:
[tex]p = \frac{3}{8}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, considering the areas of 2 and 5 counting twice, the spinner has 8 areas, out of which 3 are 2 or 3, hence the probability is given as follows:
[tex]p = \frac{3}{8}[/tex]
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what is 687/4 equal to
Answer: 171.75
Step-by-step explanation:
a basic operation of arithmeticwhere numbers are broken up into equal parts687 will need to be split evenly into 4 groups[tex]687/4 = 171.75[/tex]
Answer:
To find the result we have to divide, in a fraction the numerator is always divided by the denominator and the final result is 171.75
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
A plant is 30cm tall when planted in a garden it increases by 10 percent each week how long will it take to reach 1 meter
Answer:
12.63 weeks ~~ 13 weeks
Step-by-step explanation:
This is much like a banking question with compounded interest
FV = PV ( 1 + i)^n FV = Future value = 1 m PV = present value = .3
i = periodic interest = .10 n = periods
1 = .3(1 + .1)^n solve for n = the number of weeks
1/.3 = 1.1^n
log (1/.3) / log 1.1 = n = 12.63 weeks
216 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answer:
The no. of student failed is 36.
Step-by-step explanation:
Given, the number of student enrolled= 216
Let us suppose number of student failed = x
Given,
no. of student passed is 5 times no. of student failed.
Then, no. of student passed = 5x
x +5x = 216
6x = 216
x = 216/6
x = 36
Thus, the no. of student failed is 36.
Which expression shows the factored form of 49x² - y²?
Step-by-step explanation:
49x^2-y^2=(7x)^2-(y)^2
=(7x+y) (7x-y)
Therefore, a^2-b^3
=(a+b) (a-b)
can I return notebooks to target?
Answer: yes, as long as you haven't used them. :)
Step-by-step explanation:
please help :,)
(geometry involving arc lengths)
Answer:
bx/a (3rd choice)
Step-by-step explanation:
The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is
s = rΘ
Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.
x = aΘ
Solve for Θ:
Θ = x/a Eq. 1
Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.
s = bΘ
Solve for Θ:
Θ = s/b Eq. 2
Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.
x/a = s/b
Multiply both sides by ab.
abx/a = abs/b
bx = as
as = bx
s = bx/a
Answer: bx/a
Write the ratio 6 sodas out of 16 drinks.
Answer:
3:8 3 sodas for 8 drinks
Step-by-step explanation:
6/16
3/8
4- Evaluating Expressions
11) (2 + y - x); use x = 4 and y = 6
13) P(+²); use a = 7 and p=6
6
5-Solving Inequalities
16) 1 ≤
10 11 12
18) 6v> 54
13 14 15 16 17 18
8 9 10 11 12 15 14 15 16 17 18
12)3(8a-5b)-2(a + b); use a = 3 and b = 2
14) 3m-2+
use m = 5 and n = 6
17) 20
19) 82/2
4
14 15 16 17 15
9 10 11 12
14 15 16 17 15
Answer:
The answer is 4'
Step-by-step explanation:
The answer is 4, 123456789, 6 12, 18, 24, 30, 36, 42, 48.
What insult is meat shield I never understood it if someone calls a person a meat shield what does the insult mean
Answer: someone who is viewed as obsolete or a person you can use to save yourself from any problem/situation
Step-by-step explanation:
Answer:
The term "meat shield" is often used as an insult to refer to someone who is used by others as a protective barrier, especially in a dangerous or violent situation. The implication is that the person being referred to is expendable and not valued for their own merits or abilities.
Here are a few examples of insults that use the term "meat shield":
"You're nothing more than a meat shield for your boss."
"You're just a disposable meat shield to your friends."
"You're nothing but a human meat shield to your team."
"You're just a weak and pitiful meat shield."
"You're just a coward who hides behind others like a meat shield."
Again, it's important to remember that using insults is never a productive or kind way to communicate with others. It's always better to try to address the issue in a respectful and constructive manner.
how to find h’(3)
base on the graph
By the quotient rule for differentiation,
[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].
On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].
