find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points. f(x, y)

Answers

Answer 1

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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Related Questions

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?

Answers

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

8x = 2 write the value of x

Answers

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

What is the major difference between the alternate hypothesis and the null hypothesis?.

Answers

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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I need help please. It’s for a practice test

Answers

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–$73,999

Class width

The 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.

What is the solution ?
4/2 = √3x-2

Answers

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

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?

Answers

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

For the function f(x) = 5.92, calculate the following function values:
f(− 2) =
f(1/2)=
f(0) =

Answers

Answer:

55.92

Step-by-step explanation:

[tex]f(x)[/tex] doesn't depend on x.

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

Answers

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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Rationalize 1 / √5 - √2 and subtract is from √5 - √2




thank s

Answers

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)

J(2,-4), k(3,7), L(6,-1); x-axis

Answers

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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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?

Answers

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%

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?

Answers

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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Given (x – 1)2 = 50, select the values of x.

Answers

Answer: x=26

Step-by-step explanation:

(x-1) = 50/2

x-1 = 25

x = 25 +1

x = 26

x-1 = root of 50
X - 1 = 7.07
X = 8.07.

hats and mittens are on sale at the store

Answers

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).​

solve for x of the circle​

Answers

Check the picture below.

this graph shows a proportional relationship containing the point (3,6) and (4,8)

What is the constant of proportionality ?

Answers

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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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?

Answers

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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which function is represented on the graph

Answers

Answer: was there supposed to be a picture attached to this question ?

Step-by-step explanation:

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?

Answers

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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Find the equation of the straight line RS. A)y = -2x + 3 B)y = -2x + 6 C)y = 2x + 3 D)y = 2x + 6​

Answers

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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What is y=5x-4 in standard form?

Answers

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!

What is pie to the second power

Answers

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

Find a counterexample to how that the conjecture i fale. Conjecture: Any number that i diviible by 2 i alo diviible by 4

Answers

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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HELP PLEASEEE

Find the measure of HG

Answers

Answer:

  40 m

Step-by-step explanation:

Given midline JK = (6x -4) m and baseline HG = 10x m, you want the measure of HG.

Midline

The 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.

write an equation for the line that passes through point (0,4) and is parallel to the line with equation y = -5x + 3

Answers

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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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?

Answers

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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question above please help​

Answers

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=4.45

Need Help with geometry

Answers

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.

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.​

Answers

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=5300(1+0.075/1)^1•7

A=5300•1075^7

A=5300•1.659049

A=8792.96

*They will have $8792.96 in 7 years

Substitute the values into the appropriate formula and solve for x.

Answers

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:

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sucrose c12h22o11 which is commonly known as table sugar reacts in dulte acid solutions to form two simpler sugars glose and fructose both which have the formula c5h12o6. is the reaction first or second order with respect to c12h22o11 how do you know? How would I solve this question? I know that x and y will be equal but I'm not sure of their values.Please look at the file attached Reflection of point across x-axisReflection of point across y-axis---------------------------------------------------------------------Reflection of point across x-axis and then Reflection across y-axisHELP ?! two autosomal genes, g and h, are 80 map units apart. you perform the following test cross: g h / g h x / g h. at what frequency would you find g h / g h progeny? a compound which contains 35.5% carbon, 8.80 % hydrogen and 55.9% fluorine by mass would have which empirical formula? How was Kim Hyun Hee indoctrinated from a very young age and what was she taught about America and its allies, Japan and South Korea? (without plagiarizing write 500 words please) Ifx-xy-2y = 0 then find the equations of all tangent lines to the curve wheny = -1. Does the police officer have the right to search theirbag?O No. The Fourth Amendment requiresto have a good reason for a search.O Yes. Police officers are able to search anyone who looks suspicious.O Yes. Police officers can search anyone at any time.O No. The Eighth Amendment grants protection fromcruel and unusual punishment. He has erected a multitude of New Offices, and sent hither swarms of Officers to harass our people and eat out their substance.He has kept among us, in times of peace, Standing Armies without the Consent of our legislatures.-The Declaration of IndependenceIn this passage from the Declaration of Independence, the primary complaint of the colonists is centered around Parliament's passage of theResponsesASugar Act.BStamp Act.CQuartering Act.DTea Act. Which of the following describes a third-degree burn? acan be treated with cool water, clean covering, and pain relievers bcauses blisters, redness, and swelling caffects all layers of skin and underlying tissue dcan be treated like first-degree burns if small 7. In a triangle there are two sides that have the same length and the thirdside is 1.5 times longer than the length of the other two. Define a variableto represent the unknown quantity. Then write an algebraic expression torepresent the perimeter of the triangle. Find the quotient. nn4n= A business invests $45,000 in an account that earns 1.8% interest that is compounded monthly.What type of function best represents the growth of the investment?Choose... how many signals would you expect each of the following molecules to have in its 1h and 13c spectra? you are using the best practice methodology to troubleshoot a printer. during which phase of the methodology should you use external research based on the symptoms? what advantages do discounted bonds offer to investors? why may a bond be called if it is selling at a premium? Why does the author in Danger! This Mission To Mars Could Bore You To Death explore this topic? Retake questionSS 7.34 In what way could the Crusades be viewed as a failure?The Holy Land was completely destroyed.New ideas and inventions spread in Europe.Crusaders never gained permanent control of the Holy Land.Trade between Europe and Asia increased. Adam has 18 counters. He gives 10 of the counters to Lesley. what fraction of the 18 counters does Adam have now You are in the lifeguard office taking a break from surveillance duty and a camp counselor requests a swim test for a new camper. You use the Red Cross water competency sequence to conduct a swim test. Describe these steps in order: