This question is incomplete, the complete question is;
find the critical points and classify them as local maxima, local minima, saddle points, or none of these.
f(x,y) = (x + y)(xy + 1)
Answer:
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy² )
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
Step-by-step explanation:
Given that;
f(x,y) = (x + y)(xy + 1)
f(x,y) =x²y + xy² + x + y
for critical points fx =0 ,fy =0
fx = 2xy + y² + 1 = 0, fy = x² + 2xy + 1 = 0
2xy + y² + 1 = 0, x²+ 2xy + 1 = 0
2xy + y² + 1 - x² - 2xy - 1 = 0
x² = y²
=> x = y, x = -y
2xy + y² + 1 = 0, x = y
2yy + y² + 1 = 0
3y² = -1 , no solution
2xy + y² + 1 = 0, x = -y
-2yy + y² + 1 = 0
=> -y2 + 1 = 0
=> y = -1, y = 1
y = -1 => x = 1, y = 1 => x = -1
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy² )
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
Find the exact value of cos(a + b), given sin a = 2/5 for a in Quadrant || and cos B = 1/3 for b in Quadrant IV.
Answer:
Option (4)
Step-by-step explanation:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b) [Identity]
Since, sin(a) = [tex]\frac{2}{5}[/tex] for a in quadrant II
Therefore, cos(a) = [tex]\sqrt{1-\text{sin}^2(a)}=\sqrt{1-(\frac{2}{5})^2}[/tex]
cos(a) = [tex]\frac{\sqrt{21}}{5}[/tex]
But cosine of a is negative quadrant II
Therefore, cos(a) = -[tex]\frac{\sqrt{21}}{5}[/tex]
And cos(b) = [tex]\frac{1}{3}[/tex] for b in quadrant IV
Therefore, sin(b) = [tex]\sqrt{1-\text{cos}^{2}b}[/tex]
= [tex]\sqrt{1-(\frac{1}{3})^2}[/tex]
= [tex]\frac{2\sqrt{2}}{3}[/tex]
But sine of an angle is negative in quadrant IV,
Therefore, sin(b) = [tex]-\frac{2\sqrt{2}}{3}[/tex]
Now substituting these values in the identity,
cos(a + b) = [tex](-\frac{\sqrt{21}}{5})(\frac{1}{3})-(\frac{2}{5})(-\frac{2\sqrt{2}}{3})[/tex]
= [tex]-\frac{\sqrt{21}}{15}+\frac{4\sqrt{2}}{15}[/tex]
= [tex]\frac{4\sqrt{2}-\sqrt{21}}{15}[/tex]
Therefore, Option (4) will be the answer.
Answer: D
Step-by-step explanation:
Edge 2021
can somone help me please
Answer:
x=11.75
Step-by-step explanation:
186 subtracted from t
Answer: t-186
Step-by-step explanation:
Answer:
t - 186
Step-by-step explanation:
There's really no math involved in this one. Since t is a variable, all you have to do is write out the answer as t - 186.
a triangle has two sides of lengths 4 and 7. What could the value of the third side be? select all that apply.
Answer:
Step-by-step explanation:
5,7,9
trust the process.
Help! Best Answer = Braniest
Answer:
x=20, Angles are 70° and 110°
Step-by-step explanation:
Angles are supplementary, so their sum is 180°
5x-30+x+90 = 180
6x+60 = 180
6x = 180-60
6x = 120
x = 20
5x-30 = 5*20 - 30 = 100 -30 = 70°
x+90 = 20 + 90 = 110°
It takes Eddie 2 hours to shovel the snow from a driveway and sidewalk. Brad can shovel the snow from the same driveway and sidewalk in 5 hours. How long would it take them working together to shovel the snow? Round your answer up to the next whole minute.
Let A, B, and C be any sets. Show that A × (B – C) = (A × B) – (A × C).
Can you help justify the proof
If × denotes the Cartesian product, and if a ∈ A and b ∈ B, then (a, b) ∈ A × B.
First prove that A × (B - C) ⊆ (A × B) - (A × C):
Let a ∈ A and b ∈ B - C.
By definition of the product, (a, b) ∈ A × B.
By definition of complement, b ∈ B and b ∉ C.
So (a, b) ∈ A × B and (a, b) ∉ A × C.
By definition of complement, (a, b) ∈ (A × B) - (A × C).
Therefore, A × (B - C) ⊆ (A × B) - (A × C).
Prove the other direction, that (A × B) - (A × C) ⊆ A × (B - C):
Let (a, b) ∈ (A × B) - (A × C).
By definition complement, (a, b) ∈ (A × B) and (a, b) ∉ (A × C).
By definition of the product, a ∈ A, b ∈ B, and b ∉ C.
By definition of complement, b ∈ B - C.
By definition of the product, (a, b) ∈ A × (B - C).
Therefore, (A × B) - (A × C) ⊆ A × (B - C).
Hence the two sets are equal. QED
How many times a month do you workout? It’s for a math project!
Answer:
well 3 tike everyday so 3×31=93
brainliest fr ! ! !! After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day?
Answer: 8 weeks I believe
Step-by-step explanation:
12+6=18
18+6+6+6+6+6+6+6=60
or 18+42=60
1. Which operation should be performed first to simplify the expression below?
(19 - 2 times 8 divided by 4 + 6)
Question:
Which operation should be performed first to simplify the expression below?19-2×8÷4+6
Answer:
I'm pretty sure you multiply first because PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction) says you go left to right and do multiplication or division first, so I would say it'd be multiplication.
Marshall’s dog weighs 82 pounds. The vet
said 75 pounds would be more ideal for his
size. What percent of his weight does he
need to lose?
What is the value of x? X- 1/6 = 8
Answer:
wouldn't it just be 8 and 1/6?
Step-by-step explanation:
because 8 1/6 - 1/6 would be 8
CJ walks 8 miles in 3 hours, at what unit rate does he walk
Answer:
24
Step-by-step explanation:
you 8times3=24
2.5 miles a hour ( 2.666666666666667 miles an hour) lemme know if im
right !
Graph -9.2 + 5y = 45.
A pair of shoes is discounted 20%. The discounted price is $34.40. What was the original price of the shoes?
Answer:
ved tiwari and komore in the u.s. department for Drawing of 6:4:1.komal in the u.s. department for the u.s. department for health
8. Raven is making pillows. Each pillow requires 4/9 yards of fabric. Raven
has 12 yards of fabric. Determine the number of pillows Raven can make.
1/27
27
4
9
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco
Camila’s box holds 363 balls. Each layer has 33 balls. How many layers does the box have?
Answer:
The box has 11 layers
Step-by-step explanation:
Since there are 363 balls and each layer has 33 balls, we have to divide 363 by 33.
363÷33= 11
So, there will be 11 layers in the box.
Hope this helps!
Need Help. ( Look at the picture). Will Mark Brainliest. Graph the step function over the interval. [ Please Show me on paper].
Answer:
x = -3
Step-by-step explanation:
f(x)= x + 3
0 = x + 3
-x = 3
x = -3
Covert 54 2/7% to a fraction in lowest terms
Put it over 100.
(54 2/7)/100
Simplify.
19/35
Answer: 19/35WILL GIVE BRAINLIEST!!!
A person is shopping for cereal, oranges, and eggs at a grocery store. Which one of the following is an INPUT in this scenario? (which do you have control over?) *
A.The number of cereal boxes purchased
B.The cost per pound of oranges
C.The amount paid for eggs
Use algebra tiles to represent this polynomial x2-5x-1
get 2 shaded x tiles, 5 clear x tiles, and 1 clear tile.
Answer:
drag one tile into the product then click check. Then drag five into the product then click check. Then drag one tile into the product and click check..
Step-by-step explanation:
7th grade math help I don't get this :(
Answer:
No solution
Step-by-step explanation:
Solve the system of equations with elimination or substitution.
Add the equations together:
A + (-B) + (-A) + B = -1 + 0
0 = -1
There is no solution.
Abcd is a cyclic quadrilateral. o is the center of the circle ∠bad = 40°,then angle BCD=?,m(arc BCD) =?,m( arc BAD)=?
Answer:
m∠BCD = 140°
m(arc BCD) = 80°
m(arc BAD) = 280°
Step-by-step explanation:
In the cyclic quadrilateral, every two opposite angles are supplementary.The measure of the subtended arc to an inscribed angle equals twice the measure of this angleLet us use these facts to solve the question
∵ ABCD is a cyclic quadrilateral in circle O
∵ ∠BAD and ∠BCD are opposite angles
→ By using the 1st fact above
∴ m∠BAD + m∠BCD = 180°
∵ m∠BAD = 40°
∴ 40° + m∠BCD = 180°
→ Subtract 40° from both sides
∴ 40° - 40° + m∠BCD = 180° - 40°
∴ m∠BCD = 140°
∵ Arc BCD subtended the inscribed ∠BAD
→ By using the 2nd fact above
∴ m(arc BCD) = 2(m∠BAD)
∵ m∠BAD = 40°
∴ m(arc BCD) = 2(40°)
∴ m(arc BCD) = 80°
∵ Arc BAD subtended the inscribed ∠BCD
→ By using the 2nd fact above
∴ m(arc BAD) = 2(m∠BCD)
∵ m∠BCD = 140°
∴ m(arc BAD) = 2(140°)
∴ m(arc BAD) = 280°.
3 5 7 +2 1 9 −( 5 7 + 1 9 )
Answer: -49
Step-by-step explanation:
Answer:
518
Step-by-step explanation:
Add 357 and 219 ( 594 )
( The negative symbol by an parenthesis means that there will be a 1 so it will be -1 )
Multiply -1 by each number in parenthesis
Then subtract -19 from -57 ( -76 )
Lastly you subtract -76 and 594
You should get your answer
Hope this helped, Have an AMAZING day!!
Rewrite equation in slope-intercept form and identify its slope.
4x - 2y =5
Answer:
y=2x-5/2
Step-by-step explanation:
Originally, Juan borrowed $10, but his mother loaned him $3 more, so he borrowed a total of $13. He sells $25 worth of lemonade in his first week. After Juan pays his mother back the $13 he borrowed, his profit is $12.
If Juan’s mother forgave (or took away) his debt of –13, what equation shows the amount of money Juan will have?
Answer:
25
Step-by-step explanation:
If Juan's mother forgave his debt of -$13, then Juan will have $25 left after paying back his initial loan and making a profit of $12.
Juan's money = $12 + $13
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
If Juan's mother forgave his debt of -$13, then it means that Juan received $13 from his mother instead of owing her $13. So the equation that shows the amount of money Juan will have is:
Juan's profit = Juan's earnings - Juan's expenses
Juan's profit = $25 - $13
Juan's profit = $12
This means that after paying back his loan and making a profit of $12, Juan will have no money left.
If we want to include the amount he initially borrowed, we can modify the equation as follows:
Juan's money = Juan's earnings + Juan's initial loan
Juan's money = $25 - $13 - $13
Therefore, the equation is Juan's money = $12 + $13
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ7
Write the equation of the line in slope-intercept form that
passes through the point (-2, 4) and is perpendicular to the line
6x + 3y = 8.
Answer:
y = 1/2x + 5
Step-by-step explanation:
I checked it on desmos
I'm in 6th grade what is 9p=72 solved mentally
Answer:
p=8
Step-by-step explanation:
A normal die (numbered 1-6) is fair if each outcome is equally likely. Therefore a 1 should come up of the time. If a fair die is rolled 360 times we would expect a 1 to come up 60 times (since 1 over 6 times 360 equals 60 ). If x represents the number of times a "1" is rolled then open vertical bar fraction numerator x minus 60 over denominator square root of 50 end fraction close vertical bar less than 1.96 gives the reasonable range for the number of times a "1" will come up in 360 rolls. If we roll the die 360 times and get a "1" 30 times, is our die a fair die? Show your work using the equation editor.
Answer:
Yes the die is fair as the calculated z= -0.224 is less than the Z∝= 1.96
Step-by-step explanation:
x`- u / s/√n< Z∝
x`- 60 /√50/√360 < 1.96
From the above we find that u = 60 and the sample size n= 360 S= √ 50
Z∝= 1.96
Here p = 1/6 ( the probability of getting a 1 out of 6)
q= 5/6
Since it is normal Standard deviation = √npq = √360 * 1/6*5/6= √50
If x`= 30
then
30 - 60 /√50/√360 < 1.96
-30/7.07*18.973 < 1.96
- 0.224 < 1.96
Yes the die is fair as the calculated z= -0.224 is less than the Z∝= 1.96 the null hypothesis that die rolled is fair is accepted.
please help put the solution only if you can. Thank you!
Answer:
X=32 and Y=51
Step-by-step explanation:
first to find the answer, we must establish that the sum of 3 angles in any triangle will equal 180 degrees, and both triangles are congruent then we can start making equations. Triangle STU has 2 numbers and one equation on it, the equation for the length of NP will give us y, but first we must get X from the equation for angle TUS which is congruent to angle MNP, so first we must add angle M and angle P together to find angle N, 142+24=166, 180-166=14, so angle N and angle U are both equal to 14 degrees, so, 2x-50=14 first add 50 to both sides then divide by 2 giving us 32=X. Now that we have x, we can find y, 2x32-y=13, we can determine m is equal to 13 m because segment SU is congruent to segment NP, SU is 13 meters, thus NP is 13 meters long as well. first multiply 32 and 2 giving 64, then subtract 64 from both sides, giving you -y=-51, but we don't stop here because y itself can't be negative as that's not what's being asked for, so divide both sides by negative 1 giving you Y=51