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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Four square tiles, each of side 12 cm are used to make a bigger tile. Find the perimeter of the larger tile.
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
I NEED MORE HELP PLSSS
I’m having a bit of trouble could someone please help me??
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
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.
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%
20 points!!
Find the value of y when x=9.
y=1- 2x
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?
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
Please help I really need it
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.
True or False:
The relation shown is a function.
20 POINTS!!
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.
2.8 -3x =12.1 −6x what's x
Does 18x-(9x+2)=4x have a solution?
Answer:
Yes
Step-by-step explanation:
9x - 4x = 2
5x = 2
x = 2/5
x = 0.4
find a ⋅ b
a = 7i - 4j, b = 4i + 3j
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:
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?
Answer:
I think it will be $16.50
Step-by-step explanation:
sorry if I'm wrong
How can you use equations to solve real-world problems? PLZ
Answer:
you can use equations to find out how much tip you should give
4x - 2y = 24
y=-3x - 2
someone help me?
Step-by-step explanation:
I've used substitution method over here and got the value of X and Y
Please help quick will give brainliest!
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.
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
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
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.
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
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
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:
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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.
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
4(x + 3) = 3(3x - 1)
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!
Mr. Johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week
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!
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
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
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
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.
Solve - x/6 less than or equal to 3
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
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
Answer:
A) rectangle and square
Step-by-step explanation:
Answer:
A) rectangle and square
Step-by-step explanation:
Hope it work
Brainliest plz
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?
Answer:
12 unitsStep-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 unitsCan someone please help with this math question?
Answer:
Its easy
Step-by-step explanation:
1) 12
2)76
3)21.5
4)22.0
What is the value of X
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.
cp=Rs6250 loss%=4% find sp
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