Mathematics College

Find the absolute maximum and minimum of values of the set
d. f(x,y)= 2x^2+y^2-4x-2y+1 d={(x,y) | 0 <= 3, 0 <= y <= 2}

Answers

Answer 1
Find the critical points within the region:

[tex]f(x,y)=2x^2+y^2-4x-2y+1[/tex]
[tex]\implies\begin{cases}f_x=4x-4=0\implies x=1\\f_y=2y-2=0\implies y=1\end{cases}[/tex]

So (1, 1) is the only critical point of the function and it happens to fall within the rectangle [tex]D[/tex]. At this point, we get a value of [tex]f(1,1)=-2[/tex].

Now check along the boundaries for potential extreme values.

If [tex]x=0[/tex], then [tex]f(0,y)=y^2-2y+1=(y-1)^2[/tex], which has a maximum when [tex]y=2[/tex] and has a minimum when [tex]y=1[/tex]. So we have a potential extrema at [tex]f(0,2)=1[/tex] and [tex]f(0,1)=0[/tex].

If [tex]x=3[/tex], then [tex]f(3,y)=y^2-2y+7=(y-1)^2+6[/tex], with a max when [tex]y=2[/tex] and min when [tex]y=1[/tex]. So we have [tex]f(3,2)=7[/tex] and [tex]f(3,1)=6[/tex].

If [tex]y=0[/tex], then [tex]f(x,0)=2x^2-4x+1=2(x-1)^2-1[/tex], with a max when [tex]x=3[/tex] and a min when [tex]x=1[/tex]. So we have [tex]f(3,0)=7[/tex] and [tex]f(1,0)=-1[/tex].

If [tex]y=2[/tex], then [tex]f(x,2)=2x^2-4x+1=2(x-1)^2-1[/tex] again, with a max when [tex]x=3[/tex] and a min when [tex]x=1[/tex]. So we have, again, [tex]f(3,2)=7[/tex] and [tex]f(1,2)=-1[/tex].

So there are absolute maxima of 7 at (3, 0) and (3,2), and an absolute minimum of -2 at (1, 1).

Related Questions

Suppose that you have a goal to drive two miles at an average rate of 60 miles per hour (mph). during the first mile you travel at a rate of 30 mph. how fast would you need to travel during the second mile in order to reach your goal of 60 mph for the total two mile distance? (hint: remember that rate is found by taking distance divided by time.)

Answers

Your goal requires you complete the distance in 2 minutes. If you travel at half the target speed, you will have used up the allowed time traveling the first half of the distance.

You need to travel the second mile at infinite speed to average 60 mph.

which describes the correlation shown?

Answers

Answer:

The correlation that is shown in the scatter plot is:

         Strong positive.

Step-by-step explanation:

From the scatter plot we see that with the increase of one variable the second variable also increases.

Hence, the association is positive.

Also, if we draw a trend line that best represents the scatter plot then not all the points will lie above the line but all the data points are either over the line or very close to the line this means that the correlation coefficient is close to 1 but not exactly equal to 1.

            Hence, the correlation is:

               Strong positive.

( For perfect positive all the data points should lie above that line i.e. correlation coefficient must be equal to 1)

Answer:

Option C) Strong positive        

Step-by-step explanation:

Correlation

Correlation is a technique that help us to find or define a relationship between two variables. It is a measure of linear relationship between two quantities. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases.

Looking at the graph it could be said that the variables are strongly positively correlated as with a small increase in one variable, the other variable increases.

It is not a perfect positive relation as change in one variable does not lead to equal change in other variable.

It cannot be negative relation as well.

A pitcher contains 3 1/2 pints of lemonade. Susan pours 5/8 of a pint into a glass, and Mateo pours 1/2 pint into a glass. How much lemonade is left in the pitcher?

Answers

we have 3 1/2 pints of lemonade
3 1/2- 1/2 (Mateo)=3
3- 5/8= 2 8/8- 5/8=2 3/8 lemonade left 

I need to collect data for this table please someone help

Answers

Total number of people living in an apartment = 18 + 36 = 54
18 people living in an apartment have a pet.

