Maximize B=XY^2 , where x and y are positive numbers such that X+Y^2=5.
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.
Y= 4x +3, 4x + y =3 are they parallel or perpendicular
Answer: Neither
Step-by-step explanation:
When two lines are parallel, their slopes are the same.
When two lines are perpendicular, their slopes are opposite reciprocals. Opposite reciprocals equal -1 when multiplied together.
Equation #1: y = 4x + 3
The equation is in the form y = mx + b, so the slope is 4.
Equation #2: 4x + y = 3
We need to put this equation in slope-intercept form.
1) Subtract 4x from both sides
y = -4x + 3
The slope is -4.
-4 and 4 are neither equal nor opposite reciprocals, so they aren't parallel or perpendicular.
The slope of both lines is neither the same nor negative inverse of each other thus both lines will neither parallel nor perpendicular.
What is slope?A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.
As per the given lines,
y = 4x +3
The slope-intercept form is given as y = mx + c where m is the slope.
By comparing slope m = 4
4x + y =3 → y = -4x + 3
Slope m = -4
Since slopes are not the same thus they will be not parallel.
Perpendicular lines slope's multiplication gives -1.
Since, 4 x (-4) ≠ -1 thus both will be not perpendicular.
Hence "The slope of both lines is neither the same nor negative inverse of each other thus both lines will neither parallel nor perpendicular".
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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.
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There are 24 marbles in a jar. 3 marbles are added to the jar when the class is good. How many times can the class be rewarded to get 100 marbles
Netlfix charges $30 a month plus $5 per movie. Hulu charges $26 a month plus $ per movie. How many movies will you need to watch for the Netflix membership to pay off and cost you less?
The question is incomplete:
Netlfix charges $30 a month plus $5 per movie. Hulu charges $26 a month plus $7 per movie. How many movies will you need to watch for the Netflix membership to pay off and cost you less?
Answer:
3 movies
Step-by-step explanation:
From the information given, you can write an inequality that indicates that Netflix membership costs less than Hulu membership:
30+5x<26+7x
Now, you can solve for x:
30-26<7x-5x
4<2x
4/2<x
x>2
According to this, the answer is that you will need to watch 3 movies for the Netflix membership to pay off and cost you less.
Three partners are investing a total of $700,000 to open a garden and landscaping store. The first partner wns 30% of the business, and the second partner owns 25% of the business. What percent does the third partner own? Just input the numerals for your answer -do not add a percent sign. hip
Answer: 45
Step-by-step explanation: The 3rd partner has 45% of the store. Which is also $315,000.
Answer: the third partner owns 45% or $315,000 of the business.
Step-by-step explanation:
30 percent of 700,000=210,00
25 percent of 700,000=175,000
175,000+210,000=385,000
700,000-385,000= 315,000
the third partner owns 315,000 and 315,000=45%
Marjorie consumed 1.5 gallons of water in one day. How many milliliters are equal to 1.5 gallons, if 1 liter = 1,000 milliliters and 1 gallon = 3.785 liters? (3 points)
a.5.6775 milliliters
b.567.75 milliliters
c.5,677.5 milliliters
d.56,775 milliliters
B
Step-by-step explanation:
Steven earns extra money babysitting. He charges $25.00 for 4 hours and $43.75 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
Answer:
An easy way to solve this problem is divide $25.00 by 3 or $43.75 by 7. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:
$8.33 = y
Hope this helped :)!
Which values of a, b, and c represent the answer in simplest form?
5/8 divided by 3/8 = a b/c
O a=1, b=3, C= 2
O a = 1,b=40, C= 24
O a=1,b= 16, C = 24
O a= 1, b = 2, C= 3
Which of these equations is correct? Select all that apply.
(4-42=4 -
0 (224 = 26
D(6-5) -3 -6 15
(832=8
(35)-2-
1
Answer:
(35-2- is the correct answer you can believe me
Solve the equation
Y = -2(x+4) + 6 when x = -2 then use that value of y to evalute w = -3 - 2y
Answer:
12
Step-by-step explanation:
Plug in for x first:
Y = -2(x+4) +6
Y = -2((-2)+4) +6
Y = -4 + 6
Y = 2
Then use Y to find W;
W = -3 -2y
W = -3 - 2(2)
W = -3(-4)
W= 12
Answer:
y=8 and w=13
Step-by-step explanation:
y=-2(x+4)
-2x-2=4 sooo...
y=4+4
y=8
then plug 8 into the equation for w
w=-3-2y
then you would get
w=-3-16
-3-16
w=13
Please help ASAP!! Will give brainliest if correct!!
Given that SR QT and SQ ≈ ST, find the perimeter of QST.
A. 22
B. 27
C. 30
D. 32
Answer:
b
Step-by-step explanation:
I really need help with this ?
Answer:
j
Step-by-step explanation:
20 points
A parallelogram has one pair of parallel sides.
True or false
If a quadrilateral is a rectangle then it is also a square. *
True or False
A parallelogram always has four congruent sides.
True or False
If a quadrilateral is a square then it is also a rectangle. *
True or False
If a quadrilateral is a trapezoid then it is also a parallelogram.
True or False
Answer: true
Step-by-step explanation:
Step-by-step explanation:
"A parallelogram has one pair of parallel sides."
False. A parallelogram has two pairs of parallel sides.
"If a quadrilateral is a rectangle then it is also a square."
False. A rectangle isn't necessarily a square. Rectangles are only squares when all four sides are equal.
"A parallelogram always has four congruent sides."
False. Parallelograms have two pairs of congruent sides. All four sides aren't necessarily congruent.
"If a quadrilateral is a square then it is also a rectangle."
True. All squares are rectangles.
"If a quadrilateral is a trapezoid then it is also a parallelogram."
False. Trapezoids have only 1 pair of parallel sides, and parallelograms have 2 pairs of parallel sides.
Meredith scores a 72% on her quiz. She
misses 7 questions. What is the change in
her score in percentage points for each
question she gets incorrect?
Answer:
The answer is 4.
Step-by-step explanation:
The total percent is 100%. You subtract 100% with 72% which is 28. Then, you divide 28 with 7 and voila! The answer is 4.
The change in her score in percentage points for each question she gets incorrect is 4%.
Using this formula
Change in score percentage=(100%-Scores %)/Number of missed questions
Where:
Scores %=72%
Number of missed questions=7 questions
Let plug in the formula
Change in score percentage=(100%-72%)/7
Change in score percentage=28%/7
Change in score percentage=4%
Inconclusion the change in her score in percentage points for each question she gets incorrect is 4%.
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Sorry my kid needs help with this
Answer:
700,000
Step-by-step explanation:
Well, [tex]10^{4}[/tex] as we know is 10(10)(10)(10), or 10 multiplied by itself 4 times.
The easiest way to solve this, is knowing that because 10 is being multiplied by itself 4 times, it'll have the outcome of 10000, which has 4 zeroes. This is very good to remember, so I recommend remembering it :) Just like if the question was about [tex]10^{5}[/tex], it would be 100000, which has 5 zeroes.
So now we add on all of those zeroes to 70.
700000 would be your answer because we added on 4 more zeroes.
Write a function rule. Then find the value of y for the given value of x.
y is 4 more than the product of 7 and x; x = 3
Answer:
25
Step-by-step explanation:
x = 3
according to the condition,
y = 7× x + 4
y = 7× 3 +4
y = 21 + 4
y = 25
A hoodie that regularly costs $50 is on sale for $38.
What is the percent decrease in the price of the hoodie?
Answer:
76%
Step-by-step explanation:
38 multiplied by 100 = 3,800
3,800 divided by 50 = 76
Therefore the answer is 76%
The two-way table below describes the car rental habits of sales representatives attending a conference.
What percentage of representatives staying at least two nights rented a car?
20%
44%
55%
79%
Answer:
44 bro
Step-by-step explanation:
The percentage of representatives staying at least two nights rented a car is 44%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Given is a two way table.
From the table, the number of representatives staying at least 2 nights rented a car is 11.
Total number of representatives staying at least two nights = 14 + 11 = 25
Percentage = (11 / 25) × 100
= 0.44 × 100
= 44%
Hence the percentage for the required number is 44%.
