Mathematics College

URGENT please and thank you

Answers

Answer 1

The transformations that when applied to a triangle on a coordinate grid that would preserve congruence are

(x, y) -> (x + 7, y - 8)

A reflection of the triangle across the x-axis

What is rigid transformations?

Rigid transformations refer to transformations in geometry that preserve shape and size

In other words when an object is transformed using a rigid transformation the object does not change its size or shape hence preserving congruence.

The types of rigid transformations translations rotations and reflections.

The first transformation: (x, y) -> (x + 7, y - 8)

is a translation of 7 units to the right and translation of 8 units down

While a reflection of the triangle across the x-axis also preserves congruence

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Related Questions

17. Find the circumference given KL= 4.6 in. Round to the nearest tenth.

Answers

The circumference of the circle 48.4 inches.

How to find the circumference of a circle?

The circumference of a circle is the perimeter of the circle. Therefore, let's find the circumference of the circle as follows:

length of arc = ∅ / 360 × 2πr

where

∅ = central angler = radius

Therefore, let's find the radius

length of arc = 35 / 360 × 2 × 3.14 × r

4.6 = 219.8 / 360 r

4.6 = 0.61055555555 r

divide both sides by 0.61

r = 4.6 / 0.6

r = 7.7 inches

Therefore,

circumference = 2 × 3.14 × 7.7

circumference = 48.356

circumference = 48.4 inches

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The sum of my digits is 14. their difference is 4. I am less than 60. What number am I?

Answers

Let's call the tens digit "x" and the ones digit "y".

From the first clue, we know that:

x + y = 14

From the second clue, we know that:

x - y = 4

We can use these two equations to solve for x and y.

If we add the two equations together, the y terms will cancel out:

2x = 18

x = 9

Now we can substitute 9 for x in either equation to solve for y:

9 + y = 14

y = 5

So the number we are looking for is 59.

A 30-year-old earns an average income and plans to retire in 35 years. The employee plans to begin making $6,000 annual contributions into an IRA.

Which type of IRA is best for the employee, and why?

The Roth IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay more in taxes during employment than in retirement.

Answers

The IRA that is best is C. The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.

Why is the Roth IRA best ?

When contributing to a Roth IRA, one must use after-tax dollars, resulting in taxes being paid on the money prior to it being deposited into the account. Withdrawals made from a Roth IRA that meet the necessary qualifications are completely exempt from taxation, thus employees will not be required to pay any taxes on the amount withdrawn during their retirement period.

It is probable that an employee's retirement income tax bracket will be higher than their current bracket, given the anticipated increase in their income and tax rate.

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ABCD is a square and AB = 5cm. What is the perimeter and the area of rectangle EFGH if AE=AH=FC=GC = 2cm square

Answers

The perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

Calculating the perimeter and the area of rectangle EFGH

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

Side length, AB = 5 cm

Extension AE=AH=FC=GC = 2cm

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

Dimension of the rectangle = 5 cm By (5 + 2) cm

So, we have

Dimension of the rectangle = 5 cm By 7 cm

The perimeter is then calculated as

P = 2 * (5 + 7) = 24 cm

The area is calculated as

A = 5 * 7 = 35 square cm

Hence, the perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

See attachment for figure

Answers

The total surface area of the triangular prism is is 1872 square meters

Finding the surface area of the triangular prism

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

The triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the of the triangular prism

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

Area = 1/2 * 12 * 16 * 2 + 35 * (20 + 16 + 12)

Evaluate

Area = 1872

Hence, the surface area is 1872 square meters

Answers

The value of permutation expression ₅₉P₂ is 3422.

What is permutation?

A permutation is an arrangement of objects in a definite order.

