Use the given transformation to evaluate the integral. double integral 10y^2 dA, where R is the region bounded by the curves xy = 2, xy = 7, xy^2 = 2 and xy^2 = 7; v= xy, v- v = xy^2

Answers

Answer 1

Thus, the integral is approximately 55/112.

To evaluate the double integral 10y²dA using the given transformation

v = xy,

v - v = xy²

where R is the region bounded by the curves

xy = 2,

xy = 7,

xy² = 2 and xy² = 7, the following steps are taken:

Step 1: Sketch the region R and find the limits of integration in the u-v plane using the given transformations.

The curves xy = 2 and xy = 7 imply that 2 ≤ xy ≤ 7.

We can rewrite this as: u = xy,

so 2 ≤ u ≤ 7.

The curves xy² = 2 and xy²

= 7 imply that 2 ≤ xy² ≤ 7.

We can rewrite this as: v = xy²,

so 2 ≤ v ≤ 7.

Step 2: Solve for x and y in the transformation equations

x = u / v and

y = v / x to obtain

x = u / v and

y = v / u.

Step 3: Find the Jacobian of the transformation.

J = ∂(x, y) / ∂(u, v)

= det([∂x/∂u ∂x/∂v][∂y/∂u ∂y/∂v])

= det([1/v -u/v²][-v/u² 1/u])

= 1/u²v

Step 4: The given integral is: ∬R 10y² dA

= ∫v=2v

=7 ∫u=

2u=7 10y² |J|

dudv = ∫2⁷ ∫2⁷ 10(v/u²)² / u²v dudv

= ∫2⁷ ∫2⁷ 10v / u⁵ dudv

Step 5: Integrate with respect to u to get:

∫2⁷ 10v [ -1/4u⁴ ]₂ d v

= ∫2⁷ 5/2 (1/u² - 1/16u⁴) d v

= [ -5/2u⁻¹ + 5/32u⁻³ ]₂⁷

= 55/112.

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Related Questions

What is your favorite place to get wings and what type of wings do you like?​

Answers

american deli and honey hot

A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes?

14°
21°
35°
42°

Answers

Answer:

42

Step-by-step explanation:

Answer: D. 42°

Step-by-step explanation: RIGHT ON EDGE 2023

For each comparison below, choose the correct phrase that correctly indicates the relationship between the first and second quantity.Greater than, less than, and equal to

For each comparison below, choose the correct phrase that correctly indicates the relationship between

Answers

The table represents values of a linear function. The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

We would find the slope and y intercept. The formula for determining slope is expressed as

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

From the table,

if x1 = - 1, y1 = 1

if x2 = 0, y2 = 2

m = (2 - 1)/(0 - - 1) = 1/(0 + 1) = 1/1 = 1

To find the y intercept, we would substitute m = 1, x = - 1 and y = 1 into the slope intercept equation. We have

1 = 1 * - 1 + c

1 = - 1 + c

c = 1 + 1 = 2

This means that the y coordinate of the y intercept of g(x) is 2

The y coordinate of the y intercept of f(x) is 1

Thus,

A) The y coordinate of the y intercept of f(x) is less than the y coordinate of the y intercept of g(x)

Lookng at the graph of f(x) and table representing g(x), the maximum of f(x) is y = 3 and g(1) = 3

Thus,

B) The maximum of f(x) is equal to g(1)

f(x) has 2 zeros at the points where the lines cut across the x axis. The linear graph of g(x) has only one zero. Thus,

C) The number of zeros of f(x) is greater than the number of zeros of g(x)

A drugstore has been in the habit of ordering just one case of hand sanitizer at a time. Each case contains 24 bottles, and each bottle contains 500 mL of hand sanitizer. However, recently demand has been very strong, and they are thinking of placing larger orders, which would lower the cost per case, and hence lower the cost per bottle. If they order one case, the cost would be $14.50 per bottle; 2 cases would cost $13.75 per bottle, 3 cases would cost $12.50 per bottle. and 4 cases or more would cost $11.75 per bottle. The retail selling price will be $18.75 per bottle, however any bottles left unsold within a month of the best-before date will be sold off for $6.50 per bottle. The owner believes that at the regular price the possible demands are 1,2,3,4,5,6,7, or 8 dozens of bottles, with probabilities 0.05,0.10,0.15,0.20,0.20,0.15,0.1, and 0.05 respectively. The drugstore must place its entire order now. Assume that they will suffer no loss of goodwill if they happen to be out of stock. (a) Make and solve a model in Excel to provide a recommendation to the store based on maximizing the expected profit. (b) Determine the expected value of perfect information. (c) Suppose that the $6.50 to be received for each leftover bottle is negotiable within the range $4 to $10. Over what range for this value would the recommended order quantity found in part (a) be valid? (i) This can be found by manually varying the number in whatever cell was used for the salvage value in part (a).

