Take the first partial derivatives of f(x, y):
∂f/∂x = -2 (x - 5) = 10 - 2x
∂f/∂y = -2y
The critical points occur where both derivatives are zero:
10 - 2x = 0 ===> x = 5
-2y = 0 ===> y = 0
So there is only critical point at (5, 0), which takes on a value of f(5, 0) = 25.
Compute the Hessian matrix for f :
[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}-2&0\\0&-2\end{bmatrix}[/tex]
Since det(H(x, y)) = 4 > 0 for all x, y, the critical point (5, 0) is a relative minimum.
f has no saddle points.
If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 78, find the numbers
Answer:
52 and 26
Step-by-step explanation:
2x=y
x+y=78
3x=78
x=26
2(26)=y
y=52
To check:
52+26=78
help me ! ✬
work due tomorrow. i don’t understand this at all.
there’s 2 questions !
— don’t comment for points.
Answer:
32, 40
Step-by-step explanation:
See the image
Hope that helps! :)
Match to the other shape
Answer:
wheres the picture?
Step-by-step explanation:
Mr. Jameson has an apple orchard on his farm. He hires his daughter, Rachel, to pick apples and offers her two payment options:
Option A: $1.50 per bushel of apples picked
Option B: 1 cent for picking one bushel, 3 cents for picking two bushels, 9 cents for picking three bushels, and so on, with the amount of money tripling for each additional bushel picked
HELP ASAP
Answer:
Part A: f(x) = 1.50x/g(x) = 0.01(3)^x-1
Part B: Option A: $9
Part C: Option B: $1,771.47
Part D: The eighth bushel picked is when the exponential function exceeds the linear function.
Step-by-step explanation:
Part A: Write a function to model each option.
Option A: f(x) = 1.50x, where x is the number of bushels of apples picked
Option B: g(x) = 0.01(3)^x-1, where x is the number of bushels of apples picked.
--------------------------------------------------------------------------------------------------------------
Part B: If Rachel picks six bushels of apples, which option should she choose?
Option A: $9 Option B: $2.43
Option A is better since what the number is would be higher.
1.50x6 = 9. If I were to do the same for option b, option a would end up higher.
--------------------------------------------------------------------------------------------------------------
Part C: If Rachel picks twelve bushels of apples, which option should she choose?
Option A: $18 Option B: $1,771.47
After calculating both of them by multiplying by 12 for each, option B ends up to be much better.
--------------------------------------------------------------------------------------------------------------
Part D: How many bushels of apples does Lucy pick to make option B better for her than option A?
The eighth bushel picked is when the exponential function exceeds the linear function.
The product of a number is 221. sum of no. is 30. Find the number. . p
Answer: 13 and 17
Would appreciate brainly <3
A corporation recently sold zero-coupon $400 bonds maturing in 4 years with an annual yield of 12%. Find the price. [Hint: The price is the present value of $400 4 years from now at the stated interest rate.] (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
400*1.12^-4= 254.2072314
how do I solve this?
Its g is increasing
I guess you could just plug in 0, 1 and -1 and graph it.
How many solutions −2(+1)=2+5
Answer:
no solutions
Step-by-step explanation:
-2+1=2+5
-1=7
-1 does not equal 7 so there are no solutions
The graph of a linear is shown below on the coordinate grid. What is the y-intercept of the graph of the linear equation? Bubble is your answer.
Answer: -7 on the y-axis
Step-by-step explanation:
what is 10 divided by 8 equal?
Answer:
it is equal to 1.25
Step-by-step explanation:
hope it's helpful
Answer:
Decimal:
1.25
Mix Number:
1 1/4
Improper Fraction:
5/4
Step-by-step explanation:
10/8 is 1.25
In fraction it is 1 1/4 or 5/4
Hope this helps!
The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 870 years?
grams
Answer:
A(t) = amount remaining in t years
= A0ekt, where A0 is the initial amount and k is a constant to be determined.
Since A(1690) = (1/2)A0 and A0 = 80,
we have 40 = 80e1690k
1/2 = e1690k
ln(1/2) = 1690k
k = -0.0004
So, A(t) = 80e-0.0004t
Therefore, A(430) = 80e-0.0004(430)
= 80e-0.172
≈ 67.4 g
Step-by-step explanation:
hope it helpful for you ❤️
How many pounds are in 1 1/2 pounds and 8 ounces? There are _____ pounds in 1 1/2 pounds and 8 ounces.
Answer:
Hope this helps
Step-by-step explanation:
Since 16 ounces equal 1 pound, we’ll add 16 + 16, which is 32 ounces. For one half of a pound, simply divide the amount of ounces in a pound (16) by half. 16 divided by 2 is 8, so in total your answer would be 40 ounces in 2 1/2 pounds.
2.Một công ty sẽ bán N quyển sách sau khi chi tiêu x nghìn $ cho việc quảng cáo quyển sách
mới này, được cho bởi
2 N x x x = − 60 5 30
Answer:
that makes no sence we t guy
Step-by-step explanation:
hi hi hi hi hi hi h i hi h h ih i hi hi i hi h
PLEASE GIVE ME THE ANSWER ASAP
What is the solution to this system of linear equations?
5x + 6y = 29
3x + 6y = 27
A. (7,1)
B. (1,7)
C. (4,1)
D. (1.4)
Answer:
no answer b/c the terms are unlike term
Answer:
D. ( 1,4)
Step-by-step explanation:
After Don ate 1/8 of the pie and Ron ate 1/7 of the remainder of the pie, the other five friends divided the rest of the pie equally among themselves what percent of the original pie did each friend eat?
x = the whole pie.
well, Don ate (1/8)x, how much was it left? [tex]x -\cfrac{1}{8}x\implies \cfrac{x}{1} -\cfrac{x}{8}\implies \cfrac{8x-x}{8}\implies \cfrac{7x}{8}[/tex]
well, so that's the remainder.
Then Ron ate 1/7 of the remainder [tex]\cfrac{7x}{8}\div 7\implies \cfrac{7x}{8}\div \cfrac{7}{1}\implies \cfrac{7x}{8}\cdot \cfrac{1}{7}\implies \cfrac{x}{8}[/tex]
well, how much is it left? [tex]\stackrel{\textit{Don leftover}}{\cfrac{7x}{8}}-\stackrel{\textit{Ron's bite}}{\cfrac{x}{8}}\implies \cfrac{6x}{8}\implies \cfrac{3x}{4}[/tex]
well, there are 5 friends how much did each one get from the whole pie?
[tex]\cfrac{3x}{4}\div 5\implies \cfrac{3x}{4}\div \cfrac{5}{1}\implies \cfrac{3x}{4}\cdot \cfrac{1}{5}\implies \implies \cfrac{3x}{20}\implies \stackrel{\textit{each friend}}{\boxed{\cfrac{3}{20}x}}[/tex]
How do I do this question!
Answer:2 x 3
Step-by-step explanation:
Answer: [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
2[tex]\frac{1}{10}[/tex] barrels of almonds to make 3 batches of granola bar.
We need to turn fraction 2[tex]\frac{1}{10}[/tex] into a mixed number
2[tex]\frac{1}{10}[/tex] → [tex]\frac{21}{10}[/tex]
Now we set up an equation.
[tex]\frac{\frac{21}{10} }{3} =\frac{x}{1}[/tex]
Solve for x by cross multiplying and dividing.
[tex]\frac{21}{10}[/tex] ÷ 3 (KCF)
[tex]\frac{21}{10}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{30}[/tex]
Now we simplify the fraction.
[tex]\frac{21}{30}[/tex] → [tex]\frac{7}{10}[/tex]
[tex]\frac{7}{10}[/tex] barrels of almonds were used in each batch.
Herman saves 22% of his monthly paycheck so he can buy a new car. He earned $650 last month. How much money did he save for his car last month?
Answer:
He saved $143.00
Step-by-step explanation:
$650 x .22= 143
In a right triangle, the measures of the legs are 8 and x + 6,
and the measure of the hypotenuse is x + 8. Find the value of x.
See the attached image for the steps.
x = 9.
Identities used :-
(a + b)² = a² + 2ab + b²
Theory used :-
Pythagorean theorem (Hypotenuse² = Base² + Altitude²).
______
RainbowSalt2222 ☔
When Lucia plays golf at the Rolling Hills golf course, she loses about 12 balls on average. When she plays golf at the Meandering Meadows golf course, she loses about 8 balls on average. If Lucia lost approximately 100 balls after playing at Rolling Hills rr times and Meandering Meadows mm times, which of the following equation best represents the relationship between rr and mm?
When Lucia plays golf at the Rolling Hills golf course, she loses about 12 balls on average. When she plays golf at the Meandering Meadows golf course, she loses about 8 balls on average. If Lucia lost approximately 100 balls after playing at Rolling Hills rr times and Meandering Meadows mm times, which of the following equation best represents the relationship between rr and mm?
8r+12m=1008r+12m=100
12r+8m=10012r+8m=100
12r-8m=10012r−8m=100
8r-12m=1008r−12m=100
The relationship between the number of balls Lucia lost at the golf
courses can be expressed as an equation.
The equation that best represents the relationship between r and m is; 12·r + 8·m = 100Reasons:
The given parameters are;
The number of balls Lucia loses at the Rolling Hills, r = 12 balls
The number of balls Lucia loses at the Meandering Meadows, m = 8 balls
The total number of balls Lucia lost after playin at Rolling Hills and Meandering Meadows = 100 balls
The relationship between r and m is therefore;
Number of balls lost at Rolling Hills + Number of balls lost at Meandering Meadows = 100
12 × r + 8 × m = 100
12·r + 8·m = 100
The equation that best represents the relationship between r and m is therefore; 12·r + 8·m = 100
Learn more mathematical word problems here:
https://brainly.com/question/20425634
15.
The number of calories in a 100-g serving of fruit varies by the type of fruit. A snack consisting of
on serving each of peach, apple, and banana contains 124 calories. A snack consisting of two
servings of peach and one serving of banana contains 160 calories. A snack consisting of one
serving of peach, 2 servings of apple, and two servings of banana contains 188 calories. How
many calories are in a 100-g serving of each type of fruit?
Answer:
A=24, B=40, P=60
Step-by-step explanation:
given:
P+A+B=124
2P+B=160
P+2A+2B=188
___________
P=188-2A-2B
P=124-A-B
188-2A-2B=124-A-B
188-A-B=124
188=124+A+B
A+B=64
___
P+A+B=124
P=60
___
2P+B=160
120+B=160
B=40
___
A+B=64
A=24
___
If we substitute each variable in the three given equations for these values, the equations hold true. Therefore, these are the correct values.
How to determine the domain and range of a continuous graph
Answer:
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Eric ran 1 1/4 miles. Then he biked 3 1/2 times farther than he ran.
How far did Eric bike?
Enter your answer as a mixed number in simplest form.
Answer: He biked 4 and 3/8 miles
Step-by-step explanation:
since he ran 1.25 miles and biked 3.5 times farther than that you'd multiply both numbers and get 4.375 which simplifies to 4 and 3/8
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
PLEASEEEEE I BEG YOUUU 50 POINTS!!!!!!!~~~~~
Aubrey wrote a business plan for an entrepreneurship class, and now she has to make bound copies. Aubrey could use a printer who charges a setup fee of $38 and $3 for every copy printed. Another possibility is to go to the office supply store, where she could pay an up-front fee of $34 and $4 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How much would the copies cost? How many copies is that?
