Without using any calculus:
If x + y² = 5, then y² = 5 - x, so that
b = x y² = x (5 - x) = 5 x - x²
Complete the square to get
b = 25/4 - (x - 5/2)²
Then b gets a maximum value of 25/4 when x = 5/2.
Simple calculus method:
With b = 5 x - x², differentiate b with respect to x and set the derivative equal to 0 to solve for critical points:
db/dx = 5 - 2 x = 0 ==> x = 5/2
Take the second derivative to determine whether b is concave or convex:
d²b/dx² = -2
The second derivative is negative, which means b is concave with respect to x, and this indicates x = 5/2 is the site of a local maximum, which is b (5/2) = 25/4.
More complicated calculus method:
Lagrange multipliers. The Lagrangian is
L (x, y, λ) = x y² - λ (x + y² - 5)
where we assume λ ≠ 0.
Take its derivatives:
dL/dx = y² - λ
dL/dy = 2 x y - 2 λ y
dL/dλ = x + y² - 5
Set each derivative equal to 0 to find the critical points. The first equation tells us y² = λ, and the second equation tells us x = λ, so
x + y² - 5 = 2 λ - 5 = 0
Solving this gives λ = x = y² = 5/2, so that b has an extreme value of
b = (5/2) (5/2) = 25/4
Deciding whether this is a maximum or minimum comes down to computing the Hessian determinant at the critical value. The Hessian is
[tex]H(x,y)=\begin{bmatrix}\dfrac{\partial^2b}{\partial x^2}&\dfrac{\partial^2b}{\partial x\partial y}\\\\\dfrac{\partial^2b}{\partial y\partial x}&\dfrac{\partial^2b}{\partial y^2}\end{bmatrix}=\begin{bmatrix}0&2y\\2y&2x\end{bmatrix}[/tex]
with determinant |H (x, y)| = -4 y². At the critical point, the determinant is -10 < 0, which indicates a maximum value of 25/4.
Give brainliest answer
Answer:
6
Step-by-step explanation:
if a triangle is reflected, its area stays the same. the height is 3, and the base is 4. the formula for the area of a triangle is 1/2 (b)(h), so that is 1/2 (3)(4) which equals 6 square units.
The sum of two numbers is 43, the difference is 7. Find the numbers
Answer:
25 and 18
Step-by-step explanation:
A scale drawing of a rectangular room measures 3 1/2“ x 1 1/2“ the scale is 1/4 inch = 2 feet carpeting cost $10 per square foot how much will it cost to buy enough carpeting to cover the floor of this room
Answer:1120
Step-by-step explanation:
It's math
Answer: it’s 138
Step-by-step explanation:
What are the solutions to the quadratic equation below?
3x2 +16x + 21 = 0
Answer:
-3 and -7/3
Step-by-step explanation:
You could solve by factoring.
To do that, you find 2 numbers that multiply to 21, but add up to 16 when you multiply one of them by 3.
In this case, 3 and 7 would work, because 3*3 + 7 = 16, and 3 * 7 = 21.
Therefore, we can factor the equation to (3x+7)(x+3).
The solutions of the equations are -3 and -7/3.
4.
Which of the following lists is ordered from least to greatest?
1-1.51, -2,0
2 3
5 4
0-2
2 3
-2, -1.5, 0,
5'4.
32
-2, -1.5, 0,
4' 5
2 3
-1.5, -2,0
5'4
Answer:
2 3
2 3
-2 - 1.5 0
4 5
Step-by-step explanation:
-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 1 0
If there are 12 eggs in a carton, how many are in 5 cartons?
Answer:
60
Step-by-step explanation:
12x5 is equal to 60
Kira wants to cover hr rectangular patio in cement. The patio measures 4yd long and 3yd wide.
Answer:
The answer is 12 yds.
Step-by-step explanation:
The formula for calculating area is L x W = Area, so we multiply 4 by 3, which gives us 12.
Hope this helped!