Answers

The recommended order quantity is 4 cases, which maximizes the expected profit.

To solve this problem, we need to calculate the expected profit for each order quantity, and then choose the order quantity that maximizes expected profit. Let's assume that the drugstore orders X cases of hand sanitizer.

First, let's calculate the cost per bottle for each order quantity:

If X = 1, the cost per bottle is $14.50.

If X = 2, the cost per bottle is $13.75.

If X = 3, the cost per bottle is $12.50.

If X >= 4, the cost per bottle is $11.75.

Next, we need to calculate the expected demand for each order quantity. The possible demands are 12, 24, 36, 48, 60, 72, 84, or 96 bottles, with probabilities 0.05, 0.10, 0.15, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. So the expected demand for X cases is:

If X = 1, the expected demand is 120.05 + 240.10 + 360.15 + 480.20 + 600.20 + 720.15 + 840.10 + 960.05 = 52.8 bottles.

If X = 2, the expected demand is 2*52.8 = 105.6 bottles.

If X = 3, the expected demand is 3*52.8 = 158.4 bottles.

If X >= 4, the expected demand is 4*52.8 = 211.2 bottles.

Now we can calculate the expected profit for each order quantity. Let's assume that any bottles left unsold within a month of the best-before date will be sold off for $6.50 per bottle.

If X = 1, the expected profit is (18.75 - 14.50)52.8 - 14.5024 + min(24*X - 52.8, 0)*6.50 = $73.68.

If X = 2, the expected profit is (18.75 - 13.75)105.6 - 13.7548 + min(24*X - 105.6, 0)*6.50 = $179.52.

If X = 3, the expected profit is (18.75 - 12.50)158.4 - 12.5072 + min(24*X - 158.4, 0)*6.50 = $261.12.

If X >= 4, the expected profit is (18.75 - 11.75)211.2 - 11.7596 + min(24*X - 211.2, 0)*6.50 = $326.88.

Therefore, the recommended order quantity is 4 cases, which maximizes the expected profit.

To determine the expected value of perfect information, we need to calculate the expected profit if we knew the demand in advance. The maximum possible profit is achieved when we order just enough to meet the demand, so if we knew the demand in advance, we would order exactly as many cases as we need. The expected profit in this case is:

If demand is 12 bottles, the profit is (18.75 - 11.75)12 - 11.7524 = $68.50.

If demand is 24 bottles, the profit is (18.75 - 11.75)24 - 11.7524 = $137.00.

If demand is 36 bottles, the profit is (18.75 - 11.75)36 - 11.7536 = $205.50.

If demand is 48 bottles, the profit is (18.75 - 11.75)48 - 11.7548 = $274.00.

If demand is 60 bottles, the profit is (18.75 - 11.75)60 - 11.7560 = $342.50.

If demand is 72 bottles, the profit is (18.75 - 11.75)72 - 11.7572 = $411.00.

If demand is 84 bottles, the profit is (18.75 - 11.75)84 - 11.7584 = $479.50.

If demand is 96 bottles, the profit is (18.75 - 11.75)96 - 11.7596 = $548.00.

Using these values, we can calculate the expected value of perfect information as:

E(VPI) = (0.0568.50 + 0.10137.00 + 0.15205.50 + 0.20274.00 + 0.20342.50 + 0.15411.00 + 0.10479.50 + 0.05548.00) - $326.88 = $18.99.

This means that if we knew the demand in advance, we could increase our expected profit by $18.99.