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sara got 32 question out of 36. what was the percentage she got correct
Answer:
88.8%
Step-by-step explanation:
Answer:
89% correct
Step-by-step explanation:
32 out of 36
32/36
8/9
0.89
89 percent correct
A Karate club consists of 35 persons holding a black belt
(highest rating), 64 persons holding a brown belt (middle
rating), and 97 persons holding a purple belt (lowest rating).
What is the probability that a randomly-selected club member
holds a brown belt or a purple belt?
A) 0.238
B) 0.762
C) 0.687
D) 0.313
Answer:
B
Step-by-step explanation:
35+64+97=196 97+64=161 161/196=B
The probability that a randomly-selected club member holds a brown belt or a purple belt is 0.821 which is nearest to 0.762.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of person = 35+64+97 = 196
P(brown belt) = 64/196
P(purple belt) = 97/196
Probability that a randomly-selected club member holds a brown belt or a purple belt:
= 64/196 + 97/196
= (64+97)/196
= 161/196 = 0.821
Thus, the probability that a randomly-selected club member holds a brown belt or a purple belt is 0.821 which is nearest to 0.762.
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What is the solution of 4+ V5x+88 – X+
10?
X = -10
X = 3
X = -10 or x = 3
O no solution
Answer: no solution
Step-by-step explanation:
A line passes through the point (-10, – 7) and has a slope of 5/2
Write an equation in slope-intercept form for this line.
A football player completed a 35 yard pass. How many inches did he
throw the ball?
1,000 in
1,260 in
1450 in
105 in
Answer:
1260 inches
Step-by-step explanation:
1 yard = 36 inches
35 * 36 = 1260 inches
Which expression is another way to write 10,000,000? 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Answer:
Step-by-step explanation:
10^6
Answer:
10^6
Step-by-step explanation:
10. Solve: 3( 3x + 1)-(4x + 1) = 6x - 3(x+4)
Can’t solve this, any suggestions?
Answer:-7
Step-by-step explanation:Let's solve your equation step-by-step.
3(3x+1)−(4x+1)=6x−3(x+4)
Step 1: Simplify both sides of the equation.
3(3x+1)−(4x+1)=6x−3(x+4)
3(3x+1)+−1(4x+1)=6x−3(x+4)(Distribute the Negative Sign)
3(3x+1)+−1(4x)+(−1)(1)=6x−3(x+4)
3(3x+1)+−4x+−1=6x−3(x+4)
(3)(3x)+(3)(1)+−4x+−1=6x+(−3)(x)+(−3)(4)(Distribute)
9x+3+−4x+−1=6x+−3x+−12
(9x+−4x)+(3+−1)=(6x+−3x)+(−12)(Combine Like Terms)
5x+2=3x+−12
5x+2=3x−12
Step 2: Subtract 3x from both sides.
5x+2−3x=3x−12−3x
2x+2=−12
Step 3: Subtract 2 from both sides.
2x+2−2=−12−2
2x=−14
Step 4: Divide both sides by 2.
2x /2
=
−14 /2
x=−7
Which of the following is not a property of atoms?
A. All atoms of the same element are identical
B.Atoms have the ability to vibrate and move
C.Atoms have at least two electrons
D.Atoms have three different subatomic particles
Answer:
A. All atoms of the same elements are identical
Step-by-step explanation:
Two atoms of the same chemical element are typically not identical. They can be different if their electrons are in different states,
Helen walked 4 blocks north of her house. Then she walked 3 blocks south.
Which statement is true?
A. The sum 4 + (–3) = 1 means that Helen is 1blocks south of her house.
B. The sum 4 + (–3) = 1 means that Helen is 1blocks north of her house.
C. The sum 4 + 3 = 7 means that Helen is 7blocks south of her house.
D. The sum 4 + 3 = 7 means that Helen is 7blocks north of her house.
Answer:
b
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
What is the answer to this problem?
Answer:3
Step-by-step explanation:
C = 2()r
2*3.14 = 6.28
18.84 / 6.28
=3
If correct pls give brainly
Will give brainiest answer
Answer:
I'm pretty sure it's a.....
The answer is A
Step-by-step explanation:
common sense