Need help please!!!!!!!!!!

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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\(g^{2} +4g-32=0\)

\(g^{2} + 8g - 4g - 32=0\)

\(g(g+8)-4(g+8) = 0\)

\((g+8)(g-4) = 0\)

\(g+8=0 \implies \bf g = -8\)

\(g-4=0 \implies \bf g = 4\)

\(\implies g = 4 \ or \ -8\)

Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

Trigonometry is best used in navigation to estimate where to point the compass to get a straight line. It will be simple to pinpoint a location as well as find distance and see the horizon using a compass and trigonometric functions in navigation.

The area of mathematics known as trigonometry examines the correlation between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are used to study this relationship. The concept of trigonometry was developed by the Greek mathematician Hipparchus, and the word trigonometry is a derivative of Latin from the 16th century.

One of the most significant area of mathematic is rigometry. The words "Trigonon" and "Metron," which mean respectively "triangle" and "measure," are combined to form the word "trigonometry." It is the investigation of how a right-angled triangle's sides and angles relate to one another. Therefore, using formulas and identities based on this relationship aids in determining the measure of a right-angled triangle's unknown dimensions.

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Full question:

What is the best use of trigonometry?

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

22

Step-by-step explanation:

Range : Maximum - Minimum

Minimum = 6

Maximum = A (Let maximum be A)

Hence,

16 = A - 6

A = 22

Maximum = 22

Answer:

y = -x

Step-by-step explanation:

Slope-intercept form looks like this: y = mx + b, with m being the slope or rate of change and b being the y-intercept. We already know the rate of change, so we can put -1 as m: y = -1x + b. To find our y-intercept, we can plug the point (3, -3) into the equation and solve for b:

-3 = -1(3) + b

-3 = -3 + b

b = 0

So we have y = -1x + 0. This can be simplified to y = -x.

Answer:

$18.97

Step-by-step explanation:

Add $7.49, $8.29, and $1.79 together= $17.57.

Then, add the 8% tax. So $17.57+8% of tax= $18.97.

1. Using mathematical operations, the cost of three 5kg bags of rice at ¢2 per kg is ¢30.

2. From the 2km piece, you can cut 2,000 pieces with each one meter long.

3. The fraction of a liter that is 259 ml can be written as ²⁵⁹/₁₀₀₀.

4. 60ps expressed as a decimal of ¢240 is 0.25.

5. The groups of 4 marks in 20, based on a division operation, is 5.

6. If an orange costs ¢150, by multiplication, 9 oranges will cost ¢1,350.

7. The product of 35 and 12, which is a multiplication operation, is 420.

8. Using division operation, from 1 kg, one could obtain 5.55 units of 180g each.

The four basic mathematical operations are addition, subtraction, division, and multiplication.

In this situation, the mathematical operations involved are division and multiplication.

1) The cost of price per kg = ¢2

The number of bags bought = 3

The weight per bag = 5kg

The total weight of 3 bags = 15kg (5 x 3)

The total cost = ¢30 (¢2 x 15)

2) The total length of the piece = 2km

1 km = 1,000 meters

2km = 2,000 meters

The length of each string = 1 meter

The number of strings = 2,000 (2,000 ÷ 1)

3) 1 liter = 1,000 ml

259 ml/1,000 ml = 259/1,000

= ²⁵⁹/₁₀₀₀

4) 60p as a decimal of ¢240

= 0.25 (60 ÷ 240)

5) 20 ÷ 4 = 5

4 x 5 = 20

6) The cost per orange =  ¢150

The number of oranges bought = 9

The total cost of 9 oranges = ¢1,350 (¢150 x 9)

7) The product of 35 and 12 = 420 (35 x 12)

8) The quantity of each unit = 180g

The total quantity = 1 kg

1 kg = 1,000 g

5.55 (1,000 ÷ 180)

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Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

Answer:

5000×8×3/100

1200

1200×10/100

120

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

The answer is 19. ( i think)

Answer:

On a number line, the solution x = -10 would be located to the left of the origin (0) by a distance of 10 units. So, you would mark the point representing -10 on the number line to the left of 0.

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

F(k + 4) = k - 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

F(x) = -2x + 3x - 8

F(k + 4) is x = k + 4

Step 2: Find F(k + 4)

Answer:

b= 7

Step-by-step explanation:

here's your solution

=> perimeter of rectangle = 62 cm

=> length = 24 cm

=> let width be (b)

=> perimeter of rectangle = 2(l + b)

=> 2(l + b ) = 62

=> 2(24 + b) = 62

=> 48 +2b = 62

=> 2b = 62 - 48

=> 2b = 14

=> b = 14/2

=> b = 7

hope it helps

Given dimensions:

x=31 feet, y= 24 feet and z= 95 feet

We can split the shape above into 3 components: A, B, and C

To find the total area, we will find the sum of the areas of each component

For A

The shape of A is that of a semi-circle.

The area of a semi-circle is given to be

The radius will be the diameter divided by 2

y= diameter

r= radius = y/2

r=24/2 =12 feet

pi=3.14

For B

The shape is a rectangle

The area of a rectangle is given by

A = l x b

where l = 31 and b = 24

Area = 31 x 24

Area = 744 square feet

For C

The shape is a triangle

The area of the triangle is given by

base = 64 feet, height = 24 feet

The total area is

22

Hey there!

x + y

= -19/12 + (-7/5)

= -19/12 - 7/5

= -95/60 + -84/60

= -95/60 - 84/60

= -95 + (-84) / 60 - 0

= -95 - 84 / 60

= -179 / 60

Therefore, the answer should be:

-179 / 60

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

x+y= -2 59/60

Step-by-step explanation:

=-19/12-7/5 = -95-84

60

=-179

60

= -2/59/60

Answer:12

Step-by-step explanation:I did the math

Answer:

Step-by-step explanation:

g(f(x)) = g(x²) = x²- 3

f(g(x)) = f(x-3) = (x-3)² = x²+ 6x + 9

The composition of two functions will be ; f(g(x)) = x²+ 6x + 9 and g(f(x)) = x² - 3.

Two functions f(x) and g(x) are given in the question.

We have to find the composition of the two functions.

What is a function ?

The function is the description of how the inputs relate to the output. Each input has only one output.

As per the question ,

f(x) = x²

g(x) = x - 3

The composition of these two functions can be defined as ;

   g(f(x)) = g ( x² )  

⇒ g(f(x)) = x²- 3

and

   f(g(x)) = f(x-3)

   f(g(x)) = (x-3)²

⇒ f(g(x)) = x²+ 6x + 9

Thus , the composition of two functions will be ; f(g(x)) = x²+ 6x + 9 and g(f(x)) = x² - 3.

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Answer:

:\

Step-by-step explanation:

Answer:

\(r=4.38\)

Step-by-step explanation:

Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)

\(\frac{d}{t} = \frac{rt}{t}\)

\(t\) cancels out on the right side.

Step 2: Substitute in the numerals

\(r=\frac{d}{t}\)

\(r=\frac{5.7}{1.3}\)

Step 3: Divide

\(r=4.38\) \(mph\)

There's your answer!

Hope this helps you!

Answer:

I think it's 2275 square feet

Answer:

it is1125

Step-by-step explanation:

first 45x50=2250

next divide 2250 by 2 equals 1125