So percentage of people living in an apartment who have a pet = [tex] \frac{18}{54}*100=33 [/tex]%


Total number of people living in a house = 43 + 24 = 67
43 people living in a house have a pet.

So percentage of people living in a house who have a pet = [tex] \frac{43}{67}*100=64 [/tex]%

So answer in first blank is 33% and answer in second blank is 64%.


Three of the angles of a quadrilateral are 120° 48° and 92° what is the size of the fourth angle

Answers

360-120-48-92=100°

Each quadrilateral has 360° so simply deduct the angles to get your result.
Hi there! A quadrilateral has angles that add up to 360°. So we have the measurements of the first three angles. We will look for the 4th angle by solving. Let's add the totals of the first 3 angles. 120 + 48 + 92 is 260. Now, we subtract that number from 360. 360 - 260 is 100. There. The measurement of the fourth angle is 100°.

Who topping covers more of the pizza 2/8 or 5/8

Answers

Hello,

The answer should be "5/8".

Reason:

My teacher taught me that the fractions with the smaller numbers is the greater number than the fraction with bigger numbers therefore your answer is 5/8!

2/8 < 5/8

Therefore its greater topping.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit
5/8ths because it is larger number and if you change it into a a decimal then they would be 2/8 = 0.25
                          5/8 = 0.625 
between these two numbers 0.625 is the largest and hence 5/8 covers more toppings than 2/8 does.

I love cheese pizza

The line plot shows the measurement of a certain liquid (in milliliters) in nine beakers. If you combined the liquids and then put an equal amount of liquid in each beaker, how much liquid would be in each beaker?
A)
1/8 ml

B)
1/2 ml

C)
7/29 ml

D)
1/4 ml

Answers

There would be 1/2 mL in each beaker.

We start by adding the amounts given by the line plot:
1/4 + 1/4 + 3/8 + 3/8 + 1/2 + 1/2 + 5/8 + 3/4 + 7/8

Find a common denominator.  The smallest thing that 2, 4 and 8 will all evenly divide into is 8:

2/8 + 2/8 + 3/8 + 3/8 + 4/8 + 4/8 + 5/8 + 6/8 + 7/8

Add the numerators:
36/8

Now we divide this by 9:
36/8 ÷ 9 = 36/8 ÷ 9/1 = 36/8 × 1/9 = 36/72 = 1/2

Three cards are drawn from a deck without replacement. what is the probability that all three cards are clubs?

Answers

b.0.0129 is the answer

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 14 inches,and the bicycle wheel mkes 3 full rotations before stopping. How long is the trace of water on the floor?

Answers

radius = 14 inches
one round of the tire = [tex]2 \pi r[/tex]
one round of the tire = [tex]2 \pi (14)[/tex]
one round of the tire = 87.96 inches
three rounds of the tire = 87.96 x 3 = 263.89 inches

At the end of each year, how much money would you earn in interest if you invested $3,500 and earned 4.5% simple interest?

Answers

$157.50 would be the amount that you earn in interest

which least to greatest 125% 6/5 1.22

Answers

6/5, 1.22, 125%


Hope I helped!

Let me know if you need anything else!

~ Zoe (Rank:'Genius')

Final answer:

To compare the numbers 125%, 6/5, and 1.22, they were all converted to decimal form which revealed the least to greatest order as 1.22, 6/5, and 125%.

Explanation:

To arrange the numbers 125%, 6/5, and 1.22 from least to greatest, we first need to express all of them in the same format for an accurate comparison. Let's convert each number to a decimal:

125% as a decimal is 1.25 (since 100% is equal to 1, hence 125% is 1.25).6/5 as a decimal is 1.2 (6 divided by 5 equals 1.2).1.22 is already in decimal form.

Now, we can easily compare:

1.226/5 (1.2)125% (1.25)

The arrangement from least to greatest is 1.22, 6/5, 125%.

There are c players on the Cougars hockey team. The team scored a total of 36 goals this season. One of the players, Matthew, scored 2 more goals than the average per player.

Answers


[tex]36 \div 2 = 16 \\ 16 - 2 = 14[/tex]
so c=14

A student's cell phone plan has a monthly charge of $40 for 600 minutes of use and a $0.25/minute charge for each additional minute. Last month, the student talked on the phone for 790 minutes. Which of the following is the bill for the month?

Answers

The bill for the month is $87.50, including $40 for 600 minutes and $47.50 for 190 extra minutes.

To calculate the bill for the month, we need to consider the fixed monthly charge and the additional charge for the extra minutes used beyond the 600-minute limit.

Step 1: Calculate the additional minutes used beyond the 600-minute limit:

Total minutes used - Included minutes = Extra minutes

790 minutes - 600 minutes = 190 extra minutes

Step 2: Calculate the additional charge for the extra minutes:

Extra minutes × Additional charge per minute

190 minutes × $0.25/minute = $47.50

Step 3: Add the fixed monthly charge to the additional charge for the extra minutes:

Fixed monthly charge + Additional charge for extra minutes

$40 + $47.50 = $87.50

So, the bill for the month is $87.50.

Last year Milwaukee had the total of snow amounting to 92 inches . The normal fall is 52 1/4 inches . How much above normal was the snowfall last year .

Answers

Final answer:

The snowfall in Milwaukee last year was 39.75 inches above the normal amount, calculated by subtracting the normal annual snowfall from last year's total.

Explanation:

The student's question is related to subtraction of two amounts to find the difference between the actual snowfall and the normal snowfall in Milwaukee.

To determine how much above normal last year's snowfall was, we subtract the normal snowfall amount from last year's total snowfall.

Last year's snowfall in Milwaukee = 92 inches
Normal annual snowfall = 52 1/4 inches

To find how much above normal the snowfall was, we calculate:

92 inches - 52 1/4 inches = 92 inches - 52.25 inches

This equals 39.75 inches above normal snowfall.

According to the south carolina department of mental health web site, for every 200 u.s. women, the average number who suffer from anorexia is one. a group of 600 u.s. women is randomly chosen. part (a) correct: your answer is correct. part (b) correct: your answer is correct. part (c) how many are expected to suffer from anorexia

Answers

3 are expected to have the condition.

The expected value is the found by multiplying the probability by the number in the sample:

(1/200)×600
= (1/200)×(600/1)
= (1×600)/(200×1)
= 600/200 = 3

the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z each represent a different digit from 0 to 9 what is the value of (x)(y)(z)?

Answers

For the units positions of all numbers we have:
[tex]z+7+5=4 \\ z+12=4[/tex]
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
[tex]z+12=14 \\ z=2[/tex]

For the tens positions of all numbers we have:
[tex]4+2+x+1=1 \\ 7+x=1[/tex]
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
[tex]7+x=11 \\ x=4[/tex]

Now we insert x and z to find out y:
[tex]42+27+45=y14 \\ 114=y14 \\ y=1[/tex]

Now we need to find out the product of these three numbers:
[tex]x*y*z=4*1*2=8[/tex]

-1 + 5 * 6 is less than 29

Answers

As an inequality it would be: -1 + 5 * 6 < 29

The perimeter of a rectangle is 80 feet. Find the demensions if the length is 5 feet longer than four times the width. Then find the area of the rectangle.
-Show All Work!-

Answers

Hey there! 

The first thing we should do is review the formulas for area and perimeter. 
Perimeter can be expressed in two ways: a) l+w+l+w OR b) 2l+2w. 
The formula for area is: l*w

We know that the length is 5 feet longer than the width, so when we're defining our variables we can say that width is equal to 'w', and length is equal to 4w+5. 
Since we know that the perimeter is equal to 80, we can say that [tex]80= 2(4w+5) + 2(w)[/tex]. 