Then
[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]
Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT
Step-by-step explanation:
important of festival in nepali languages for class seven
Answer:
b
Step-by-step explanation:
URGENT!!!!!!
Use arrow notation to describe the translation of point P(–5, –4) to point P′(–8, –7).
The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:
(x,y) -> (x - 3, y - 3).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:
(x,y) -> (x - 3, y - 3).
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2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?
Answer:
no solution
Step-by-step explanation:
16x - 32y = 27 → (1)
8x - 16 = 16y ( subtract 16y from both sides )
8x - 16 - 16y = 0 ( add 16 to both sides )
8x - 16y = 16 → (2)
multiply (2) by - 2 and add to (1)
- 16x + 32y = - 32 → (3)
add (1) and (3) term by term
0 + 0 = - 5
0 = - 5 ← not possible
this indicates the system has no solution
(b)
the solution to a system is the point of intersection of the 2 lines
since there is no solution, no point of intersection, then
this indicates the lines are parallel and never intersect
Answer:
a) no solution
b) the two lines never intersect
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]
Part (a)To solve by linear combination (elimination):
Step 1
Write both equations in standard form: Ax + By = C
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 8x-16y=16[/tex]
Step 2
Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]
Step 3
Subtract one of the equations from the other to eliminate one of the variables:
[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]
Therefore, as 0 ≠ 5, there is no solution to this system of equations.
Part (b)
The solution to a system of equations is the point(s) of intersection.
As there is no solution to the given system of equations, this tells us that the two lines never intersect.
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E4.2 Simplify the following using suitable properties (a) 109x 50
109×50
100×50+9×50=5000+450
5450
Answer:
5450
Step-by-step explanation:
You can just use a caculater to get the answer.
HELP PLS BRAINLIEST IF POSSIBLE
For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.
Simply put, a set in mathematics is a grouping of different items.
An element of the set is any component of the set. When writing a set, curly brackets are utilized.
The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.
According to the question,
A = {11,22,33,44}
The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.
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if 6m of a uniform iron rod weighs 21 kg what will be the weight of 16 m of the same rod?
Answer:
56kg
Step-by-step explanation:
If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg
16*3.5 = 56 kg
19 ft
4 ft
l
Find l.
l = √ [?] ft
Answer :LF is the abbreviation for linear feet Sq ft is the abbreviation for square feet L – lenght (e.g. room length) W – width (e.g. room width)
Liters to Cubic Feet formula. ft³ =. L * 0.035315. Show working Show result in exponential format More information: Cubic Feet.
Step-by-step explanation:
Pls help answer this before 8pm
Answer:
Step-by-step explanation:
16 + 12 + 5 + 3 = 36
16 prefer email, 36 total students surveyed
16:36 / 4 = 4:9
4 out of 9 students prefer email
4:9 x 680 = 302.222
302 students can be expected to prefer email.
I need help with the question
Answer:
B
Step-by-step explanation:
Comment
√15 = 3.87
√12 = 3.46 Subtract these 2
Difference = 0.41
please help!!!
Using long division, what is the quotient of this expression?
3x42x³-x-4
x²+2
OA. 3x²
3x - 4
OB. 3x² + 2x + x² + 2
O C.
3x² 2x
O D.
-
2x
3x² + 2x
- 6 +
-
- 5+
-
3x + 8
x² + 2
-
3x+6
x²+2
5x8
x² + 2
Rese
Check the picture below.
notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.
Here is the solution process:
3 x² - 2 x - 6
x² + 0x + 2 | 3 x⁴ - 2 x³ + 0 x² - x - 4
3 x⁴ + 0 x³ + 6 x²
- 2 x³ - 6 x² - x - 4
- 2 x³ + 0 x² - 4 x
- 6 x² + 3 x - 4
- 6 x² + 0 x - 12
3 x + 8
Long division:
Standard: [tex]\sf{3x^{2} -2x-6+\dfrac{3x+8}{x^{2} +2} \ \ \to \ \ \ Option \ "A" }[/tex]Quotient: 3x² - 2x - 6Rest: 8 + 3xTherefore, the correct option is "A".