Finally, if the salvage value for each leftover bottle is negotiable within the range $4 to $10, we need to adjust the formula for expected profit accordingly. Let's assume that the salvage value is S dollars per bottle. Then the expected profit formula becomes:

If X = 1, the expected profit is (18.75 - 14.50)52.8 - 14.5024 + min(24*X - 52.8, 0)S = $73.68 + min(24X - 52.8, 0)*S.

If X = 2, the expected profit is (18.75 - 13.75)105.6 - 13.7548 + min(24*X - 105.6, 0)S = $179.52 + min(24X - 105.6, 0)*S.

If X = 3, the expected profit is (18.75 - 12.50)158.4 - 12.5072 + min(24*X - 158.4, 0)S = $261.12 + min(24X - 158.4, 0)*S.

If X >= 4, the expected profit is (18.75 - 11.75)211.2 - 11.7596 + min(24*X - 211.2, 0)S = $326.88 + min(24X - 211.2, 0)*S.

Therefore, for the recommended order quantity of X=4, the valid range of salvage value S is $4 <= S <= $10, because if the salvage value is less than $4, it would be more profitable to sell the bottles at the regular price, and if the salvage value is more than $10, it would be more profitable to discard the bottles instead of selling them at a loss.

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Zack wants to map an abandoned line of reasoning. Which shape should Zack use? (a) line with one arrowhead. (b) orange oval. (c) green rectangle. (d) red

Answers

Zack should use a line with one arrowhead to map an abandoned line of reasoning.

A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.

The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.

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Sherry draws a triangle. The length of side AC is 8 inches. The length of side AB is 9 inches. She wants to draw a line XY that is parallel to BC. If she draws point X 2 inches from B, how far from C does she need to draw point Y do that XY || BC?

Answers

see the figure below to better understand the problem

we have that

If XY is parallel to BC

then

Triangle ABC is similar to triangle DBE

Remember that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.

I will assume that triangle ABC is a right triangle

so

AB^2+AC^2+BC^2

BC^2=9^2-8^2

BC^2=17

BC=√17

Applying proportion

DE/AC=BE/BC

substitute given values

DE/9=2/√17

DE=(2/√17)*9

DE=4.37

therefore

Point Y should be 4.37 inches from point C

Sherry draws a triangle. The length of side AC is 8 inches. The length of side AB is 9 inches. She wants

All athlets are hard workers alice is not a hard worker is the final statement is true

Answers

How is this a math question? Anyway, it depends it could be one persons truth, people view hard work differently.

2x+y=3 x-2y=-1 if equation 2 was multiplied by -2

Answers

Answer:

List all of the solutions.

2x+y=3=2x+y=3=

x−2y=−1=x-2y=-1=

2=2=

−2=

Step-by-step explanation:

Hope this helps, If it did, then I would really appreciate it if you gave me Brainliest, I only need one more to rank up and it has taken forever to get to where I am currently. Thanks.

Please help me the picture is above I’ll mark you as the brainliest but please show the work. Thank you! :)

Please help me the picture is above Ill mark you as the brainliest but please show the work. Thank you!

Answers

a) whatever is in the bracket you substitute into x.

c(100) = (1.25*100) + 2175

          = 125 + 2175

          = 2300

Another exmaple: if it says c(2 + x) then you substitute that into x

→ 1.25(2 + x) + 2175  (and then expand that)

b) A physical interpretation of this could be:

For every 1.25 w-widget that is produced, you would add $2175 for the other costs. (something like that)

important: do not click score lab until after you have attempted all tasks. once you click score lab, you will advance to the next lab question and will not be able to restart this lab. this applies to all subsequent labs in this exam. complete the following tasks: connect the components for an internet connection. add the cable modem to the workspace. use an rg-6 coaxial cable to connect the modem to the wan connection on the wall plate. connect the computer to the cable modem. connect the modem to the power outlet. verify the internet connection using the network

Answers

The steps to connect the components for an internet connection are as follows:

Step 1: Add the cable modem to the workspace. Modems are small boxes that are responsible for converting digital signals to analog signals and vice versa. Modems are necessary for accessing the internet. Therefore, it is important to add the cable modem to the workspace first.

Step 2: Use an RG-6 coaxial cable to connect the modem to the WAN connection on the wall plate.A WAN (Wide Area Network) connection is a type of internet connection that is typically used for larger networks. In order to connect a cable modem to the internet using a WAN connection, an RG-6 coaxial cable is needed.

Step 3: Connect the computer to the cable modem.In order to access the internet, the computer must be connected to the cable modem. This can be done using an Ethernet cable.

Step 4: Connect the modem to the power outlet.Modems require power in order to function. Therefore, it is necessary to connect the modem to a power outlet.

Step 5: Verify the internet connection using the network. After completing the above steps, the internet connection can be verified by opening a web browser and attempting to access a webpage. If the webpage loads successfully, the internet connection has been successfully established.Important: It is important to not click Score Lab until after all tasks have been attempted. Once Score Lab is clicked, the user will advance to the next lab question and will not be able to restart this lab. This applies to all subsequent labs in this exam.

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Use the slope formula and state what is the slope of a line with the following two points: (-2, 7) and (8, -9)?

Answers

Answer:

m = -8/5

Step-by-step explanation:

\(m=\frac{-9-7}{8-(-2)} =\frac{-16}{10} =-\frac{8}{5}\)

Hope this helps

Read the following statements I through V: I. Zero (0) II. One (1) III. Two (2) IV. Three (3) V. Either Zero (0) or One (1) VI. Either One (1) or Two (2) VII. Either Two (2) or Three (3) What is the kurtosis measure of the normal distribution

Answers

Correct option is (IV). kurtosis measure of the normal distribution = 3

What is Kurtosis?

Kurtosis is frequently defined as a measure of peakedness or flatness. However, this is deceptive. It is a measure of the distribution's tail heaviness (and skewness measure whether one tail is heavier than the other).

Normal distribution curve determines the skewness of the data as to what extent is is disoriented from the normal distribution curve. Also, it is the probability distribution curve that determines whether the data set is two legged, one legged or it lies under which probability curve.

Because these parameters are purely shape-related, they should not be affected by the mean or standard deviation. Pearson's measures use moments about the mean to avoid relying on the mean and scale the variables to eliminate the standard deviation. Because the normal distribution has only two parameters, the skewness and kurtosis are constants. The kurtosis value is 3.

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PLS ASAP !!! Help me out please :((

PLS ASAP !!! Help me out please :((

Answers

Answer:

v = 87.96 cubic mi

Step-by-step explanation:

v = π r^2 h. but diameter is 4 so r =4/2 =2

v = 3.143 * 2^2 * 7

v = 3.143 * 4 *7

v =3.143 *28

v =87.96 cubic mi

according to professor dave, how far beyond the scale reported is it appropriate estimate a measurement? (i.e. if the ruler below has cm labeled and lines for mm, what is an appropriate estimate?)

Answers

Option C is the correct choice - It is not appropriate to estimate beyond the scale at all. (i.e 2.3 cm)

The scale has two divisions, one for centimeters and the other for millimeters, so it can only measure between 2 (cm) and 3 (mm) and no more.

A measuring device is used to compare the unknown quantity to a standard, and the comparison is then expressed as a number to ascertain the magnitude of the quantity. To properly convey the measurement, a number expressing the magnitude must also have a unit associated with it. For instance, it makes no sense to simply record someone's height as 64. It must be measured at 64 inches. Thus, a number and unit must be assigned to each measurement.

Because the scale has two divisions—centimeter and millimeter—it can only measure up to three centimeters (2.3).
Therefore, option C is the correct choice which states that Any estimate made outside of the scale is entirely inappropriate. (i.e 2.3 cm)

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COMPLETE QUESTION:

According to Professor Dave, how far beyond the scale reported is it appropriate to estimate a measurement? (i.e. If the ruler below has cm labeled and lines for mm, what is an appropriate estimate?) 0 1 2 3 4 5 6 7 8 9 10 cm

a) It is appropriate to estimate 1 digit beyond the scale (.e. 2.33cm)

b) It is appropriate to estimate 2 digits beyond the scale (.e. 2.333cm)

c) It is not appropriate to estimate beyond the scale at all. (.e 2.3 cm)

d) There are no guidelines. Students should do whatever they feel most comfortable doing.

Did you know you could rate your own questions?
whyyyyy like whattt

Answers

lol that's cool because i didn't know either

Which statement is true ?

Which statement is true ?

Answers

Answer:

the second one

Step-by-step explanation:

Using transformations, graph the following function and its inverse
f(x) = 2x+1 +5

Answers

Answer:

yes that correct

Step-by-step explanation:

y=x/4+1/2 find the x and y Pls help asap

Answers

Answer:

y = 1/4x + 1/2 and x = -2 +4y

Step-by-step explanation:

Solving it in a way that x/4 is a fraction and not division so you would make that 1/4x. y = x/4 +1/2 x/4 is 1/4x so then you subtract 1/2 from both sides to get y - 1/2 = 1/4x. You can then divide 1/4 on both sides. -1/2 divided by 1/4 is -2 and 1/4y. This will get your answer of x = 1/4y -2 for x. Y is just 1/4x + 1/2

Jack is standing on the ground talking on his mobile phone. He notices a plane flying at an altitude of

2400 metres. If the angle of elevation to the plane is 70° and by the end of his phone call it has an angle

of elevation of 50°, determine the distance the plane has flown during Jack’s phone call - use the cosine rule

Answers

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Prepare a frequency table of the following scores obtained by 40 students in a
test:
24,16,17,30,28,20,15,24,16,18,18,15,16,20,25,24,25,20,16,15,18,25,20,18,28,27
,25,24,24,18,18,25,20,16,25,20,27,28,28,16.

This contains 20 points please help me quick

Answers

This isn’t with the tally counter since I don’t have paper atm

Score | Frequency
15. 3
16. 6
17. 1
18 6
20. 6
24. 4
25. 6
27. 2
28. 4
30. 1

Answer:

Element  Frequency Cumulative Frequency

15                   3              3

16                   6              9

17                   1              10

18                   6             16

20                   6            22

24                   5            27

25                   6            33

27                   2            35

28                   4            39

30                   1             40

Step-by-step explanation:

Find out how many times an element(data value) appears. That will be the frequency(column 2). The cumulative frequency is the total of all frequencies prior to that element plus the current element frequency

Cumulative frequency for first element is same as its frequency

Cumulative frequency for element 16 is 3 + 6 = 9

Cumulative frequency for element 17 = 3 + 6 + 1 = 9 + 1=10. Basically it is the sum of the previous element cumulative frequency + the current frequency

What is h?

NO LINKS!! I repeat NO LINKS!! Keep them to your self

What is h?NO LINKS!! I repeat NO LINKS!! Keep them to your self

Answers

Answer:

120°

Step-by-step explanation:

The total sum of the interior angles of a decagon is 1440°

Find the maximum and minimum values of the function g(θ) = 4 θ – 6 sin(θ) on the interval (0, phi) Minimum value = Maximum value =

Answers

To find the maximum and minimum values of the function g(θ) = 4θ - 6sin(θ) on the interval (0, φ), we need to analyze its critical points and endpoints.

First, let's find the critical points by setting the derivative equal to zero:
g'(θ) = 4 - 6cos(θ) = 0
=> cos(θ) = 4/6 = 2/3

Now we need to determine if θ exists in the given interval (0, φ) that satisfies cos(θ) = 2/3. If it does, we need to evaluate the function at this critical point and at the endpoints of the interval (0 and φ).

However, since we don't know the value of φ, we can't determine the exact values for the minimum and maximum. If you provide a specific value for φ, we can proceed with finding the maximum and minimum values for the function within the given interval.

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find the z value for 0.99 if e O¨zlem likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ?.
likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ
a) What is the table value of Z for 0.99? (Z0.99)? (b) What can we use for σ ? (sample size is large) (c) What is the value of? Zcσffiffin p (d) Determine the confidence interval level for μ.

Answers

a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

How to solve for the z critical value

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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The weights of adult women are approximately normally distributed about a mean of 142 lbs. with a standard
deviation of 14 lbs. If Renee is at the 96 percentile in weight for adult women, then her weight, in lbs. is closest
to

Answers

Answer:

166. 5

Step-by-step explanation:

Given the following :

Mean weight (m) = 142 lbs

Standard deviation (sd) = 14 lbs

Renne = 96 percentile, what is Renne's weight

Using the equation :

Zscore = (score - mean) / standard deviation

96 percentile = 0.96 is equivalent to a Zscore of

1.75

Hence,

1.75 = (score - 142) / 14

14 * 1.75 = score - 142

24.5 = score - 142

24.5 + 142 = score

Score = 166.5

say what an irrational number is. Give at least two examples.