Now all we have to do is combine like terms and solve for 80: 

[tex]80 = 2(4w+5) +2w [/tex]
[tex]80 = 8w + 10 +2w[/tex]
[tex]80 = 10w +10[/tex]
[tex]80-10 = 10w +10 -10[/tex]
[tex]70 = 10w[/tex]
[tex] \frac{70}{10} = \frac{10w}{10} [/tex]
[tex]7 = w[/tex]

We now know that the width is equal to 7 feet. To find the length, we can substitute the width into 4w+5: 
[tex]l = 4w + 5 = 4(7)+5[/tex]
[tex]l = 28 + 5[/tex]
[tex]l = 33[/tex]

Now we know that the length is equal to 33 feet. 

So there's your dimensions: 7ft by 33 ft. 

Next, to find the area, we take l*w
[tex]33*7 = 231ft^{2} [/tex]


Hope this is helpful! If any of this doesn't make sense or there's more I can help with, please let me know!

Which represents the solution set of 5(x+5)<85?

A.) x<12
B.) x>12
C.) x<16
D.) x>16

Answers

Isolate the VARIABLE by dividing each side by FACTROS that don't contain the VARIABLE .
YOUR answer is x<12


The correct answer is:  [A]:  " x < 12 " .
__________________________________________________
Given:
__________________________________________________
  " 5(x + 5) < 85 " ;  Simplify/ solve for "x" ; 
__________________________________________________
Method 1)
__________________________________________________

Note the "distributive property of multiplication" :
__________________________________________________
  a(b +  c)  =   ab + ac ;

  a(b – c)   =  ab – ac .
__________________________________________________
So, take the "left-hand side" of the inequality; and expand:
__________________________________________________
  →  5(x + 5) = (5*x) + (5*5) = 5x + 25 ; 

Now, rewrite the inequality:

  →  5x + 25 < 85  ;

Subtract "25" from each side of the inequality ; 

  →  5x + 25 – 25 < 85 – 25  ;

to get:
_______________________________________
  →  5x  <  60  ;

Divide each side of the inequality by "5" ; 

  →  5x / 5  <  60 / 5 ; 

  →  x  <  12 ;  which is:  Answer choice:  [A]:  " x < 12 " .
_______________________________________

Method 2)
_______________________________________
Given:
_______________________________________
 " 5(x + 5) < 85 " ;  Simplify/ solve for "x" ; 
_______________________________________
 Divide EACH SIDE of the equation by "5" ; 

  [5(x + 5) ] / 5 < 85 / 5 ; 

to get: 

  →  x + 5 < 17 ; 

Subtract "5" from EACH SIDE of the inequality:

  →  x + 5 – 5  <  17 – 5 ; 

to get:

  →  x  <  12  ;  which is:  Answer choice:  [A]:  " x < 12 " .
_________________________________________________

What similarity statement can you write relating the three triangles in the diagram ?

Answers

answer is B.
triangle RST ~ triangle RUS ~ triangle SUT

The similarity statement that can be written is;

D(RST) ~ D(RUS) ~D(SUT)

Discussion:

The triangles as represented are right-angled triangles.

In essence, they all have one of their angles to be 90°.

The similarity statement therefore involves the right-angles and is thus; D(RST) ~ D(RUS) ~D(SUT)

Read more on similar triangles:

https://brainly.com/question/20453539

CAN I GET SOME HELP (RIGHT ANSWER)

Answers

it can be found using the formula 1/2 |major arc - minor arc|

1/2 |105 - 23|
1/2 |82|
41
105-23= 82
82/2= 41
An easier way :)

Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?

Answers

1/2 would not be a useful benchmark to compare these 2 fractions because both of them are greater than half. The benchmark fraction 1/2 is most useful when one fraction is less than half and the other more than 1/2. 5/8 is more than 4/8(1/2), and 9/10 is more than 5/10(1/2).

For the data in the table, does y vary directly with x? If it does write an equation for the direct variation. x 2 6 10 y 5 15 25

Answers

The data does show direct variation (otherwise known as direct proportionality);
2 + 4 = 6               5 + 10 = 5
6 + 4 = 10              15 + 10 = 25
The proof is that everytime we increase x by a number (in this case 4), y also increases by some number (in this case 10);
So increasing x by 4, we increase y by 10;
The equation of data that shows direct proportionality is that of a line;
The gradient (represented by m) of the line is going to be how much y changes when we change x;
Using the information above, we can deduce the gradient (m) like so:
m = +10/+4
= 5/2
Now, we use the formula for the equation of the line:
y - y₁ = m(x - x₁)
y - 5 = 5/2(x - 2)
2(y - 5) = 5(x - 2)
2y - 10 = 5x - 10
2y = 5x
y = 5x/2

A carton has a length of fraction 2 and 2 over 3 feet, width of fraction 1 and 1 over 8 feet, and height of fraction 1 and 1 over 5 feet. What is the volume of the carton?

Answers

Answer:

V = 3.6 ft³

Step-by-step explanation:

The formula of a volume of rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have

[tex]l=2\dfrac{2}{3}\ ft=\dfrac{(2)(3)+2}{3}\ ft=\dfrac{8}{3}\ dt\\\\w=1\dfrac{1}{8}\ ft=\dfrac{(1)(8)+1}{8}\ ft=\dfrac{9}{8}\ ft\\\\h=1\dfrac{1}{5}\ ft=\dfrac{(1)(5)+1}{5}\ ft=\dfrac{6}{5}\ ft[/tex]

Substitute:

[tex]V=\left(\dfrac{8}{3}\right)\left(\dfrac{9}{8}\right)\left(\dfrac{6}{5}\right)=\dfrac{432}{120}=3.6\ ft^3[/tex]

Answer:

3 3/5

Step-by-step explanation:

covert mixed fractions to improper fractions

2 2/3 becomes 8/3

1 1/8 becomes 9/8

1 1/5 become 6/5

then you multiply across will give you 432/120

since the numerator os greater than the demoninator, you have to divide 432

into 120 which then will give you 3 72/120. When you simplify the fraction the final answer is 3 3/5.

Ewan makes chess boards from wood. Each board has three different kinds of wood. He has five kinds of wood it is workshop maple, cherry walnut, Poplar and birch how many different types of chess board can he make?

Answers

He can make 10 different types of boards.

This is a combination of 5 objects chosen 3 at a time:

[tex]_nC_r=\frac{n!}{r!(n-r)!} \\ \\_5C_3=\frac{5!}{3!2!}=\frac{120}{12}=10[/tex]

Answer:

D.10

Step-by-step explanation:

One kilometer equals 0.62 miles. How many kilometers equal 16 miles? Round the answer to the nearest tenth. 2.6 kilometers
9.9 kilometers
25.8 kilometers
99.2 kilometers

Answers

25.8 kilometers that is the answer to your question

Answer: 25.8 kilometers

Step-by-step explanation:

Given: One kilometer = 0.62 miles

Then, [tex]1\text{ mile}=\dfrac{1}{0.62}\text{ kilometers}[/tex]

Then to find the number of kilometers in 16 miles, we need to multiply 16 to [tex]\dfrac{1}{0.62}[/tex], we get

[tex]\text{ 16 miles =}16\times\dfrac{1}{0.62}=25.806451612\approx25.8\text{ kilometers}[/tex]

Hence, 25.8 kilometers equals to 16 miles.

Mike used a rectangular prism and two cubes to create a model bench for his class project as shown below.

What is the surface area of the model bench?

A. 850 sq in
B. 800 sq in
C. 750 sq in
D. 700 sq in

Answers

surface area = 2(wl + hl + hw)

top section 2(5*25 + 5*25 + 5*5) = 550

lower part = 2(5*5 + 5*5 + 5*5) = 150

150 + 150 + 550 = 850

 answer is A

Rules for multiplying and dividing by 1 and 0

Answers

Mutiplying: the product is always 0
Multiplying anything by 1 is always the number your multiplying it by so for example 1*2=2

calculate the length of a scarf with sections if each section is 1/2 foot long

Answers

It’s six because, 1/2 is half. And a foot long is twelve inches. And half of twelve is six.

cody has $700 in a savings account that pays 4% simple interest how much will he have in one year

Answers

28$$$$$$$$$$$$$$$$$$$$
700(1.04)= $728 the 700 dollars is multiplied by 1.04 to get 728

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