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.
Convert the fraction to a decimal: 1/6 =
Answer:
1/6 as a decimal is 1.66 or 1.6 repeating.
Identify if each given value is a zero of the equation 0=18c3−50c
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[tex]18 {c}^{3} - 50c = 0 [/tex]
[tex]2c(9 {c}^{2} - 25) = 0 [/tex]
[tex]2c(3c + 5)(3c - 5) = 0[/tex]
_________________________________
[tex]2c = 0[/tex]
[tex]c = 0[/tex]
_________________________________
[tex]3c + 5 = 0[/tex]
[tex]c = - \frac{5}{3} \\ [/tex]
_________________________________
[tex]3c - 5 = 0[/tex]
[tex]c = \frac{5}{3} \\ [/tex]
Done...
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The only zero of the equation 0=18c³−50c is c = 0, as it makes the equation true when substituted.
value is a zero of the equation 0 = 18c³ - 50c,
putting in the value for c
If c = 0:
0 = 18(0)³ - 50(0)
0 = 0 - 0
0 = 0 (True)
If c = 2:
0 = 18(2)³ - 50(2)
0 = 18(8) - 100
0 = 144 - 100
0 = 44 (False)
If c = -1:
0 = 18(-1)³ - 50(-1)
0 = 18(-1) + 50
0 = -18 + 50
0 = 32 (False)
only c = 0 is a zero of the equation 0 = 18c³ - 50c.
The equation 0 = 18c³ - 50c has only one zero, which is c = 0, as it satisfies the equation when substituted.
learn more about equation here
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What’s another name for plane P?
Answer:
DAB is correct if you have the option for it. if not can you post the possible answers?
Convert the decimal 0.92¯¯¯ to a fraction.
Question 4 options:
83100
8390
839
9299
Answer:
83/90
Step-by-step explanation:
you need to multiply the variable by 10. x =
0.9222… 10x = 9.222… 10x – x = 9.222… – 0.9222… 9x = 8.3 x =83/90
The decimal 0.92¯¯¯ is equal to the fraction 92/99.
So, the correct answer is 92/99.
Given that, a decimal 0.92¯¯¯, we need to convert it into fraction,
To convert the decimal 0.92¯¯¯ to a fraction, we can follow these steps:
Let's represent 0.92¯¯¯ as x.
Step 1: Multiply x by 100 to remove the repeating decimal:
100x = 92.92¯¯¯
Step 2: Subtract x from 100x to eliminate the repeating decimal:
100x - x = 92.92¯¯¯ - 0.92¯¯¯
99x = 92
Step 3: Divide both sides of the equation by 99 to solve for x:
x = 92/99
Therefore, the decimal 0.92¯¯¯ is equal to the fraction 92/99.
So, the correct answer is 92/99.
Learn more about Repeating decimal click;
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Given f(x) = -x + 7, find x when f(x)= -4
Answer:
x = 11
Step-by-step explanation:
f(x) = -x + 7
f(x) = -4
Using substitution, -x + 7 = -4
Then you can solve from there
-x + 7 = -4
-x = -11
x = 11
Hope this helps!
(I apologize if I'm incorrect)
please help me asap
7. option 2 : 104
8. option 4 : 54
9. option 2 : 23
10. option 2 : 6
11. option 2 : 6
5 x 7 = 7 x 5
What algebraic property is illustrated above?
A. commutative property of multiplication
B. associative property of multiplication
C. distributive property
D. transitive property
Answer:
A. commutative property of multiplication
Step-by-step explanation:
The commutative property of multiplication ,
States that when two numbers are being multiplied, their order can be changed without affecting the product.
Please help me with this question because I am lost
Answer:
C
Step-by-step explanation:
The formula = 21+ 2m is used when calculating:
a area of a rectangle
C area of a circle
b. perimeter of a rectangle
d circumference of a circle
The table shows the unit prices for items Darryl
purchased to improve Downtown Deli.
Darryl places an order for 128 ounces of pickles, 24
loaves of bread, and 25 pounds of coffee. What is the
total cost of the order?
$
Answer:
94.85
Step-by-step explanation:
0.20x128=25.60
0.75x24=18.00
2.05x25=51.25
25.60+18.00+51.25= 94.85
Answer:
it is 94.85
explanation:
i took this applications of unit rate test trust me. :D
Please help ASAP in math I have a picture
Answer:
x = 25
Step-by-step explanation:
Those 2 angles together form a straight line which is equal to 180°. So you can set up an equation:
3x + 18 = 93
-18 -18
3x = 75
Divide both sides by 3
x = 25
There were 150 total movies at the store. They sold 70% of their stock. How many did they se
Answer:
They sold 105 movies.
Step-by-step explanation:
70÷100×150
= 0.7×150
= 105
Hope it helps :)
Find the equation of the line that passes through the point (-3, -4) and (5, -4)
Answer:
y=-4
Explanation:
you have to use the equation y₂-y₁/x₂-x₁ and what ever answer you get from this equation will be your slope
ONE OF THE COLDEST TEMPERTURES EVER RECORDED WAS -128F IN ANTARCTICA. ONE OF THE WARMEST TEMPERATURES EVER RECORDED WAS 134 DEGREES FAHRENHEIT IN DEATH VALLET CALIFORNIA. HOW MANY DEGRESS DIFFERENCE ARE THERE BETWEEN THE COLDEST AND WARMEST RECORDED OUTSIDE TEMPERTURE
Answer:
271 degrees
Step-by-step explanation:
143-(-128)=143+128=271 degrees
rewrite 2-2/3x=3/4 so it does not have fractions.
Answer:
I'm guessing you convert to decimals?
2-0.666666667x=0.75
Let me know if that is wrong
Stay Safe,
evancorral7
3(a – 7) = -9 + 3a.
Answer:
0=12
No Solution
Step-by-step explanation:
Hope this helps (:
Look at the attachment
Find the quotient below. Write the answer as a fraction in the simplest form 7 1/2 divided 5/6
Answer:
9
Step-by-step explanation:
steps for dividing mixed numbers.
Change every mixed number to an improper fraction.
Multiply the reciprocal of the divisor, simplifying if possible.
Put answer in lowest terms (or simpliest form)
Check to be sure the answer makes sense.
which of the following should one consider when choosing a career?
Answer:
all of the above
have a good day keep working
Which of the following describes the location of the opposite of the number that R represents on this line?
vertical number line from negative 6 to positive 6 in increments of 2 is shown. Only the whole even numbers are labeled. A point labeled R is placed onthe 6th tick mark below the 0.
At a distance of 6 tick marks below 0
At a distance of 6 tick marks above 0
At a distance of 12 tick marks below 0
At a distance of 12 tick marks above 0
PLEASE HELP I REALLY NEED IT
Answer:
B
Step-by-step explanation
Answer:
A
Step-by-step explanation:
Because on the number line it has the point 6 spots below the zero so it has to be A: At a distance 6 tick marks below 0
What is the length of the arc on a circle with radius 16 ft intercepted by a 60° angle?
Use 3.14 for pie
Round the answer to the hundredths place.
Answer:
16.75
Step-by-step explanation:
What is the answer to m<4
Answer:
124°
Step-by-step explanation:
Supplementary angles are when two angles add up to 180°
If angle 3 is 56° then you subtract
180 - 56 = 124
-9x + 1 = - 80 Find the value of x
Answer:
Step-by-step explanation:
80+1=9x
81=9x
x=9
Step by step explanation:
Step 1:
→[tex]-9x + 1 = - 80[/tex]
Step 2:
→[tex] - 9x = - 80 - 1[/tex]
Step 3:
→[tex] - 9x = - 81[/tex]
Step 4:
→[tex]x = \dfrac{ - 81}{ - 9} [/tex]
Step 5:
→[tex]x = 9✓[/tex]
2x + 3x = 60 for x = 12
True or false
Answer:
true
Step-by-step explanation:
Trust me
Answer:
True
Step-by-step explanation:
2(12)+3(12)=60
24+36=60
What is the slope of this line?
Enter your answer as a fraction in the simplest term in the box.
Answer:
1/4
Step-by-step explanation:
using your value of x for question number 11 find the measure of angle h will mark brainiest this is so hard ty so much
Answer:
∠H = 58Step-by-step explanation:
using the value of x = 20 from number 11
solve the angle H
∠H = 3x - 2
plugin the value of x=20 into the equation
∠H = 3(20) - 2
∠H = 58
Vertex (3,2) and point(2,-3) written in vertex form
Answer:
which principle prevents a brach from abusing its power
Step-by-step explanation:
which principle prevents a brach from abusing its power
only answer 5 and 6 for brainliest
Answer:
5. Midpoint: (3.5,0.5)
Quadrant: 1st
6. Midpoint: (-5,0.5)
Quadrant: 2nd
Answer:
1.
midpoint: (3.5, 0.5)
Quadrant: 1
2.
midpoint:(-5, 0.5)
Quadrant: 2
hope this helps :)
Step-by-step explanation:
Six adult tickets to a movie at the theater cost
$52.50. Find the price for one ticket.
Answer:
$8.75
Step-by-step explanation:
The total cost is $52.50. And you got eight "items". So you would do $52.50 divided by 8. This would give you the cost of one item/ticket
Lucy wants to buy a skateboard that had an original price of $60. It is marked down 30%. She lives in a state that has a 10% sales tax. What is the final price she will pay for the skateboard, including tax?
Answer:
$46.20
Step-by-step explanation:
First you find the markdown price which you can find by doing 60x.7 and you get 42. Then you multiply that by .1 and add that answer to 42 and you have an answer.
Order these numbers from least to greatest based on there absolute value
|-2.5|,|-2|,|-2.4|,|-3|
Answer:
3, 2.5, 2.4, 2
Step-by-step explanation:
Answer:
|-3|,|-2.5|,|-2.4|,|-2|
Step-by-step explanation:
Treat them as if they were all positive numbers .