Answers

Answer:

all square roots of natural numbers, other than of perfect squares, are irrational.

Step-by-step explanation:

like 3 or 71

Answer:

5.12369..... and square root of 15

Step-by-step explanation: the first number is a non terminating non repeating decimal and the square root of 15 is a non perfect square

In a kite ABCD, AB=CB , AD = CD, <B= 115 degree, <D=30 degree. Find <A = ?​

Answers

Answer:

The measure of ∠A = 107.5°

Step-by-step explanation:

Given that

ABCD is a kite such that

AB = BC and AD = DC

Join A and C

Since AB = BC

→ ∠BAC = ∠BCA

Since , the angles opposite to equal sides are equal.

Let ∠BAC = ∠BCA = x°

and

Since AD = DC

→ ∠CAD = ∠ACD

Since , the angles opposite to equal sides are equal.

Let ∠CAD = ∠ACD = y°

Now

In ∆ ADC ,

∠ADC + ∠CAD + ∠ACD = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 30° + y°+ y° = 180°

⇛ 30°+2y° = 180°

⇛ 2y° = 180°-30°

⇛ 2y° = 150°

⇛ y° = 150°/2

⇛ y° = 75°

Therefore, ∠CAD = ∠ACD = 75°

and

In ∆ ABC,

∠ ABC + ∠BAC + ∠BCA = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 115° + x° + x° = 180°

⇛ 115°+2x° = 180°

⇛ 2x° = 180°-115°

⇛ 2x° = 65°

⇛ x° = 65°/2

⇛ x° = 32.5°

Therefore, ∠BAC = ∠BCA = 32.5°

Now, ∠ A = ∠BAC + ∠CAD

⇛ ∠A = 32.5° + 75°

⇛ ∠A = 107.5°

Therefore, ∠A = 107.5°

Answer:-

) The measure of ∠ADC = 145°) The measure of ∠A = 107.5°

Read more:

Similar Questions

ABCD is a kite with AD=AB A= 116° B=2x° D=(5x-147)° Find the size of the smallest angle of the kite.

https://brainly.com/question/22571892?referrer

In a kite ABCD, AB=CB , AD = CD, &lt;B= 115 degree, &lt;D=30 degree. Find &lt;A = ?

Question 1
o
In A CDE, U is the centroid, UK = 12, EM = 21, and UD = 9. Find CU.
-
U 12
K
9
Next Question
M
Check Answer
2021 McGraw-Hill Ede

Answers

Answer:

is it this?I just searched

Question 1oIn A CDE, U is the centroid, UK = 12, EM = 21, and UD = 9. Find CU.-U 12K9Next QuestionMCheck

Solve p + 15 = 4.

Select the correct answer.


A:
p = 19

B:
p = 11

C:
p = -11

D:
p = -19

Answers

Answer:

C

Step-by-step explanation:

Given

p + 15 = 4 ( isolate p by subtracting 15 from both sides )

p = - 11 → C

Answer:

p -11 + 15 = 4

cause a negative × positive equals to positive

Can someone help (image below)

Can someone help (image below)

Answers

Answer: -2x^2+16x-30

Step--by-step explanation:

Alice's wholesale reported its sales in the year ended 30th June 2019as RM511,000. If her trade receivables on 30th June 2019 were RM63,000, calculate her receivable days. 45 days 30 days 25 days 60 days

Answers

To calculate the receivable days, divide the trade receivables (RM63,000) by the average daily sales (RM1,400) to get approximately 45 days.



To calculate the receivable days, we need to determine the average daily sales and then divide the trade receivables by that figure.

First, we calculate the average daily sales by dividing the total sales by the number of days in the year:

Average daily sales = Total sales / Number of days

Since the year ended on 30th June 2019, there are 365 days in total.

Average daily sales = RM511,000 / 365 = RM1,400

Next, we divide the trade receivables by the average daily sales to find the receivable days:

Receivable days = Trade receivables / Average daily sales

Receivable days = RM63,000 / RM1,400 ≈ 45 days

Therefore, Alice's receivable days on 30th June 2019 is approximately 45 days.

To learn more about average daily sales click here brainly.com/question/15711496

#SPJ11

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