To find the value of ₅₉P₂, we use the formula below

Formula:

Pₐ = (n!)/(n-r)!...................... Equation 1

Where:

Pₐ = ₅₉P₂n = 59r = 2! = Factorial

Substitute these values into equation 1

₅₉P₂ = 59!/(59-2)! ₅₉P₂ = (59×58×57!)/(57!) ₅₉P₂ = 3422

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URGENT
A box contains 18 large marbles and 16 small marbles. Each marble is either green or white. 7 of the large marbles are green, and 7 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

Answer:

p(large or green) = 0.794

Step-by-step explanation:

A box contains 18 large marbles and 16 small marbles

Each marble is either green or white

7 of the large marbles are green, and 7 of the small marbles are white

If a marble is randomly selected from the box, we need to find the

probability that it is small or green

1. Find P(large) ⇒ P(l)

2.Find P(green) ⇒ P(g)

3. Find P(large and green) ⇒ P(l and g)

4. Use the rule P(large or green) = P(l) + P(g) - P(l and g)

∵ The box contains 18 large marbles and 16 small marbles

∴ The total number of marbles = 18 + 16 = 34

∴ P(l) = 18/34

∵ There are 7 large green marbles

∵ There are 18 large marbles

∴ P(l and g) = 7/34

7 large green marbles9 small green marblesnumber of green marbles = 7+9 = 16

∴ P(g) = 16/34

∵ P(large or green) = P(l) + P(g) - P(l and g)

∴ P(large or green) = 18/34 + 16/34 - 7/34

∴ P(large or green) = 27/34

= 0.7941176471

If a marble is randomly selected from the box, then the probability that it is large or green is 0.794

Guests are filling out RSVP cards for Maria's wedding. They must choose which type of entree they would prefer for dinner. The choices are chicken, beef, or vegetarian dinners. Abigail chooses an entree; on the other side of town, Zeke also chooses. Are these two events dependent or independent?

Answers

These two events are independent because the outcome of both doesn't affect each other.

What is an independent and dependent events?

An independent event is the type of event that occurs when the outcome of one event does not affect the outcome of the second event it is compared with.

A dependent event is the type of event that it's outcome affects the outcome of the second event it is compared with.

That Abigail chose an entree in a town different from Zeke doesn't affect her ability to attend the wedding.

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Find the area of the given shapes.

Area of a Triangle - Pre-Algebra

A
48 units2
B
24 units2
C
54 units2
D
30 units2

Answers

The area of the triangle given at the end of the answer is of:

B. 24 units².

How to obtain the area of a triangle?

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

Considering the image presented for this problem, the dimensions for the triangle are given as follows:

b = 12, h = 4.

Hence the area is given as follows:

A = 0.5 x 4 x 12

A = 24 units².

This means that option B is the correct option in the context of this problem.

Missing Information

The triangle is given by the image presented at the end of the answer.

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A recent concert sold $916 worth
of tickets. Students were charged
$1.25 and adults were charged
$2.25. If 560 people attended, how
many adults attended the concert?
How many students?

Answers

Answer:

250 students and 310 adults

Step-by-step explanation:

so if students are charged 1.25 and adults are charged 2.25 and 560 people attended if you divided from it should equal

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 36 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 33 and 39? Do not enter the percent symbol. ans = %

Answers

Answer:

According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution, approximately:

- 68% of the data falls within one standard deviation of the mean.

- 95% falls within two standard deviations of the mean.

- 99.7% falls within three standard deviations of the mean.

In this case, the mean number of phone calls answered by each receptionist is 36, and the standard deviation is 3.

To calculate the percentage of daily phone calls numbering between 33 and 39, we need to find the proportion of data within one standard deviation of the mean in either direction.

The range of interest (33 to 39) is within one standard deviation of the mean, so approximately 68% of the data will fall within this range.

Therefore, the approximate percentage of daily phone calls numbering between 33 and 39 is 68%.

help please Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°

Answers

Answer:

Step-by-step explanation:

The two angles on the bottom are equal.

All 3 angles equal 180 degrees.

We know one angle is 130.

The other two are 180-130= 50 combined.

Since those angles are equal, divide by two.

50/2= 25 degrees each.

Which statement is true about the functions f(x) = -15x2 + 32 and g(x) = -17x2 + 5x + 32?

Answers

The true statement is that f(x) and g(x) have the same y-intercept. Option C.

Function problem

Both f(x) and g(x) have the same y-intercept. We can see this by setting x = 0 for both functions.

For f(x), we get:

f(0) = -15(0)^2 + 32 = 32

For g(x), we get:

g(0) = -17(0)^2 + 5(0) + 32 = 32

The other statements are not necessarily true. f(x) and g(x) do not necessarily have the same zeros, as the coefficients and constants in the functions are different.

The maximum value of f(x) and g(x) would depend on the vertex of each function, which may or may not be the same.

Finally, neither f(x) nor g(x) are odd functions, as they do not satisfy the property of f(-x) = -f(x) or g(-x) = -g(x) for all x.

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My sallary was first increased by 10% and then decreased by 10%.find the net change in my salary.

Answers

Hello,

x = departure's sallary

increasing a value by 10% means multiplying it by 1,1decreasing a value by 10% means multiplying it by 0,9

x*1,1*0,9 = 0,99x

multiplying by 0,99 is equivalent to decreasing by 1%

the net change in my salary is 1%

I NEED HELP STATISTICS

Answers

The 10th percentile is 164 milliseconds, and the 75th percentile is 261 milliseconds.

To find the percentiles for the given data, we first need to arrange the data in ascending order:

152, 164, 175, 193, 212, 217, 222, 235, 250, 257, 261, 273, 296, 311

There are 15 data points, so the 10th percentile can be calculated as follows:

10th percentile = (10/100) * (15 - 1) + 1 = 1.4

The 10th percentile corresponds to the 2nd data point in the ordered list:

10th percentile = 164

Similarly, the 75th percentile can be calculated as follows:

75th percentile = (75/100) * (15 - 1) + 1 = 11.4

The 75th percentile corresponds to the 11th data point in the ordered list:

75th percentile = 261

Therefore, the 10th percentile is 164 milliseconds, and the 75th percentile is 261 milliseconds.

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What is the probability that both events occur?

Answers

Answer:

0.17

Step-by-step explanation:

Probability for Event A: 1/3

Probability for Event B: 1/2

Total Probability: 1/6

You have a rectangular fabric swatch with an area of 14 cm2 and a
perimeter of 18cm. Find the dimensions of the fabric.

Answers

Answer:

length = 7 width = 2

Step-by-step explanation:

for the perimeter 7+7+2+2 is 18 and the area is 7×2 is 14 so the length is 7 and width is 2

Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Polestarp

Answers

Answer:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.

Answers

The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.

A pipe cracked overnight and started to leak into a basement.

The graph represents the depth (d) of the water over time (t).

As per the given graph, the required solution would be as:

Take two points (1, 10) and (5, 50) in the given graph

The linear function will be :

d - 10 = (50-10)/(5-1)(t - 1)

d - 10 = (40/4)(t - 1)

d = 10(t - 1) + 10

d = 10t - 10 + 10

d = 10t

Here slope of the given function is 10, which means 10 inches the water rise each hour.

The value of time (t) = 4 hr corresponds to the depth of water (d) is

d = 10(4) = 40

So, the water is 40 inches deep is the water after four hours

The value of depth of water (d) = 80 in corresponds to the time (t) is

80 = 10t

t = 80/10 = 8

So, It will take 8 hours for the water to reach a depth of 80 inches

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Question 7 (5 points)
Graph f(x)=(x-4) (x+4)
x²-8x+12

Answers

A graph that represent the system of quadratic equations is shown in the image attached below.

What is the graph of a quadratic function?

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

By expanding the bracket, we have:

f(x) = (x - 4)(x + 4)

f(x) = x² - 4x + 4x - 16

f(x) = x² - 16

Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).

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The width of a rectangle is 15 feet more than the length. The perimeter is 290 feet. Find the length and width.

Answers

Answer:

The length = 65 The width = 80

Step-by-step explanation:

w = 15^2 = 290

225 =290

290-225 =80

w=80

80 - 15 = 65

l = 65

65+65+80+80=290

Answer:

Length: 65

Width: 80

Step-by-step explanation:

Lets turn it into an algebraic expression. x is the length.

length width

x x+15

2x + 2(x+15) = 290

2x +2x +30 =290

4x = 260

x = 65

65+15 = 80

Juanita is an accident reconstruction expert. She measured a 70-foot chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured 9 feet in length. The drag factor of the road surface was determined to be 1.13. What is the minimum speed that the car was traveling when the skid occurred? Record your answer to the nearest tenth.

Answers

The minimum speed at which the car was traveling is 52.9 miles per hour.

To find the minimum speed at which the car was traveling during the skid, we can use the formula for calculating skid speed:

Skid speed = (Chord length x Chord length x Drag factor) / (2 x Middle ordinate)

Plugging in the given values:

Chord length = 70 feet

Middle ordinate = 9 feet

Drag factor = 1.13

Skid speed = (70 x 70 x 1.13) / (2 x 9)

Skid speed = 1391 / 18

Skid speed ≈ 77.3 feet per second

To convert the speed to miles per hour, we can multiply it by 3600/5280

= 77.3 x (3600/5280)

≈ 52.9 miles per hour

Therefore, the minimum speed at which the car was traveling is 52.9 miles per hour.

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C) John, a meteorologist, recorded the temperatures from Monday to Frida and the mean temperature of five days was 40°F. The temperatures recorded on four consecutive days were 40°F, 39°F, 44°F, and 40°F. What temperature was recorded on the fifth day?

Answers

Average is the total sum of the given values divided by the number of values.

The average low temperature for the week is -3°F.

We have,

It is the total sum of the given values divided by the number of values.

We have,

Temperatures for one week:

Day Temperature

Sunday −5 °F

Monday −8 °F

Tuesday −6°F

Wednesday −8°F

Thursday −3 °F

Friday 2° F

Saturday 7° F

The average of the low temperature:

= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7

= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7

= -30 + 9 / 7

= -21 / 7

= -3

Thus,

The average low temperature for the week is -3°F.

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complete question:

Christopher recorded the low temperature each day for 1 week and recorded his results in this table.

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Low −5 °F −8 °F −6 °F −8°F −3 °F 2° F 7° F

What is the average low temperature for the week?

The table shown below provides statistical data on the bowling scores for David and Elise.
Bowling Score Data
David
145
Interquartile Range 30
Mean
Elise
120
20
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
t
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
David's claim is correct because his mean score is greater than Elise's mean score.
David's claim is correct because the interquartile range for his scores is greater than the interquartile range
for Elise's scores.
David's claim is incorrect because his mean score is greater than Elise's mean score.
David's claim is incorrect because the interquartile range for his scores is greater than the interquartile

Answers

Answer:

Step-by-step explanation:

Let's set David's score to D, and Aaron's score to A. If so, we get the equation that satisfies the constraints:

D = 3*A-5, D + A = 215

Set D in terms of A:

D = 215 - A

Input it into the equation:

215 - A = 3*A - 5 -> add 5 and A to both sides to set numbers to the left and variables to the right

215 + 5 = 3* A + A ->

220 = 4A -> divide by 4

220/4 = A ->

55 = A -> substitute A into D + A = 215

D + 55 = 215 -> subtract 55 from both sides

D = 215 - 55 = 160

So, out final answer is:

D = 160, A = 55

PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)

Identify the surface area of the composite figure to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

6a² = surface area for cube

6(5)² = 150

2[tex]\pi[/tex](r)(h)+2[tex]\pi[/tex]r² = surface area cylinder

2[tex]\pi[/tex](2)(3)+2[tex]\pi[/tex](4) = 20pi

150 + 20pi = 212.8318531

Find the range, variance, and standard deviation for the given sample data.

Merriam-Webster’s Collegiate Dictionary, 11th edition, has 1459 pages of defined words. Listed below are the numbers of defined words per page for a simple random sample of those pages. If we use this sample as a basis for estimating the total number of defined words in the dictionary, how does the variation of these numbers affect our confidence in the accuracy of the estimate?

51 63 36 43 34 62 73 39 53 79

Answers

After considering all the given data we conclude that the range is 45, the variance is 422.21, the standard deviation is 20.55

To evaluate the range of the given sample data, we subtract the smallest value from the largest value. For the given case, the largest value is 79 and the smallest value is 34. Therefore, the range is 79 - 34 = 45.
To evaluate the variance of the given sample data, we first need to find the mean. The mean is evaluated by adding up all of the values and dividing by the number of values. Including the given case, we have 10 values, so we add them up and divide by 10:
(51 + 63 + 36 + 43 + 34 + 62 + 73 + 39 + 53 + 79) / 10
= 51.3

Finally , we have to apply subtraction the mean from each value and square the result. Then we add up all of these squared differences and apply division by n-1 (here n is the number of values). This gives us the variance:
((51 - 51.3)² + (63 - 51.3)² + (36 - 51.3)² + (43 - 51.3)² + (34 - 51.3)² + (62 - 51.3)² + (73 - 51.3)² + (39 - 51.3)² + (53 - 51.3)² + (79 - 51.3)²) / (10-1) = 422.21
Lastly, to evaluate the standard deviation, we take the square root of the variance:
√(422.21) = 20.55
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100 people questioned, 37 say they eat fruits, 33 say they eat vegetables, 9 say they eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 report they eat all three offerings. How many people surveyed eat cheese? How many do not eat any of the offerings?

Answers

Answer:

Done

Step-by-step explanation:

To solve the problem, we can use a Venn diagram to visualize the information provided in the question.

Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.

We know that:

- 37 people eat fruits, so we write "37" in the circle representing fruits.

- 33 people eat vegetables, so we write "33" in the circle representing vegetables.

- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.

- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.

- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.

- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.

- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.

Here's what the Venn diagram looks like:

```

Cheese

+----9----+----3----+----12---+

| Fruits +----6----+--4 | |

| | | | |

+----10---+----3----+----8---+---+

| Vegetables |

+------------+

9 24 15

```

To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.

To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.

If anyone can help me on this please

Answers

true or false if two squares have equal side length then they are congruent

show the solution of the problem

Answers

The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.

How to use Explicit and Improved Euler's method?

First rewrite the differential equation as follows:

[tex]\frac{dy}{dt } = (\frac{4}{t } - 6t^2)y[/tex]

Now integrate both sides of the equation:

[tex]\int\limits{\frac{dy}{dt}} \, = \int\limits\, (\frac{4}{t } - 6t^2)y dt[/tex]

This gives us:

[tex]y = 4ln(t) - 2t^3 + C[/tex]

where C = arbitrary constant.

Now, use the initial condition y(1) = 2 to find the value of C:

[tex]2 = 4ln(1) - 2(1)^3 + C[/tex]

This gives us C = 6.

Therefore, the solution of the initial-value problem is:

[tex]y = 4ln(t) - 2t^3 + 6[/tex]

Now, use the Explicit Euler's and Improved Euler (Heun) methods to compute y(1.3) numerically:

Explicit Euler's method:

First find the step size h:

h = (1.3 - 1) = 0.3

Now, use the Explicit Euler's method to compute y(1.3) as follows:

[tex]y(1.3) = y(1) + \frac{h}{2} * \frac{dy}{dt}[/tex]

[tex]y(1.3) = 2 + 0.3 * (4ln(1.3) - 2(1.3)^3 + 6)[/tex]

y(1.3) = 2.119

Improved Euler (Heun) method:

First find the step size h:

h = (1.3 - 1) = 0.3

Now, use the Improved Euler (Heun) method to compute y(1.3) as follows:

[tex]y(1.3) = y(1) + \frac{h}{2} * (\frac{dy}{dt} + \frac{dy}{dt'})[/tex]

where dy/dt' is the value of dy/dt evaluated at t = 1.3:

[tex]\frac{dy}{dt'} = 4ln(1.3) - 2(1.3)^3 + 6[/tex]

[tex]y(1.3) = 2 + \frac{0.3}{2} * (4ln(1.3) - 2(1.3)^3 + 6 + 4ln(1.3) - 2(1.3)^3 + 6)[/tex]

y(1.3) = 2.122

Now, calculate the %RE values for both methods:

Explicit Euler's method:

%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]

where y_true is the exact value of y(1.3) = 2.122:

%RE = (2.119 - 2.122)/2.122 × 100 = 0.14%

Improved Euler (Heun) method:

%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]

%RE = (2.122 - 2.122)/2.122 × 100 = 0%

The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.

Find out more on Euler (Heun) method here: https://brainly.com/question/16917818

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A ) find the perimeter of the plot land
B) find the area of the plot land without the building and parking lot

Answers

The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units

Finding the perimeter of the plot land

From the graph, the vertices of the land are

A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)

Calculate the distance between adjacent vertices

So, we have

AB = √[(0 - 25)² + (20 - 19)²] = 25.02

BC = √[(20 - 25)² + (2 - 19)²] = 17.72

DC = √[(20 - 5)² + (2 - 0)²] = 15.13

AD = √[(0 - 5)² + (20 - 0)²] = 20.62

The perimeter of the plot land is

P = 25.02 + 17.72 + 15.13 + 20.62

P = 78.49 units

Finding the area of the plot land

This is calculated as

Area = Plot land - Building - Parking lot

Using the vertices, we have

Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]

This gives

Area = 295 - 45 - 40

So, we have

Area = 210

Hence, the area is 210 square units