Find h(x, y) = g(f(x, y)). g(t) = t + Vt, f(x, y) = 7x + 4y – 28 h(x, y) = Find the set on which h is continuous. OD = {(x, y) | y 22x - 7} Oh is continuous on R2 OD = {(x, y) |(x, y) + ( )} OD = {(x, y) |(x, y) + (0, 0); OD = {(x,y) y 2 - 2x + 7}

Answers

Answer 1

The set on which h(x,y) is such that:

y ≤ (22/7)x - 7 and [tex]9x^2 + 16y^2 + 38xy \geq 231[/tex]

How to find the set on which h(x, y) and h is continuous?

First, we can compute f(x,y) = 7x + 4y - 28, and then substitute into g(t) to get:

g(f(x,y)) = f(x,y) + Vf(x,y) = (7x + 4y - 28) + V(7x + 4y - 28)

Expanding the expression inside the square root, we get:

[tex]g(f(x,y)) = (8x + 5y - 28) + V(57x^2 + 56xy + 16y^2 - 784)[/tex]

To find the set on which h(x,y) is continuous, we need to determine the set on which the expression inside the square root is non-negative. This set is defined by the inequality:

[tex]57x^2 + 56xy + 16y^2 - 784 \geq 0[/tex]

To simplify this expression, we can diagonalize the quadratic form using a change of variables. We set:

u = x + 2y

v = x - y

Then, the inequality becomes:

[tex]9u^2 + 7v^2 - 784 \geq 0[/tex]

This is the inequality of an elliptical region in the u-v plane centered at the origin. Its boundary is given by the equation:

[tex]9u^2 + 7v^2 - 784 = 0[/tex]

Therefore, the set on which h(x,y) is continuous is the set of points (x,y) such that:

y ≤ (22/7)x - 7

and

[tex]9(x+2y)^2 + 7(x-y)^2 \geq 784[/tex]

or equivalently:

[tex]9x^2 + 16y^2 + 38xy \geq 231[/tex]

This is the region below the line y = (22/7)x - 7, outside of the elliptical region defined by [tex]9x^2 + 16y^2 + 38xy = 231.[/tex]

Learn more about functions and continuity

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Related Questions

At her restaurant, Yolanda opened 34 cans of tomato sauce. She needs to use 4 cans of sauce for one pan of lasagna. How many pans of lasagna could Yolanda make if she uses all of the cans? Write the answer as a mixed number.

Answers

she could make 8 and a half pans of lasagna

Step-by-step explanation:

so divide 34 and 4 you will get 17 / 2 so to make it into a mixed number divide it by 8 and it will 16 so 1 will be remaining so it will be 8 1/2 hope it helps :D

I NEED MORE HELP PLSSS

Answers

The answer is the first one.

BRAINLIEST FOR 1ST AND SECOND WHO ANSWERS.... EMERGENCY


Marcie pays someone to clean the salon. She pays them $15.00 per hour. She offers them a 3% raise on their hourly pay. How much will she now pay them per hour?

Answers

Answer:

I think it will be $16.50

Step-by-step explanation:

sorry if I'm wrong

Name all the quadrilaterals that have the given property.


two pairs of parallel sides and all angles congruent


a

rectangle, square

b

trapezoid

c

rhombus, square

d

rhombus

Answers

Answer:

A) rectangle and square

Step-by-step explanation:

Answer:

A) rectangle and square

Step-by-step explanation:

 

 Hope it work

Brainliest plz

True or False:
The relation shown is a function.

20 POINTS!!

Answers

Answer:

True

Step-by-step explanation:

For a relation to be a function each value of x must pair up with one and only one value of

The relation shown is a function.

Sami has 12 Balloons . 2/3 of them are Green and the rest is Red balloons. What's is the ratio of Green to Red balloons

Answers

8:4 or 2:1 simplified

20 points!!

Find the value of y when x=9.
y=1- 2x

Answers

Answer: The answer is -17

Step-by-step explanation:

Brainlist Plz?

*Solve by Graphing* Greg went to the hardware store to buy bolts and washers. The bolts cost $0.55 each and the washers cost $0.07 each. George paid $2.41 for a total price of 7 pieces. How many of each item did he get?​

Answers

Answer:

He got 4 bolts and 3 washers

Step-by-step explanation:

Because 0.55 · 4 = 2.2

0.07 · 3 = .21

and put it together, 2.2 + .21 = 2.41

Four square tiles, each of side 12 cm are used to make a bigger tile. Find the perimeter of the larger tile.

Answers

Answer:

192 cm

Step-by-step explanation:

Given that:

Side length of small tiles = 12cm

Number of small tilea used to make a bigger tile = 4

The perimeter of larger tile:

Perimeter of a square = 4s

Where, s = side length

Side length of larger tile :

4 * side length of smaller tile

4 * 12

= 48 cm

Hence,

Perimeter of a larger square tile = 4s

4 * 48cm

= 192 cm

Mr. Johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week

Answers

Answer:

288

Step-by-step explanation:

it's pretty simple, if u do 96 * 3, it will be that. yw :)

Answer:

He made $324.

Step-by-step explanation:

96 x 3 = 288

204 x 3 = 612

So, then 612-288 = 324

Hope this helped!

Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
O y=x-2
y = x + 2
O y = x + 3
O y=x-5
Save and Exit

Answers

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-3=1(x-5)

y-3=x-5

y=x-5+3

y=x-2

Jaden is building a fence around his yard. He wants to know how much fencing he needs. His yard is shaped like a rectangle that is 96 feet long and
33 feet wide.
How many feet of fencing does Jaden need to buy? Enter the answer in the box.
feet

Answers

Answer:

258 ft

Step-by-step explanation:

area of the rectangle =96+33×2=258 ft

hope it helps you to

please mark me as brainlist

ASAP PLEASE I WILL MAKE BRAINIEST

The coordinates of the point UU are (-4,3)(−4,3) and the coordinates of point VV are (-4,-9).(−4,−9). What is the distance, in units, between the point UU and point V?V?

Answers

Answer:

12 units

Step-by-step explanation:

Given points:

U(-4, 3) and V(-4, -9)

The line segment between the given points is vertical as their x-coordinates are same.

The distance between the points is the difference between their y-coordinates:

3 - (-9) = 12 units

300 ml of pure alcohol is poured from a bottle containing 2 l of pure alcohol. Then, 300 ml of water is added into the bottle. Again 300 ml of the diluted alcohol is poured out and 300 ml of water is added into the bottle, Find the percentage of pure alcohol in the solution now.

Answers

Answer:

The present percentage of pure alcohol in the solution is 72.25% of pure alcohol

Step-by-step explanation:

The volume of pure alcohol poured from the 2 l bottle of pure alcohol = 300 ml of pure alcohol

The volume of water added into the bottle after pouring out the pure alcohol = 300 ml of water

The volume of diluted alcohol poured out of the bottle = 300 ml of diluted alcohol

The volume of water added into the bottle of diluted alcohol after pouring out the 300 ml of diluted alcohol = 300 ml of water

Step 1

After pouring the 300 ml of pure alcohol and adding 300 ml of water to the bottle, the percentage concentration, C%₁ is given as follows;

C%₁ = (Volume of pure alcohol)/(Total volume of the solution) × 100

The volume of pure alcohol in the bottle = 2 l - 300 ml = 1,700 ml

The total volume of the solution = The volume of pure alcohol in the bottle +  The volume of water added = 1,700 ml + 300 ml = 2,000 ml = 2 l

∴ C%₁ = (1,700 ml)/(2,000 ml) × 100 = 85% percent alcohol

Step 2

After pouring out 300 ml diluted alcohol from the 2,000 ml, 85% alcohol and adding 300 ml of water, we have;

Volume of 85% alcohol = 2,000 ml - 300 ml = 1,700 ml

The volume of pure alcohol in the 1,700 ml, 85% diluted alcohol = 85/100 × 1,700 = 1,445 ml

The total volume of the diluted solution = The volume of the 85% alcohol in the solution + The volume of water added

∴ The total volume of the twice diluted solution = 1,700 ml + 300 ml = 2,000 ml

The present percentage of pure alcohol in the solution, C%₂ = (The volume of pure alcohol in the 1,700 ml, 85% diluted alcohol)/(The total volume of the diluted solution) × 100

∴ C%₂ = (1,445 ml)/(2,000 ml) × 100 = 72.25 %

The present percentage of pure alcohol in the solution, C%₂ = 72.25%

cp=Rs6250 loss%=4% find sp​

Answers

Formula:
Selling price = Cost price x (1 - 4%)


Selling price:
= 6250 x (1 - 4%)

= 6250 x 96%

= 6250 x 96/100

= 6250 x 24/25

= Rs 6000

Hope it helps!

4(x + 3) = 3(3x - 1)​

Answers

Answer:

Either 4x+12 ≠ 9x-3 OR x = 3

Hope this helps!! (Please mark Brainliest if possible!!)

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

[tex]4(x+3)=3(3x-1)[/tex]

Distribute 4 and 3 into the parentheses

[tex]4x+12=9x-3[/tex]

Combine like terms; subtract both sides by 12

[tex]4x+12-12=9x-3-12\\4x=9x-15[/tex]

Combine like terms; subtract both sides by 9x

[tex]4x-9x=9x-15-9x\\-5x=-15[/tex]

Divide both sides by -5 to isolate x

[tex]\frac{-5x}{-5} =\frac{-15}{-5} \\x=3[/tex]

I hope this helps!

Solve - x/6 less than or equal to 3

Answers

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

Can someone please help with this math question?

Answers

Answer:

Its easy

Step-by-step explanation:

1) 12

2)76

3)21.5

4)22.0

find a ⋅ b
a = 7i - 4j, b = 4i + 3j

Answers

Answer:

28i^2 + 5ij - 12j^2

Step-by-step explanation:

(7i-4j)(4i+3j)

7i times 4i is 28i^2

7i times 3j is 21ij

-4j times 4i is -16ij

-4j times 3j is -12j^2

In equation it looks like this:

28i^2+21ij-16ij-12j^2

Simplify 21ij and -16ij

21ij-16ij is 5ij

So the answer is:

28i^2 + 5ij - 12j^2

Hope this helps!

Answer:

The answer is 16

Step-by-step explanation:

She needs altogether 2 2/4. that is 2 wholes and 2/4 fraction. if we consider using 1/4 cup, 1 whole is made of four quarter cups. Therefore 2 wholes require eight quarter cups. Then theres a remaining fraction of 2/4 which is equivalent to two quarter cups. 1/4 + 1/4 = 2/4. Therefore altogether 8 + 2 = 10 of the 1/4 cups are required for the recipe. 10 of 1/4 cups are needed is this right? Yes or no

Answers

Answer:

Yes

Step-by-step explanation:

According to the analysis;

There are four 1/4 cups in one whole

There are eight 1/4 cups in two wholes

Then the fraction 2/4 = 1/4 + 1/4 Hence there are two 1/4 cups in 2/4.

Altogether we have the fraction 2 2/4 as 8 + 2 = 10 measures of 1/4 cups

To confirm, 10 * 1/4 = 2 2/4

Therefore, the analysis is correct.

you ride through some wet paint on your bike creating a red spot on the tire. write a cosine equation to model the height of the red spot over the distance you ride.
Your bike tire has a radius (r) of 11 inches.
The period is the circumference of the tire (2pir)
start the cycle when the spot is at the top of the tire

Answers

Answer: y = 11 cos (1/11x) +11

Step-by-step explanation:

Writing a cosine equation to model the height of the red spot over the distance you ride will be:

D. [tex]y=11 cos (1/11x) + 11[/tex]

Some cosine formulas are:

[tex]cos A= (b2+c2-a2)/(2bc)[/tex]

What is a cosine equation?

A cosine equation or formula is is one of the three most common trigonometric function. It is the trigonometric function that equals the ratio of the side adjacent to an acute triangle to the hypotenuse.

Therefore the correct answer is option D.

Read more about cosine equation here:

https://brainly.com/question/17075439

Please help I really need it

Answers

Answer:

X = -2, Y = 13

X = 0, Y = 9

X = 2, Y = 5

X = 4, Y = 1

Step-by-step explanation:

Take the value given for X and plug it into the equation. For example, when X = -4, you will make your equation look as follows:

y = -2(-4) + 9

Simplify it:

y = 8 + 9

y = 17

Repeat this process with the rest of the X values to get your Y values.

How can you use equations to solve real-world problems? PLZ

Answers

Answer:

you can use equations to find out how much tip you should give

construction is a big one!

4x - 2y = 24
y=-3x - 2


someone help me?

Answers

Step-by-step explanation:

I've used substitution method over here and got the value of X and Y

Hi how is your day going

What is the value of X

Answers

Answer:

The Value of X in 2nd one can be 14√3.

The Value of X in 1st one can be 6√3.

Step-by-step explanation:

2.)here we used tan 60° formula with P/B as x/14 respectively.

as the value of tan 60° is √3, we got,

√3= x/14

x= 14√3.

1.) Here we used sin 30° formula with 1/√2 as P/H

so we got,

6/x= 1/√2

hence the answer comes:-

x= 6√2..

Hope so it helped you........

Something and 14√3.

Steps

The person above me has calculated something.

The way to get 14√3 can be seen in the image above.

Does 18x-(9x+2)=4x have a solution?

Answers

Answer:

Yes

Step-by-step explanation:

9x - 4x = 2

5x = 2

x = 2/5

x = 0.4

Unrestrained growth of cells in a petri dish can be extremely rapid, with a single cell growing into a number of cells, N, given by the formula, N(t) = 8t, after t hours.

Enter the formula for the number of cells in the petri dish when a culture is started with 30 isolated cells.

The new formula is N(t) = .

How many cells do you expect after 3 hours?

You should expect ___
cells.

Answers

Answer:

New Formula is [tex] N(t) = 30t [/tex]

You should expect 90 cells

Step-by-step explanation:

✔️The new formula that would represent the number of cells when 30 isolated cells are used to start a culture would be:

[tex] N(t) = 30t [/tex]

✔️Number of cells, N(t), to expect after 3 hours, t:

Substitute t = 3 into [tex] N(t) = 30t [/tex]

Thus:

[tex] N(30) = 30*3 [/tex]

[tex] N(30) = 90 [/tex]

You should expect 90 cells

2.8 -3x =12.1 −6x what's x

Answers

X= 3.1 is the answer
The answer is X=3.1!

Please help quick will give brainliest!

Answers

Answer: Choice A) There must be a vertical asymptote at x = c

Explanation:

The first limit [tex]\displaystyle \lim_{x\to c^{-}}h(x) = -\infty[/tex] says that as x approaches c from the left side, the f(x) or y values approach negative infinity. So the graph goes down forever as x approaches this c value from the left side.

The limit [tex]\displaystyle \lim_{x\to c^{+}}h(x) = \infty[/tex] means that as x approaches c from the right side, the y values head off to positive infinity.

Either of these facts are enough to conclude that we have a vertical asymptote at x = c. We can think of it like an electric fence in which we can get closer to, but not actually touch it.

I’m having a bit of trouble could someone please help me??

Answers

Answer:

1.Conduction

2.the second one

sorry if these are wrong

Step-by-step explanation:

Answer:

#1 Convection

#2 From the hot to the mug

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