Which expressions are in simplest form? Check all that apply.
x Superscript negative 3 Baseline + y cubed
StartFraction 1 Over x Superscript 4 EndFraction
StartFraction w Superscript 7 Over x squared EndFraction
a Superscript negative 9
StartFraction 1 Over a squared EndFraction + b squared
StartFraction 1 Over b Superscript 5 EndFraction
Answer:
b. 1/x^4
c. w^7/x^2
e. 1/a^2+b^2
f. 1/b^5
Step-by-step explanation:
Simpilest form means that the exponents must be a postive number. That's what the Edge guy said. I entered these answers in and I got it right on Edge 2021. Today is Janurary 3rd.
The expressions in the simplest forms would be as follows:
b). [tex]1/x^4[/tex]
c). [tex]w^7/x^2[/tex]
e). [tex]1/a^2+b^2[/tex]
f). [tex]1/b^5[/tex]
Write the expressions in the simplest forms:
The simplest form is described as the most compact form of an expression that cannot be broken anymore and does not have any other factor in common than 1.
All the above-mentioned expressions exemplify the simplest forms as they do not have any other factor in common except for 1.
Thus, options b, c, e, and f are the correct answers.
Learn more about "Expressions" here:
brainly.com/question/13947055
Write and expression equivalent to - 1/2(6x-8+4x please help
Step-by-step explanation:
I won't say the answer, but will give an explanation. the explanation for solving the expression is above.
the fully simplified expression is 5x - 4. All you need to do now is make an expression that will equal 5x - 4 simplified.
An example is: 20(1/4x-1/5)
if I read the questions wrong and it's just asking to simplify the expression then the answer is 5x - 4.
Math question Pls help Im dumb
Answer:
I think it's J
Step-by-step explanation:
Because the ratio is 5:3:2
There are 150 raisins
And since 2 is one less than 3 my estimate would be subtracting 50 from 150 making there be 100 chocolate chips. Then if the unit is 50, 50 x 5 ( 5 in the ratio) would be 250.
I hope this helps, have a good day.
W/4 -4=3
Solve the eqution pls!
Answer:
W=28
Step-by-step explanation:
(W/4)-4=3
(W/4)=7
W=28
Mutiply. Express your answer 7/10 times 2/5
Answer:
7/25
Step-by-step explanation:
the answer is 7/25
because 7/10 x 2/5 =7/25
(2.10-6) · (6 · 10^7)=__
There are 40 players on Bill's football team, 2/5 of the players walk to practice and 1/4 of the players ride with their parents. The remaining players ride the bus. How many students ride the bus?
Answer:
22 students.
Step-by-step explanation:
There are a total of 40 players on the football team. 2/5 walk, 1/4 ride with their parents, and the rest ride the bus. To solve, I'm going to be using fractions to find out how many students ride the bus.
1/4 of 40 or 40/4 is equal to 10.
So we know 10 players ride with their parents.
2/5 of 40 or 40/5 is equal to 8.
Cool, 8 students walk to practice.
Now the rest ride the bus. Let's use addition to find the total amount of players that dont use the bus and subtract it from the total amount of players.
10+8=18
40-18=22.
22 students/players ride the bus to football practice.
g Benton Industries manufactures carpets and draperies in the Atlanta area. Employee absenteeism was becoming a problem, so HR conducted a study involving a random sample of employees. The number of absences during the past year was tabulated by marital status. What is the probability that an employee is not married and has between 1 and 5 absences in the past year
Answer:
The probability that an employee is not married and has between 1 and 5 absences in the past year is 0.204.
Step-by-step explanation:
The probability of an event, say E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n (E)}{N}[/tex]
The number of absences during the past year tabulated by marital status is as follows:
Marital Status 0 Absences 1 - 5 Absences More than 5 Absences
Married 100 98 52
Not Married 77 102 71
Compute the probability that an employee is not married and has between 1 and 5 absences in the past year as follows:
[tex]P(\text{NM}\cap 1-5\ \text{Absences})=\frac{n(\text{NM}\cap 1-5\ \text{Absences})}{N}[/tex]
[tex]=\frac{102}{100+98+52+77+102+71}\\\\=\frac{102}{500}\\\\=0.204[/tex]
Thus, the probability that an employee is not married and has between 1 and 5 absences in the past year is 0.204.