Answer:
Copies cost for the first case = $ 12
Copies cost for the second case =$16
Number of Copies = 4
Step-by-step explanation:
Let the number of copies = N
. for the first case: total cost (T1) = 38 + 3N
. for the second case: total cost (T2) = 34 + 4N
Determine the ‘N’ when the cost is equivalent
So, 38 + 3N = 34 + 4N
38 – 34 = 4N – 3N
N = 4
Therefore, number of copies = 4
Copies cost for the first case = 3 × 4 = $12
Copies cost for the second case = 4 × 4 = $16
#1.
Set up fee=$38Cost per copy=$3Expression
[tex]\sf\longmapsto 38+3x[/tex]
#2
Set up fee=$34Cost per copy=$4Expression
[tex]\sf\longmapsto 34+4x[/tex]
Now
[tex]\sf\longmapsto 4x+34=3x+38[/tex]
[tex]\sf\longmapsto x=4[/tex]
There were 4copies
75 is what percent of 150
75 is what percent of 150
Explanation:Percentage Calculator:75 is what percent of 150=50
Answer:50
Answer:
75 is 50 percent of 150.
Step-by-step explanation:
This is a pretty simple concept. First of all for this question, you should have noticed that 75 is half of 150. 50% is equal to 1/2.
There are a couple of methods you could use to solve this problem, if you are using a calculator, a simple way to solve percentage problems is to do 75 divided by 150 (in this case) which gives you 0.50.
If you do not have a calculator and you have to do this on paper, you need to do the classic proportion method. Make two fractions, 75 over 150, and x over 100. (x is what is used to represent an unkown amount.)
We are using over 100 because that is what a percent represents: an amount that is a fraction of 100. now you need to cross multiply. That would be 75 x 100. That equals 7,500. Now cross multiply the other way. That is 150x or represent 150 times x. Now solve the equation 150x = 7,500. To solve this you need to isolate the variable, x by dividing the 150 multiplying the x. That is the coefficient. the attached number next to it. After you do that, you need to divided the other side of the equation by 150. 7,500 divided by 150 equals 50.
After that you will find that the equation shows the value x = 50. You have now found the value of x.
I hope this helps :)
Please find the value of each of the variables. Show all work.
Answer:
W=20 V=42 X=87
Step-by-step explanation:
all sides are equal meaning that two corners from across each other are equal so v is 42 and w 20 this also means x is 87 im not too sure about y
Please look at the picture.
12x3y2z3 - 8x2y2z2 + 20xy2z3
Qiang is inviting 4 friends to a party each friend wants 4 cookies each box has 10 cookies how many boxes should qiang get
Graph algebra problem! Can anybody help me out as graphs are definitely not my strong suit.
Answer:
f(2) = 5
Step-by-step explanation:
Definitions:Input values = x-coordinates.
The input values are also known as the domain, which is the set of all real numbers. With the domain of a function, you could substitute any real number into a given function for x and produce a valid output.Output values = y-coordinates
The range is the set of all real numbers that depend on the input values plugged into the function. Thus, the range represents the output (y-values) that corresponds to the input values used into the function. Function Notation:In the function notation f(x), f is the function name, and x is your input variable. Output values are also called functional values. You could use any letter to represent a function name, such as g(x), w(x), etc.,.Explanations:This particular question asks for you to identify the corresponding output (y-value) of the given input value, x = 2. If you look at the graph, the x-coordinate, x = 2, corresponds to the y-coordinate of 5.
Therefore, f(2) = 5.
Attached is an edited screenshot of the graph that you posted, where it shows where f(2) = 5 is located on the graph.
Answer:
f(2) = 5
Step-by-step explanation:
The 2 in f(2) means you're looking for the value of the function when x=2.
Find the vertical line that is the 2nd one to the right of the y-axis. Follow it up until you reach the function line (at the top edge of the graph). The y-value there is the value of f(2). That is 5 squares above the x-axis, so ...
f(2) = 5
expression:
x + 20 + x + 20 + x + 20 + x + 20
Answer: if is simplify the answer is 4x+80
Step-by-step explanation: