Use the word bank provided to fill in the blanks in this proof

Given function is

z=f(x,y)=(xy)²-ln(xy)

To find: fxy and fyx We have the function

z=f(x,y)=(xy)²-ln(xy)

Differentiate the function partially w.r.t x keeping y constant

f(x,y)=(xy)²-ln(xy)

Differentiating partially w.r.t x keeping y constant gives:

∂f/∂x = 2xy - (1/x)

equation (1)Differentiate the function partially w.r.t y keeping x constant

f(x,y)=(xy)²-ln(xy)

Differentiating partially w.r.t y keeping x constant gives:

∂f/∂y = 2yx - (1/y) equation

(2)Hence, the values of fxy and fyx are given by

fxy ≡ ∂²f/∂y∂x = ∂/∂y(2xy - (1/x)) = 2xfyx

∂²f/∂x∂y = ∂/∂x(2yx - (1/y)) = 2y

Therefore,

fxy = 2x

and f

yx = 2y

Thus, the correct options are:fxy ≡ 2xy-1/y2fyx ≡ 2xy-1/x2

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To trade stocks in a stock market is called all of these except A; exchange.

The act of purchasing and selling stocks is called as trading stocks.

A trader might purchase stock and keep it for a long time, allowing the price to appreciate and/or receive dividends.

There was nothing wrong with this method, that has helped brilliant entrepreneurs like Warren Buffet amass large sums of money.

Then the incorrect option is A exchange.

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Answer:

d) 19/4

Step-by-step explanation:

Given mixed number,

→ 4 3/4

Now the improper fraction is,

→ 4 3/4

→ 19/4

Hence, option (d) is correct.

the approximate values of the given trigonometric functions are:

(a) sin(π/16) radians ≈ 0.1961

(b) cos(π/16) radians ≈ 0.9808

(c) sin(9) radians ≈ 0.1564

(d) cos(9) radians ≈ 0.9880.

Given:

(a) sin(π/16) radians

(b) cos(π/16) radians

(c) sin(9) radians

(d) cos(9) radians

Using a calculator set for radians, we can approximate these values. Rounding the answers to two decimal places:

(a) sin(π/16) radians:

Using the calculator, the value of sin(π/16) is approximately 0.1961.

(b) cos(π/16) radians:

Using the calculator, the value of cos(π/16) is approximately 0.9808.

(c) sin(9) radians:

Using the calculator, the value of sin(9) is approximately 0.1564.

(d) cos(9) radians:

Using the calculator, the value of cos(9) is approximately 0.9880.

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Answer:

x=5,3

Step-by-step explanation:

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

160 newspapers (400 × .4 = 160)

Answer:

it would take 20 miles and cost 10 dollars.

Step-by-step explanation: Like up the equations so that 50x=40x+200. When you solve for x (number of miles) you find that x=20. Use 20 in either equation (0.5x or 0.4x+2) to get 10 (total cost).

The expressions with radicals which are variables and numbers raised to a fractional indices are simplified as follows.

13. √(9·x)  = 3·√x

14. √(4·y) = 2·√y

15. √(8·x²) = 2·x·√2

16. √(9·x²) = 3·x

17. √(3·x²) = x·√3

18. √(5·y²) = y·√5

19. √(13·x²) = x·√(13)

20. √(29·y²) = y·√(29)

21. √(64·y²) = 8·y

22. √(125·a²) = 5·a·√5

23. ∛(16) = 2·∛2

24. √(50·a²·b) = 5·a·√(2·b)

A radical expression is one that contains the radical (square root or nth root) sign, √.

13. √(9·x)

√(9·x) = √(3²·x) = 3·√x

14. √(4·y)

√(4·y) = √(2²·y) = 2·√y

15. √(8·x²)

√(8·x²) = √(4 × 2·x²) = √(2² × 2·x²)

√(2² × 2·x²) = √(2²·x² × 2) = 2·x·√2

16. √(9·x²)

√(9·x²) =  √(3²·x²) = 3·x

17. √(3·x²)

18. √(5·y²)

√5 × √(y²) = √5 × y = y·√5

19. √(13·x²)

√(13·x²) = √(13) × √x² = √(13) × x = x·√(13)

20. √(29·y²)

√(29·y²) = √(29) × √(y²) = √(29) × y = y·√(29)

21. √(64·y²)

√(64·y²) = √(8²·y²) = √(8²) × √(y²) = 8 × y = 8·y

22. √(125·a²)

√(125·a²) = √(25 × 5 × a²) = √(25) × √5 × √(a²) =  5 × √5 × a

5 × √5 × a  = 5·a·√5

23. ∛(16)

∛(16) = ∛(16) = ∛(8 × 2) =  ∛(2³ × 2) = 2·∛2

24. √(50·a²·b)

√(50·a²·b) = √(25 × 2 × a² × b) = √(5² × 2 × a² × b) = √(5² × a² × 2 × b)

√((5² × a²) × 2 × b) = 5·a·√(2·b)

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Answer:

-2

Step-by-step explanation:

x-1(-7)=5

x+7=5

-7 bot sides

-2

Answer:

y=3x-12

Step-by-step explanation:

We need to find the m of y = mx+b which is the slope:

-3-(-6)/3-2 = 3 as our slope

We know have y = 3x+b.

If we keep applying slope to the point (2,-6) and go downwards. We hit (0,-12). That's our y intercept. So we replace b with our y intercept which is -12. We know get y = 3x-12

The correct option is b (4x+2)(4x-2).

Assuming that the expression is \(16x^2-4\), we can factorize the expression as follows:

\(16x^2-4=(4x)^2-(2)^2\\ 16x^2-4=(4x+2)(4x-2)\)

Note that we can further simplify the expression as:

4(2x+1)(2x-1)

25

8×1=8

8 +2=10

10+15=25

The answer is the 1st image, and the explanation is the 2nd image.

The answer in text if seeing the image is not possible; x + y = 5 and x + 2y + 8 = 15

The given function is,

The graph of the g(x) will be shifted 3 units upward with respect to the parent function f(x),

Thus, the above figure is the graph of g(x).

To utilize the gross profit method, the following information is needed:

1. Beginning Inventory: The value of inventory at the beginning of the accounting period is required.

It represents the cost of inventory available for sale before any purchases or sales occur.

2. Net Sales: The total amount of sales made during the accounting period, excluding any sales returns, allowances, or discounts.

3. Gross Profit Percentage: The gross profit percentage is calculated by dividing the gross profit by net sales. It represents the proportion of net sales that contributes to covering the cost of goods sold.

4. Ending Inventory: The value of inventory at the end of the accounting period is necessary. It represents the cost of unsold inventory that remains on hand.

By using the gross profit percentage, the method allows for estimating the cost of goods sold (COGS) during the accounting period based on the net sales and the desired gross profit percentage. The estimated COGS can then be subtracted from the beginning inventory to determine the estimated ending inventory.

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In the equation:

y = 3x² + 6x + 4

the leading coefficient, a, is equal to 3. Given that a is greater than zero, then the parabola has a shape of a U. Therefore, the parabola has a minimum.

To find the minimum, we need to find the vertex (h, k).

The x-coordinate of the vertex, h, is found as follows:

The y-coordinate of the vertex, k, is found substituting h into the equation of the parabola, as follows:

The minimum is placed at (-1, 1)

Answer: .75 or 3/4

Step-by-step explanation:

Answer:30/40

Step-by-step explanation:

to answer this question, we need to calculate 5/8x3/5x2

5/8 x 3/5 is just both top and bottom of each multiplied, 5 x 3 which is 15 and 8 x 5 which is 40, so 15/40 x 2/1 = 30/40

also try figure it out on your own.

Answer:

2 4/8 or 2 1/2

Step-by-step explanation:

Hope its helpful!

The height of the cylinder is approximately 5.97 cm.

A cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved lateral surface that connects the bases. The bases are perpendicular to the lateral surface, which means that the lateral surface forms a curved rectangle.

Given;

The circumference of the cylinder is 32π.

The lateral surface area of the cylinder is 750 cm².

Lateral surface area of a cylinder = 2πrh

Circumference of a cylinder = 2πr

We can use the circumference formula to find the radius of the cylinder:

2πr = 32π

r = 16

Now we can use the lateral surface area formula to find the height of the cylinder:

750 = 2π(16)(h)

750 = 32πh

h = 750/(32π)

h ≈ 5.97

As a result, the cylinder's height is around 5.97 cm.

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Answer:

x=-1

Step-by-step explanation:

0=-6x-14-3x+5

0=-9x-9

-9x=9

x=-1

Comparing the final prices, we can see that Sally would get a better deal by purchasing the shirt at Lulu, where the final price is $80 after the 20% discount.

what is discount ?

A discount is a reduction in the original price of a product or service, offered by a seller to a buyer. It is a common marketing strategy used to attract customers and increase sales

In the given question,

To determine which store offers the better deal, we need to calculate the final price of the shirt after applying the discounts.

At Lulu, the shirt is on sale for 20% off, so the discounted price is:

Discounted price = Original price - Discount

Discounted price = $100 - (20% x $100)

Discounted price = $80

At H&M, the shirt is on sale for 15% off, so the discounted price is:

Discounted price = Original price - Discount

Discounted price = $100 - (15% x $100)

Discounted price = $85

Sally also has a 5% off coupon that she can use on the discounted price at H&M. Therefore, the final price at H&M would be:

Final price = Discounted price - Coupon

Final price = $85 - (5% x $85)

Final price = $80.75

Comparing the final prices, we can see that Sally would get a better deal by purchasing the shirt at Lulu, where the final price is $80 after the 20% discount.