Which of the following is closest to the value of the expression 3 x (square root of 2)?
Select one:
01.4
03.8
04.2
04.4
Answer:
4.2
Step-by-step explanation:
3 x (sqrt 2)
3 x (1.41421356237)
4.24264068712
4.2
HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSssssssss
if i could get 3 apples, and i got 5 mapples, how much apples do i get?
Answer:
3 Apples and 5 Mapples!!!
Step-by-step explanation:
Answer:
you have 8 apples
Step-by-step explanation:
A car travels at 60 mph for 2 minutes. How far does the car travel?
Answer:
2 miles
Step-by-step explanation:
Car travels at 60 miles/1 hour
1 hour has 60 minutes
Car travels at 60 miles/60 minutes, which can be reduced to 1 mile/1 minute
In 2 minutues, the car travels two miles
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number
Answer: the equation would be x-6 = 5(x+2) and x= 0.666666666666667
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
Hi can someone please help me with this question
Answer:
-5
Step-by-step explanation:
-8-(-3) = -8+3
-8+3 = -5
How to round 141.999 to the nearest one
Answer:
It's 142
(✿◠‿◠)
If you have a 5 or more on the tenths place, then you make one go up to the next number.
Answer:
142Step-by-step explanation:
To round 141.999 to the nearest hundredth consider the thousandths’ value of 141.999, which is 9 and equal or more than 5. Therefore, the hundredths value of 141.999 increases by 1 to 0.Which number is closest to V90 ?
Pls answer these correctly I need it ASAP
Simply ask your parents or someone to help you your welcome.
equation of the horizontal line that passes through the point (-5,1)
Answer:
y = -1.
Step-by-step explanation:
The value of y is -1 as it passes through the y axis. The values of x on the line are infinite.
This line's equation is y = -1.
After how many years will $1,500 you invested now will be worth $3000 if it is compounded monthly at 4% interest?
On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C has points (negative 4, 3), (4, 4), and (1, 1). A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the image △A'B'C'? Check all that apply.
AB is parallel to A'B'.
DO,1/2(x, y) = (one-half x, one-half y)
The distance from A' to the origin is half the distance from A to the origin.
The vertices of the image are farther from the origin than those of the pre-image.
A'B' is greater than AB.
Answer:
A, B, C
Step-by-step explanation:
It's correct, I took the activity before the quiz and got it right.
Happy to help :3
Heather wants to purchase an electric guitar the price of the guitar with tax is $2,240.if she can save $90 per month how linf will it take her to save up for the guitar
Answer:
25
Step-by-step explanation:
que es suma y resta de fracciones homogeneas
Answer:
responder
Step-by-step explanation:
Para sumar y restar fracciones, sus denominadores deben ser iguales. Por tanto, sumar o restar fracciones homogéneas es más fácil, dado que ya tienen el mismo denominador.
Answer:
Recuerda que cuando se suman fracciones homogéneas se hace lo mismo que cuando se suman objetos del mismo tipo. Por ejemplo, la suma tres décimos más dos décimos da como resultado cinco décimos: , por la misma razón que sumar tres vacas más dos vacas da como resultado cinco vacas.
Step-by-step explanation:
SOMEONE PLEASE HELP ASAP!!!
Answer:
Step-by-step explanation:
Recall that (a-b)(a+b) = a^2 - b^2
So,
(x-2i)(x+2i) = x^2 - (2i)^2 = x^2+4
(x+i-i)(x+1+i) = (x+1)^2 + 1 = x^2 + 2x + 2
(x-2+2i)(x-2-2i) = (x-2)^2 + 4 = x^2 - 4x + 8
Alli can mop Strong Hall in 10 hours. Working together, Alli and Zach mop Strong Hall in 4 hours. How long would it take Zach to do this job alone?
Answer:
8 hour
Step-by-step explanation: