The local maxima is(1,0) , local minima is indefinite and the saddle point is (1,0).
As per given in the question ,
f(x,y)=[x2+1 ]
[-2y ]
The critical points are therefore (1,0) and (1,0).
The Hessian is currently
∇²f(x,y)=[−2x 0
0 −2]
2 and 2 are the eigenvalues of the function 2f(1,0).
As a result, (1,0) is a saddle point and 2f(1,0) is indefinite.
Two and two are the eigenvalues of 2f(1,0).
As a result, (1,0) is a maximum and 2f(1,0) is negative definite.
Critical point: If f (p) = 0, then a point p U is f's critical point.
In light of this, the tangent plane to z = f when f is differentiable (x) at (p, f (p)) is horizontal.
Theorem: Assume that f exists and possesses a local extremum at position p. Then, p is a f critical point, with the result that f (p) = 0.
Example: Take into account f (x, y) = x 2 y 2. Once again demonstrating that (0, 0) is the only crucial point of f, fx = 2x = 0 and fy = 2y = 0
However, (0, 0) is not a f local maxima.
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What is the major difference between the alternate hypothesis and the null hypothesis?.
The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
What is Hypothesis?A hypothesis is a put forth explanation for a phenomenon (plural: hypotheses).
A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.
Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.
A working hypothesis is a theory that has been tentatively accepted and is proposed for future study[1], starting with an informed guess or thinking.
Hence, The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
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if a clock's second hand is one inch long, how many miles, to the nearest mile, does the second hand on the clock above travel in 7 days?
The hand will cover a distance of 1055.04 inches in 7 days.
To establish the distance covered by the hand's point would go in a week, we would first need to determine the radius of the clock's circle, for which the hand serves as a proxy .
To accomplish this, we would utilize the equation 2(pi*radius),
where pi equals 3.14.
The solution to p=2(3.14*1 ) is 6.28 inches.
This indicates that the hand's point moves 6.28inch every 1 hours.
To determine how far the hand moves in a 168 hour, we would multiply 6.28 inch by 168.
As a result, we arrive at the final calculation of 168 inches covered in 7 days as 1055.04 inches.
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How much money will be in an account with an annual interest rate of 7.5% compounded annually, if $5300 was deposited 7 years ago? Be sure to write your answer as money.
Answer:
Step-by-step explanation:
To find the amount of money in the account after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount in the account, P is the initial deposit (5300), r is the annual interest rate (7.5%), n is the number of times the interest is compounded per year (1, since the interest is compounded annually), and t is the number of years the money is invested (7).
Plugging these values into the formula, we get:
A = 5300(1 + 0.075/1)^(1*7)
= 5300(1.075)^7
= $7953.33
So, the amount of money in the account after 7 years would be $7953.33.
a line passes through the point (-9,-8) and is parallel to the line with equation y=5x-7. what is the slope of this line?
Answer:
5
Step-by-step explanation:
slopes of the parallel lines are always same this line has slope five
because equation in y intercept form is y=mx+b
where m is the slope.
so the slope of the new line will be five
HELP PLEASEEE
Find the measure of HG
Answer:
40 m
Step-by-step explanation:
Given midline JK = (6x -4) m and baseline HG = 10x m, you want the measure of HG.
MidlineThe midline of a triangle is half the length of the parallel baseline.
JK = 1/2·HG
6x -4 = 1/2(10x)
x -4 = 0 . . . . . . . . . subtract 5x
x = 4
10x = 10·4 = 40
The measure of HG is 40 meters.
In a survey, 80 people were asked whether they prefer to vacation in the mountains or at the beach. Sixty-two people said they prefer beaches. What percent of the people prefer beaches?
Answer: 77.5% of people prefer beaches
Step-by-step explanation:
It's pretty easy to find the percent of people that prefer beaches.
First, find the total amount of people in the survey and you get 80.
Then, also find the amount of people that prefer beaches. 62.
Then you follow this equation:
(Total # of people who prefer beaches) divided by (Total # of people in survey)
= 62/80 = 0.775
After that, you multiply 0.775 x 100 and you get your percentage :D
0.775 x 100 = 77.5% or 77%
Hope this help ^_^
Answer:
77.5%
Step-by-step explanation:
Total number of people = 80
Number of people who prefer beaches = 62
% of people who like beaches = (62/80)x100% = 77.5%
Substitute the values into the appropriate formula and solve for x.
Answer: Hi so its pretty straight forwad use the cosine formula as you have 2 sides and angle opposite of the x. Answer: 21.35
Step-by-step explanation:
hats and mittens are on sale at the store
On solving the question, we got that - one hat costs $2, while a pair of mittens costs $5.
What is equation?A mathematical equation is a statement that contains two algebraic expressions on each side of the equal sign (=). Both of the expressions—the one on the left and the one on the right—are shown as being equal. LHS = RHS is shown.
The shop has hats and mittens on sale!
For $30, one woman was able to get four pairs of mittens and five hats.
For $19, another woman bought two hats and three pairs of mittens.
x is the cost of one hat.
One pair of mittens costs y dollars.
We must locate x and y.
One woman spent $30 to purchase 4 pairs of mittens and 5 hats.
One hat costs x dollars.
The cost of a single pair of mittens is y.
- Divide four pairs of mittens by y, multiply five hats by x, and equal
30 times their total
[tex]5x + 4y = 30 ........................ (1)[/tex]
For $19, another woman bought two hats and three pairs of mittens.
- Divide three pairs of mittens by y, multiply two hats by x, and equate
multiplied by 19
[tex]2x + 3y = 19 ............................ (2)[/tex]
Now,
[tex]-10x - 8y = -60 ................(3)\\10x + 15y = 95 .......... (4)\\Add equations (3) and (4)\\ 7y = 35\\Divide both sides by 7\\ y = 5\\Substitute the value of y in equation (1) or (2) to find x\\ 2x + 3(5) = 19\\ 2x + 15 = 19\\ Subtract 15 from both sides\\ 2x = 4\\ Divide both sides by 2\\x=2\\[/tex]
One hat costs $2, while a pair of mittens costs $5.
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The correct question -
Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30. Another woman purchased 3 pairs of mittens and 2 hats for $19. Find the price of one hat (x) and one pair of mittens (y).
Mabel pend 4 hour to edit a 3-minute long video. She edit a contant rate. How long doe Mabel pend to edit a 15-minute long video?
We know that it would take Mabel 20 minutes to edit a 15-minute-long video by solving simple mathematical operations.
What are mathematical operations?An operation, in maths, is a mathematical function that converts zero or more input values into a precisely defined output value.
The arity of the operation is decided by the number of arithmetic operations.
Most people seem to agree that addition, subtraction, multiplication, and division are the four basic mathematical processes.
So, what time it will take Mabel to dit a 15-minute long video:
Time to edit 15 min videos = New video * Total time taken/Length of added video
Time to edit 15 min videos = 15 * 4/3
Time to edit 15 min videos = 5 * 4
Time to edit 15 min videos = 20
Therefore, we know that it would take Mabel 20 minutes to edit a 15-minute-long video by solving simple mathematical operations.
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If a cubic millimeter of blood contains 5,800,000 red blood cells, how many red blood cells are contained in 50 cubic of blood? Express your answer in scientific notation
In linear equation, Total number of red blood cells in the body is 29 * 10¹¹ .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Red blood per cubic millimeter = 5,800,000 = 5.8 * 10⁵
Red blood in 5 litres of blood = 5.8 * 10⁵ * 5 * 10⁵
= 29.0 * 10¹⁰
= 29 * 10¹⁰ * 10
= 29 * 10¹¹
Total number of red blood cells in the body is 29 * 10¹¹.
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write an equation for the line that passes through point (0,4) and is parallel to the line with equation y = -5x + 3
The equation of a line which is parallel to line y = -5x + 3 and passes through points (0, 4) is 5x + y -4 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given line of equation is,
y = -5x + 3
The slope of the given line m = -5.
The slope of the required line which is parallel to given line will be equal to -5.
To find the line of equation that passes through the point (0, 4),
Use formula y - y₁ = m(x - x₁)
The required equation of line having slope -5 and passes through points (0, 4) is,
y - 4 = -5(x - 0)
y - 4 = -5x
5x + y -4 = 0
The required equation of line is 5x + y -4 = 0.
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Find a counterexample to how that the conjecture i fale. Conjecture: Any number that i diviible by 2 i alo diviible by 4
A number that is divisible by 2 is also divisible by 4. The counterexample of this conjecture should be a number that is divisible by 2 but not divisible by 4 .
What is Conjecture ?
A conjecture is a statement that is guessed by someone and it may or may not be true.
What is counterexample ?
A counterexample is an example that proves the conjecture to be false.
Let's go through the list of values and test the claim
Is 32 divisible by 2? Yes because 16*2 = 32. Is it also divisible by 4? Yes because 8*4 = 32. So we can cross choice A off the list
Is 12 divisible by 2? Yes because 6*2 = 12. Is it also divisible by 4? Yes because 3*4 = 12. So we can cross choice B off the list.
Is 40 divisible by 2? Yes because 2*20 = 40. Is it also divisible by 4? Yes because 4*10 = 40. Choice C is also crossed off the list.
Is 18 divisible by 2? Yes because 2*9 = 18. Is it also divisible by 4? No. We can see that by dividing 18/4 = 4.5 which is not a whole number result. Or you can list out the multiples of 4 which are 4, 8, 12, 16, 20 and we see that 18 is not on the list. This is a counter example to show that the claim "if number is divisible by 2, then it is also divisible by 4" is a false statement.
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Rationalize 1 / √5 - √2 and subtract is from √5 - √2
thank s
Answer:
1/√5-√2 = −√2+√5 (-0.967)
√5-√2 = −√2+√5 (0.821854)
Subtract the answers as the decimal and/or the equation:
-0.967-0.821854 = -1.518854
As equation:
−√2+1/5√5 - √2+√5 = −2√2 + −4/5√5 (Decimal: -4.617282)
solve for x of the circle
Check the picture below.
What is the solution ?
4/2 = √3x-2
Answer:
x = 2
Step-by-step explanation:
[tex] \frac{4}{2}=\sqrt{3x-2} [/tex]
[tex] 2=\sqrt{3x-2} [/tex]
4 = 3x - 2
3x = 6
x = 2
Given (x – 1)2 = 50, select the values of x.
Answer: x=26
Step-by-step explanation:
(x-1) = 50/2
x-1 = 25
x = 25 +1
x = 26
Sara and Behzad are saving to make a down payment
on a house. With an initial deposit of $8,000, they have
opened an account that compounds interest at an
annual rate of 2.1%. Assuming that Sara and Behzad
make no additional deposits or withdrawals, which of
the following expressions gives the dollar value of the
account 4 years after the initial deposit?
The total value of the account after 4 years is; $8800.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
We have given Principal = P = $8,000
Rate = R = 2.1%
Amount = A
Time = 4 years
Simple Interest = (P x R x T) / 100
= (8000 x 2.1 x 4 ) / 100
= 800
Amount = Simple interest + Principal
A = 800 + 8000
A = 8800
Thus, The total value of the account after 4 years is; $8800.
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which function is represented on the graph
Answer: was there supposed to be a picture attached to this question ?
Step-by-step explanation:
What is pie to the second power
Answer:
9.869604...
Step-by-step explanation:
Pie to the second power, or pi squared, is the mathematical operation of multiplying pi (3.14159...) by itself. The result of this operation is equal to 9.869604...
In mathematical notation, pi squared is written as π^2, which is the same as saying "pi to the power of 2". This means that π^2 = π * π = 9.869604...
In general, raising a number to the second power means multiplying the number by itself. For example, 2^2 = 2 * 2 = 4, and 3^2 = 3 * 3 = 9. Similarly, pi squared is just the product of pi multiplied by itself.
pi is approximately 3.14159265359
pi^2 (pi to the second power) is approximately 9.86960440109
What is y=5x-4 in standard form?
Answer:5x-y=4
Step-by-step explanation:
The standard form of a linear equation is
Ax+By=C
Move all terms containing variables to the left side of the equation.
5x-y=4
Answer: 5x-y=4
Step-by-step explanation:
The standard form equation is Ax+By=C
So y=5x-4
So first we have to add 4 both side
y+4=5x
then we subtract y from both side
4= 5x-y
If you can, please give me a Brainliest, thank you!
question above please help
Answer27.1
Step-by-step explanation: c=a^2+b^2 =4.1^2+23^2=27.1
Answer:
4.45
Step-by-step explanation:
the above question it is solve by cos that means cos=adjacent/hypotneus cos(23)=4.1/X then it become X=4.1/cos(23)X=4.45this graph shows a proportional relationship containing the point (3,6) and (4,8)
What is the constant of proportionality ?
The constant of proportionality is 2.
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
A proportional relationship is described by ...
y = kx
The value of k can be found by dividing by x:
k = y/x
For the given non-zero point (3,6), the value of k is found to be ...
k = 6/3 = 2
k = 2
The constant of proportionality is 2.
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J(2,-4), k(3,7), L(6,-1); x-axis
The reflection of the points J(2,-4), K(3,7), and L(6,-1) is (2, 4), (3, -7) and (6, 1) respectively.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
The given points are,
J(2,-4), K(3,7), and L(6,-1)
The reflection of a point (x, y) over the x-axis (x, -y),
So the reflection of point J(2, -4) is M(2, 4)
Reflection of point (3, 7) is (3, -7)
And reflection of point (6, -1) is (6, 1)
The reflection of the points J(2,-4), K(3,7), and L(6,-1) is (2, 4), (3, -7) and (6, 1) respectively.
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Find the equation of the straight line RS. A)y = -2x + 3 B)y = -2x + 6 C)y = 2x + 3 D)y = 2x + 6
The equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.
What is the slope of the equation?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
To find the equation of the line passing through the points (0, 6) and (3, 0), we can use the two-point form:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we get:
m = (0 - 6) / (3 - 0)
= -6 / 3
= -2
Substituting this value for m and the coordinates of one of the given points into the two-point form, we get:
y - 6 = -2(x - 0)
Combining like terms and multiplying through the parentheses, we get:
y = -2x + 6
Hence, the equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.
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Joey, Keith, and Eli have a combined height of 7 meters. If Joey is 1 2/5 meters tall and Eli is 2 7/10 meters tall, how tall is Keith?
Answer: 2 9/10 or 2.9 metres
Step-by-step explanation: Form an equation with the information given
1 2/5 + 2 7/10 +x =7
Let x represent the height of Keith
Change mixed fractions into improper fractions
1 2/5=7/5 as an improper fraction we say 1*5+2=7 and put it over the denominator 5
2 7/10 =27/10 as an improper fraction we say 2*10+7 =27 and put it over the denominator 10
we now have the following:
7/5+27/10+x=7
We simplify these fractions by adding them up
7/5
7/5*2/2+27/10=14/10+27/10=41/10
41/10+x=7
To solve for x
take 41/10 from both sides
7-41/10
Making the denominators the same we get the following:
x=70/10-41/10=29/10=2 9/10
Two rectangles are similar. The first rectangle has a length of 21 cm and a width of 14 cm. The width of the second rectangle is 20 cm. What is its length?
The length of the second rectangle is 30cm
When are two rectangles said to be similar?Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.
all rectangles are not similar rectangles. The ratio of the corresponding adjacent sides may be different.
length the length and width of first rectangle be L1 and W1 and length and width of second rectangle be L2 and W2
then the ratio of length should be equal to ratio of width since both rectangles are similar
L1/L2 = W1/W2
L1 = 21cm, W1 = 14cm, W2 = 20cm
21/L2 = 14/20
cross multiply
14L2 = 420
L2 = 420/14
L2 = 30cm
In conclusion the length of second rectangle is 30cm
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8x = 2 write the value of x
Answer: x=1/4
Step-by-step explanation:
1. You want to isolate the variable, in other words get it by itself. You do that be dividing by 8 to both sides, 8x/8 is just x and 2/8 is 1/4, so therefore x=1/4
2. you can plug in 1/4 for x to check it. 8 x 1/4 is 2, and 2=2 ✅
Answer:x=1/4 or x=0.25 I hope this helpful mark me brainlist if correct
Step-by-step explanation:
8x=2
Divide both sides of the equation by 8
8x divide 8=2 divide 8
Any expression divided by itself equals 1
x=2 divide 8
then write the the division as a fraction
X=2/8
Cancel out the common factor 2 and 8
X=1/4 or x=0.25
For the function f(x) = 5.92, calculate the following function values:
f(− 2) =
f(1/2)=
f(0) =
Answer:
55.92
Step-by-step explanation:
[tex]f(x)[/tex] doesn't depend on x.
Need Help with geometry
Answer: 23
Step-by-step explanation: ML is in between JL. Line ML is 15 and KL is 8.
Since ML is in between we already know there is 15, and the space left is about the same size as line KL. so 15+8=23.
I need help please. It’s for a practice test
Answer:
$13,000
Step-by-step explanation:
You want to know the class width when the class ranges are defined as ...
$35,000–$47,999$48,000–$60,999$61,000–$73,999Class widthThe class width is the difference between adjacent corresponding boundaries. These are the differences of the low boundaries.
$48,000 -$35,000 = $13,000
$61,000 -$48,000 = $13,000
The class width is $13,000.
__
Additional comment
Often, the class boundaries are defined to be values that cannot be part of the data set. If data is rounded to the nearest dollar, the boundaries might be defined as $34,999.50 and 47,999.50, for example. That way, it is clear that both of the values $35,000 and $47,999 will fall into the first class.
The way the classes are defined here, we have to assume that both $35,000 and $47,999 will fall into the first class. However you define the classes, the class for any given data value should never be ambiguous.
The problem with gaps, such as the gap between 47,999 and 48,000, is that you don't know how to assign an "in-between" value to a class. We have to assume here that the ambiguity is resolved by not allowing any data values in that gap.
For your test, you'll want to know how your curriculum defines class width, data or class range, and class boundary, and the procedure recommended for determining class boundaries.