Use the equation to construct a table
y=1/3x+2

Correct me if im wrong :)

The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).

By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.

Given function is xy²= 4. The given expression will be different as below,

dy / dx ( xy² ) - 4 = 0

2xy( dy / dx) + y² = 0

dy / dx = -y / 2x

Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).

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The longest side of a triangle is always opposite the,

A. angle with the greatest measure.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

We know, The length of the largest side in a triangle is opposite to the largest angle.

The statement, The longest side of a triangle is always opposite the

angle with the greatest measure.

Because A longer angle will be more spread out and hence the opposite side will be longer too.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]

An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.

The equation of a line with slope m passing through the point (x1, y1) can be written in the form:

y - y1 = m(x - x1)

Since the slope of the line is undefined, the equation of the line would be in the form:

x - x1 = constant

To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:

x - 3 = constant

So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:

x - 3 = constant

or simply:

x = 3.

[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.

Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

Annie made 4 glasses of juice

To find = fraction of juice that was left

Total glasses of juice = 4

Her 5 friends drank 1/2 glass each

= 5 × [tex]\frac{1}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

Fraction of juice that left,

5 - [tex]\frac{5}{2}[/tex]

Subtracting by taking LCM,

= [tex]\frac{10 - 5}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.

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It can  be estimated that there are 395 penguins in the area.

Proportion is a mathematical comparison between two numbers.  According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".

We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.

The proportion should therefore be [tex]x:53=82:11[/tex]  where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:

[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]

Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.

395 penguins are in the area according to our estimation.

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The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.

In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.

The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:

z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])

where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).

In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:

z - 7 = (-3)(x - 5) + (7)(y - 4)

Simplifying this equation, we get:

z = -3x + 7y + 8

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a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.

b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.

c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.

A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.

A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.

The current total world oil reserves, R = 2,090 billion barrels

Average decrease per year = 18 billion barrels

a) Linear equation for R is 2,090 - 18t

b) In 15 years, the total oil reserves = 2,090 - 18(15)

= 2,090 - 270

= 1,820

c) The constant rate of decrease = 18 billion barrels per year

The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).

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Answer:The answer is 2.5 pints.

The answers are mentioned below.

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).

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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.

Therefore, the displacement can be calculated as the

√(500² + 300²)

= 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.

Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be

360 - 31.39

= 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.

However, the true bearing is measured from the north and therefore, the true bearing would be

90 + 59.04

= 149.04 degrees (rounded to the nearest hundredth).

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12 hours

If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours

Answer:

5.333 hours.

Step-by-step explanation:

Put this on a chart:

6 people = 8 hours

4 people = ? hours

To find ? Use crisscross multiplication and solve:

? = (4 * 8) / 6

? = 32 / 6

? = 5.333

Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.

The solution of the question sin(50)sin(80)cos(50)cos(80) is cos^2(80o), the correct option is D.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).

Given;

sin(50)sin(80)cos(50)cos(80)

Now,

=sin(20°)cos(80°) – cos(20°)sin(80°)

=sin(A-B) = sinA.cosB – cosA.sinB

=sin(20°-80°)

=sin(-60°)

=cos^2(80o)

Therefore, by trigonometry the answer will be cos^2(80o).

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This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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Answer:

Step-by-step explanation:

The graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x-5.

Substitute x=0, 1, 2, 3, 4, ..... in the equation y=2x-5, we get

When x=0,

y=-5

When x=1,

y=-3

When x=2,

y=-1

When x=3

y=1

So, the ordered pair is (0, -5), (1, -3), (2, -1), (3, 1) and so on.

Therefore, the graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

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Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.

In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:

x₁ + x₂ = b

x₁ · x₂ = c

Whose solution can be found by numerical methods.

Now we proceed to determine the values for each cases:

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Answer:

Step-by-step explanation:

Answer:

2

:

5STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 5-3x2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

5 - 3x2 = 0

STEP

3

:

Solving a Single Variable Equation:

3.1 Solve : -3x2+5 = 0

Subtract 5 from both sides of the equation :

-3x2 = -5

Multiply both sides of the equation by (-1) : 3x2 = 5

Divide both sides of the equation by 3:

x2 = 5/3 = 1.667

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 5/3

The equation has two real solutions

These solutions are x = ±√ 1.667 = ± 1.29099

Two solutions were found :

x = ±√ 1.667 = ± 1.29099

The volume of the cone shown can be described to be A. 513 π cubic units

The volume of a cone can be found by the formula :

= π x radius ² x height / 3

The radius of this cone is 9 units and the height is 19 units.

The volume of this cone then is :

= π x radius ² x height / 3

= π x 9 ² x 19/ 3

= π x 81 x 19/ 3

= π x 513

= 513 π cubic units

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Zion Sun Chairs must sell each chair for at least $75.21 to earn a monthly profit of $65,000.

To determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $65,000, we can use the following formula:

Total Profit = Total Revenue - Total Cost

We know that the monthly fixed costs are $17,363.50, and the variable cost per chair is $52.17. Therefore, the total cost to produce 3,575 beach chairs each month can be calculated as follows:

Total Cost = Fixed Cost + (Variable Cost per Chair x Number of Chairs)

Total Cost = $17,363.50 + ($52.17 x 3,575)

Total Cost = $203,871.25

To earn a monthly profit of $65,000, we can set up the equation as follows:

$65,000 = Total Revenue -  $203,871.25

Total Revenue =$268,871.25

To find the minimum sales price per chair, we can divide the total revenue by the number of chairs:

Minimum Sales Price per Chair = Total Revenue / Number of Chairs

Minimum Sales Price per Chair = $268,871.25 / 3,575

Minimum Sales Price per Chair ≈ $75.208

Therefore, Zion Sun Chairs must sell each chair for at least$75.21 to earn a monthly profit of $65,000, given the monthly fixed costs, variable cost per chair, and production quantity.

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On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4

The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.

By BODMAS

2.4of4.5-5.6/1.4+3.8*2

10.8-5.6/1.4+3.8*2

10.8-4+3.8*2

10.8-4+7.6

14.4

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Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:

lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞

As x approaches negative infinity, the square root of x approaches 0, so the function approaches:

lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7

Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.

Step-by-step explanation:

Answer:

  $20M

Step-by-step explanation:

You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.

The minimum rent is ($5/ft²)×(120000 ft²) = $600,000.

The amount of sales that makes $600,000 equal to 3% of sales is ...

  $600000 = 0.03s

  s = $600000/0.03 = $20,000,000

The "natural breakpoint" is $20M in sales.

__

Additional comment

When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.

Answer:

The correct answer is D. Step 4 is incorrect and should be 10x = 24.

The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.

In trianngles ΔKTW and ΔRWT, then we have

KW = TR        {Given}

∠W = ∠T       {Isosceles angles}

WT = WT       {Common side}

Then the trianngles ΔKTW and ΔRWT are congruent to each other.

The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

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Answer:

The width of the living room is 10 feet.

Step-by-step explanation:

Let the width of the living room is w.

And the length of the room is 2w - 8 ft.

Given,

The area of the room is 192  feet^2, by using the formula of area of a rectangle we get,

A = l × w

192 = (2w - 8) × w

Now,

192 = 2w^2 - 8w                              ( By expanding)

200 = 2w^2                                     (By adding 8w to both sides)

100 = w^2                                        (Dividing both sides by 2)      

If we take square root on both sides,

w = 10

So,

The width of the living room is 10 feet.

1. The difference between the temperature is 14°C.

2. The value of the expression will be -3x - 6y + 27.

The difference between the temperature will be:

= -10 + 24

= 14°C.

For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:

x + 2y - 5

Next, multiply this expression by 3:

3(x + 2y - 5) = 3x + 6y - 15

Finally, substitute this back into the original expression:

12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27

So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.

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Answer:

1. -7

2. -1

3. 5

Step-by-step explanation:

Substitute the value given into the equation