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Answer:

Cost of fries = $ 1.17

order of fries =4

Total cost of fries =4 × 1.17

                           =  $ 4.68

cost of drinks  = $0.90

no. of drinks    = 5

total cost of drinks =0.90 × 5

                                =$4.50

total cost of drinks and fries = cost of drinks + cost of fries

                                              =$ 4.50 + 4.68

                                      ans        = $ 9.18

Step-by-step explanation:

At a food restaurant, it costs $ 9.18 to get 4 orders of fries and 5 drinks.

It is obtained by adding the individual costs for a given number of orders of fries and drinks. It costs \(1.17f + 0.90d\) for f orders of fries and d order of drinks.

Cost for an order of fries = $ 1.17

Then, the cost for 4 orders = 4 × $ 1.17 = $ 4.68

Cost for an order of drink = $ 0.90

Then, the cost for 5 drinks = 5 × $ 0.90 = $ 4.50

Then the total cost = Cost for 4 fries + Cost for 5 drinks

                                = $ 4.68 + $ 4.50

                                = $ 9.18

Similarly,

The cost for f fries = f × $ 1.17 = 1.17f

The cost for d drinks = d × $ 0.90 = 0.90d

Therefore, the total cost for f fries and d drinks = 1.17f + 0.90d

Thus, it costs $ 9.18 to get 4 orders of fries and 5 drinks and it costs 1.17f + 0.90d to get f orders of fries and d drinks.

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Answer:

3/7 : 1 OR 1 : 7/3

Step-by-step explanation:

You can set up ratios as a fraction and solve for the missing piece. See images.

Answer:

1 : 2.33 aka 1: 2 1/3

Step-by-step explanation:

1) 6 : 14

2) divide both sides by 6

6/6=1

14/6=2 1/3

3) 1 : 2 1/3

Answer:

The difference in the lowest temp refers to the variation or gap between the lowest recorded temperature in a particular period or location.

For instance, if the lowest temperature in January 2020 was -10 degrees Celsius and the lowest temperature in January 2021 was -5 degrees Celsius, then the difference in the lowest temp would be 5 degrees Celsius. This difference could be due to various factors such as changes in weather patterns, location, or time of year. Understanding the difference in the lowest temp can help us anticipate and prepare for extreme weather conditions and their potential impact on our surroundings.

It seems like you want to know the difference in the lowest temperature. The "difference" refers to the subtraction of two values. In this case, we're discussing the "lowest" temperatures, which means the smallest or least extreme temperatures recorded. To find the difference in the lowest temperatures, you'll need to know the specific values you're comparing.

For example, if the lowest temperature in City A is -10°C and the lowest temperature in City B is -5°C, the difference in the lowest temperatures would be calculated as |-10 - (-5)| = 5°C. The "temp" is short for temperature, which is a measure of the thermal energy in an object or environment.

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By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

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Cladograms are considered to be hypotheses because they depict possible evolutionary relationships variable between organisms based on their shared characteristics.

Cladograms are diagrams that depict the evolutionary relationships between organisms based on shared characteristics. They are used to illustrate the evolutionary history of organisms and to show how different species are related to each other. Cladograms are considered to be hypotheses because they are used to make inferences about evolutionary relationships and are based on the assumption that organisms with similar characteristics are more closely related. Cladograms are used to reconstruct the phylogeny of organisms and to identify new species or recent evolutionary changes. Cladograms provide a visual representation of how organisms are related and can be used to make predictions about how organisms may have evolved in the past and how they may continue to evolve in the future.

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Answer:

3/4 75/100 12/16 24/32

Step-by-step explanation:

9/12 is the equivalent of 75% and fractions that express the same proportions.

The area of the triangle RTS will be (8×4) - 1/2 (16+12+10). Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

We start by drawing a rectangle around the triangle as shown in the diagram below.

Area of the RST = area of the rectangle - (area of triangle A + area of triangle B + area of triangle C)

\(\rm Area\ of\ RST = (8 \times 4) - [(\dfrac{1}{2} \times 8 \times 2) + (\dfrac{1}{2} \times 4 \times 3) + (\dfrac{1}{2} \times 5\times 2)]\\\\\\Area\ of\ RST = (8 \times 4) - \dfrac{1}{2} (16 + 12 + 10)\)

The area of the triangle RTS is (8×4) - 1/2 (16+12+10).

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Answer:Option A

Step-by-step explanation:

The conclusions that can be made about the two distributions are:

Options A and D are correct.

The means-to-MAD ratio is found by dividing the mean of a dataset by its Mean Absolute Deviation (MAD).

We have that in Data Set 1, the means-to-MAD ratio is 54/4 = 13.5, and in Data Set 2, the means-to-MAD ratio is 60/2 = 30.

Since the means-to-MAD ratio in Data Set 1 is 13.5 and in Data Set 2 is 30, we can conclude that the two distributions are not similar.

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