The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
How to find the resistance of 1800ft of the same type of wire with a diameter of 0.45inchesLet R be the resistance of the wire,
L be the length of the wire,
d be the diameter of the wire, and
k be a constant of variation.
Then we have the equation:
R = k * L / d^2
Solving for k to find the resistance of a wire of varying length and diameter.
We can create an equation using the information provided:
15611 = k * 700 / 0.2^2
Solving for k, we get:
k = 15611 * 0.2^2 / 700
k ≈ 0.1799
Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:
15037.45 ohms = 0.1799 * 1800 / 0.452 R
As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Constantin has a small sunflower farm. One day, he measures and
records the height of each sunflower on his farm. The information is
given below in centimetres:
301, 285, 20, 351, 35, 205, 311, 25, 45, 310, 301, 305
Find the mean height of sunflowers on Constantin’s farm. Round your
answer to two decimal places
The mean height of sunflowers on Constantin's farm is 210.33 centimetres, rounded to two decimal places.
To find the mean height of sunflowers on Constantin's farm, we need to sum up all the heights and divide by the total number of sunflowers.
Adding up all the heights, we get:
301 + 285 + 20 + 351 + 35 + 205 + 311 + 25 + 45 + 310 + 301 + 305 = 2524
There are 12 sunflowers in total, so we divide the sum by 12:
2524 / 12 = 210.33
This means that if we were to select a sunflower at random from Constantin's farm, on average, we would expect it to be about 210.33 centimetres tall.
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Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (x−5)(50−2x)
to represent her profit based on the price per scarf, x
.
Enter Sofie's average change in profit for two different sections of the graph.
A graph has price per scarf (dollars) on the x-axis, and profit (dollars) on the y-axis. A parabola with equation f (x) = (x minus 5) (50 minus 2 x) opens down and goes through (5, 0), has vertex (15, 200), and goes through (25, 0).
CLEAR CHECK
What is Sofie's average change in profit from x=5
to x=15
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
What is Sofie's average change in profit from x=15
to x=25
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
Answer explication question
The solution is:
The equations are;
4(2x + 5) = 3(2x + 8)
x = 2
Perimeter of each shape is 36
Here, we have,
Mathematically;
The perimeter of a square is 4L
while the perimeter of an equilateral triangle is 3L
where L represents the lengths of the sides
Mathematically, from what we have in the question, since the perimeter are equal;
4(2x + 5) = 3(2x + 8)
8x + 20 = 6x + 24
8x-6x = 24-20
2x = 4
x = 4/2
x = 2
The side of the square will measure;
2(2) + 5 = 9
Its perimeter is 4(9) = 36
The side of the triangle will measure
2(2) + 8 = 12
Its perimeter will be 3(12) = 36
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Please answer this as quick as possible, wrong answers or chatgpt will be reported:
Q3. A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a 4 m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the
ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) [2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
For Matthew, the height is given as [tex]52 + 8 sin (\pi/6t)[/tex]
What is a Sine Function?To express the characteristic repetition of certain actions or events, a sine function is often employed.
This mathematical function links a position on the edge of a unit circle with the height of its corresponding y-coordinates. Conveyed generally as sin(x), it represents angle measurement in radians.
This repeatable pattern attains values between -1 to 1 and reappears once per every 2π radians. There are numerous applications of this type of sinusoidal oscillation pattern, including signal processing, engineering, and physics among others.
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PLEASE HELP I DO NOT UNDERSTAND!
A high school baseball player has a 0.197 batting average. In one game, he gets 8 at bats. What is the probability he will get at least 2 hits in the game?
The probability of the high school baseball player getting at least 2 hits in a game with 8 at bats, given his 0.197 batting average, is approximately 0.378.
To calculate the probability of the player getting exactly 2 hits in the game, we can use the binomial probability formula:
P(X = x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ
Where:
P(X = x) is the probability of getting exactly k hits
n is the number of trials (in this case, 8 at bats)
k is the number of successful trials (in this case, 2 hits)
p is the probability of a successful trial (in this case, 0.197)
Using this formula, we can calculate the probability of the player getting exactly 2 hits in the game:
P(X = 2) = (8 choose 2) x 0.197² x (1-0.197)⁸⁻² = 0.214
So the probability of the player getting exactly 2 hits in the game is 0.214.
To calculate the probability of the player getting at least 2 hits in the game, we need to add up the probabilities of getting exactly 2 hits, exactly 3 hits, exactly 4 hits, and so on, up to 8 hits. This can be a bit cumbersome to do by hand, but fortunately, there are tools available to help us with this.
Using a binomial probability calculator or a statistical software program, we can find that the probability of the player getting at least 2 hits in the game is approximately 0.378.
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The maximum grade allowed between two stations in a rapid transit rail system is 2.6% between station and station B, which are 260 feet apart. The tracks rise 5 feet. What is the grade of the track between the stations round answer to the nearest 10th.
The grade of the track between the stations is approximately 1.9%.
How to calculate the grade of the track between the stations round answer to the nearest 10th.The grade of the track is given as a percentage by the change in elevation (climb) divided by the horizontal distance (run) between the two stations:
(climb / run) x 100% = grade
We are given a 5 foot ascent and a 260 foot horizontal distance (run). When we enter these values into the formula, we get:
1.92% = (5/260) x 100% = grade
Rounding to the nearest tenth, the grade of the track between the stations is approximately 1.9%.
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A local wine equipment manufacturer is planning to issue stocks. The company just paid a dividend of $3.60. They now expect to pay dividends to grow at 15% for the next 3 years and thereafter grow at an annual rate of 8%. What should be the price of the stock given these revised forecasts? Assume a rate of return of 16%
a.How does a cumulative voting system allow minority representation in corporations?
Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.
To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.
For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:
Year 1: $3.60 x 1.15 = $4.14
Year 2: $4.14 x 1.15 = $4.76
Year 3: $4.76 x 1.15 = $5.47
The Gordon growth model is as follows:
P = D / (r - g)
where:
P = price of the stock
D = expected dividend payment
r = rate of return required by investors
g = expected dividend growth rate
Using the formula, we can calculate the price of the stock as follows:
Year 1: P = $4.14 / (0.16 - 0.15) = $414
Year 2: P = $4.76 / (0.16 - 0.15) = $476
Year 3: P = $5.47 / (0.16 - 0.15) = $547
After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.
Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24
Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53
Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49
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Which addition equation can you make a 10 to add choose 2 that apply
13+15=
49+28=
20+47=
45+35=
We can add 13 and 15, or 49 and 28, or 20 and 47, or 45 and 35 to make 10 in the equations
To add choose 2 numbers to make 10, we can use the fact that 10 is the sum of 6 and 4.
Therefore, we can add a number that is 6 more than 10 and another number that is 4 less than 10.
This gives us the following equations:
13 + 15 = 28, since 13 + 15 = 28 and 10 = 6 + 4
49 + 28 = 77, since 49 + 28 = 77 and 10 = 6 + 4
20 + 47 = 67, since 20 + 47 = 67 and 10 = 6 + 4
45 + 35 = 80, since 45 + 35 = 80 and 10 = 6 + 4
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Please answer the question
please and thank you for helping
I have to divide
to find the area of each wing to founds the total area In square inches
And to find the wing area in square meters inches
The area of each wing to founds the total area as; 26000 square inches
We need to find the area of each wing to founds the total area In square inches
The dimensions are;
Length = 100 + 100 = 200 unit
Width = 70 + 70 = 130
Now the area of the wing
= Length x width
= 200 x 130
= 26000
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What is the surface area of this triangular pyramid?
5 yd
5 yd
4.3 yd
7 yd
5 yd
square yards
The surface area of the triangular prism that is shown above is calculated as: 63.25 square yards. .
What is the surface area of a triangular pyramid?The surface area of a triangular pyramid is calculated using the formula below:
SA = A + 3a
where we have:
A = the area of the triangular base of the pyramid
a = the area of one of the pyramid's faces.
Area of one of the pyramid's face (a) = 1/2 * base * height = 1/2 * 5 * 7
a = 17.5 square yards
Area of triangular base (A) = 1/2 * base * height = 1/2 * 5 * 4.3
A = 10.75 square yards
Surface area (SA) = 10.75 + 3(17.5) = 63.25 square yards.
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What are the domain and range of the inequality? Refer to photo
The domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.
Given is a function, y ≤ √(x-1) -4, we need to find the domain and the range,
Domain = all the input values.
Range = all the output values.
So, the function is =
y ≤ √(x-1) -4
The related function can be written as =
y = √(x-1) -4
The function is defined if =
√(x-1) ≥ 0
∴ (x-1) ≥ 0
x ≥ 1,
In the given inequality, the sign of inequality is ≥, it means the points on the boundary line are included in the solution set. Thus, 1 is included in the domain.
So, the domain of the given inequality is x ≥ 1.
Now,
√(x-1) ≥ 0
√(x-1) -4 ≥ 0 - 4
y ≥ -4
The points on the boundary line are included in the solution set. Thus, -4 is included in the range.
So, the range of the given inequality is y ≥ -4.
Hence, the domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.
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The diameter of a cylindrical construction pipe is 15 ft . If the pipe is 26 ft long, what is its volume?
Answer:
390
Step-by-step explanation:
−3a+6b=a+4b, what does A =
Answer:
a= b/2
Step-by-step explanation:
it is in internet
A suitcase weighs 12 kg to the nearest kilogram. Another suitcase weighs 17 kg to the nearest kilogram. Work out the smallest amount, in kilograms (kg), that the two suitcases could weigh in total.
Answer:
28 KG
Step-by-step explanation:
To find the smallest possible weight, we need to consider the possible range of weights for each suitcase based on the rounding.
The 12 kg suitcase could actually weigh anywhere from 11.5 kg to 12.4 kg (since rounding to the nearest kg means it could be as low as 11.5 kg or as high as 12.4 kg, with 12 kg being the nearest whole number).
The 17 kg suitcase could actually weigh anywhere from 16.5 kg to 17.4 kg.
To get the smallest possible total weight, we want to add the lowest weights of each suitcase:
11.5 kg + 16.5 kg = 28 kg
Therefore, the smallest possible amount that the two suitcases could weigh in total is 28 kg.
4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f
The representation of 4.67 on the number line upto 4-decimal places. can be given in image. A picture of numerals along a straight line is called a number line.
A picture of numerals along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Just to refresh your memory, the entirety of a number is a collection of numbers that contains both zero (0) and all the numbers that count (1, 2, 3,4,5,6), while the number that is natural is a collection of all counting values (1, 2, 3,4, 5, 6). The representation of 4.67 on the number line upto 4-decimal places. can be given in below image.
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Your question is incomplete but most probably your full question was,
Visualise the representation of 4.67 on the number line upto 4-decimal places.
V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?
The correct statement is B. After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the function, V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail.
Therefore, the statement V(2)=T means that after Erica had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
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The complete question is:
Erica walked down a trail into a valley. V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail. What does the statement V(2)=T mean?
A-Erica's vertical distance from the top of the valley was the same after she had walked 2km and after she had walked T kilometres.
B- After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
C- After she had walked T kilometres along the trail, Erica's vertical distance from the top of the valley was equal to 2km.
Which expression is equivalent to 7m+5.5(2+m)
?
Pour développer il faut appliquer la distributivité de la multiplication :
7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m
= 7m + 11 + 5.5m
Il faut combiner les termes contenant m :
= 7m + 5.5m + 11
= (7 + 5.5)m + 11
= 12.5m + 11
what is the surface area of the cylinder
help me teacher does teach us this and it’s on my test
[tex]surface \: area = 2\pi {r}^{2} + 2\pi \: rh \\ 2\pi {(6)}^{2} + 2\pi(6)(15) \\ = 2\pi(36) + 2\pi(90) \\ = 72\pi + 180\pi \\ = 252\pi {in}^{2} [/tex]
create a scatterplot for the data in the table. based on the appearance of the scatterplot, which model does the data appear to follow?
a. the data appears to follow a linear model
b. the data appears to follow a quadratic model
c. the data appears to follow a cubic model
d. the data appears to follow an exponential model
Answer:
C. The data appear to follow a cubic model.
Step-by-step explanation:
Plot the points on the graphing calculator, and then generate the best regression model.
For the linear equation, r = -.0529
For the quadratic equation, R^2 = .8992
For the cubic equation, R^2 = .9678
For the exponential equation, r = -.0814
A cubic regression equation would best fit this data. So the correct answer is C.
x/9=7/15 answer plss
Answer: To solve for x in the equation x/9 = 7/15, we can cross-multiply to get:
15x = 9 * 7
Simplifying the right side, we get:
15x = 63
To solve for x, we can divide both sides by 15:
x = 63/15
Simplifying the fraction on the right side, we get:
x = 4 3/5 or x = 4.2 (rounded to one decimal place)
Therefore, the solution to the equation x/9 = 7/15 is x = 4.2 or x = 4 3/5.
Step-by-step explanation: kinda easy ngl lol but hope this helps :D
What is the height of the cylinder?
Answer: 6.996
Step-by-step explanation:
As given in the problem, V = πr²h
We are given V and r, so all we must do is plug them in and solve for h
[tex]351.68=\pi (4)^2h\\351.68=\pi 16h\\h=6.996[/tex]
If John solved the equation x² - 10x +8=0 by completing the square, one of the steps in his process would
be:
(z-5)² = 17
(z+4)² =10z+16
(z+4)² =10z
(2-5)² = -8
If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
x² - 10x + 8 = 0
x² - 10x = -8
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = 8 + (-10/2)²
x² - 10x + 25 = -8 + 25
x² - 10x + 25 = 17
By simplifying, we have;
(x - 5)² = 17
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In casino games the player roll a pair of dice . If the first throw is a 7or 11 the player wins automatically what is the probability that theplayer will win on the first throw
The probability of winning on the first roll is 0.22
Solution-
As in the game of casino, two dice are rolled simultaneously.
So the sample space would be,
|S| = 36
Let E be the event such that the sum of two numbers are 7, so
E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
|E| = 6
P(E) = 6/36
Let F be the event such that the sum of two numbers are 11, so
F = {(6,5), (5,6)}
|F| = 2
P(F) = 2/36
Now,
P(E∪F)= 0.22
The probability of winning on the first roll is 0.22
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Please answer the question
The correct statement about the product of 5/12 and 7 is given as follows:
C. The product is greater than 5/12 but less than 7.
How to calculate the product?The multiplication operation for this problem is given as follows:
5/12 x 7.
The factors of the operation are given as follows:
5/12 and 7.
When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:
5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.
35/12 is a number close to 3, which is:
Greater than 5/12.Less than 7.Hence option C is the correct statement.
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Michelle works for 33 hours this
week. She earns $10 per hour.
Her pay after taxes is $277.11.
How much does she pay in
payroll tax?
This week, Michelle works 33 hours. She is paid $10 per hour. Her take-home pay is $277.11 after taxes. She pays $ 52.89 in payroll tax.
We know that Michelle works for 33 hours this week and her pay for one hour is $10. So, firstly we will calculate her total pay for this week.
Total pay for week = pay for one hour × hours worked
= 10 × 33
= $ 330
Now, after taxes her pay is $277.11. So,
Tax = Pay before tax - pay after tax
= 330 - 277.11
= $ 52.89
A payroll tax is a tax paid by both employees and employers on wages, tips, and salaries. Employers withhold taxes from employees' paychecks and pay them to the government.
Federal, state, and municipal income taxes, as well as the employee's contribution of Social Security and Medicare taxes (FICA), are all included.
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work out the lengths of sides a and b give your answer to 1dp
The lengths of sides a and b are given as follows:
a = 14.3. b = 24.What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:
m < B + 81 + 33 = 180
m < B = 180 - 114
m < B = 66º.
Then the relation is:
26/sin(81º) = a/sin(33º) = b/sin(66º).
Then the value of a is obtained as follows:
26/sin(81º) = a/sin(33º)
a = 26 x sine of 33 degrees/sine of 81 degrees
a = 14.3.
The value of b is obtained as follows:
26/sin(81º) = b/sin(66º)
b = 26 x sine of 66 degrees/sine of 81 degrees
b = 24.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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3^17 mod 25. Can anyone tell me how they got 6?
17 in binary is 10001.
How to Convert 17 in Binary?
Step 1: Divide 17 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 17.
Therefore, the binary equivalent of decimal number 17 is 10001.
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Please answer this Calculus webwork question about differential equations:
The area of the enclosed region is 16√2 - 8 squared units
We have,
The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.
First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.
Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:
A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx
Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:
A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx
= ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx (since sin(x + π/2) = sin(x))
= 8 ∫[0, π/4] sin(x) dx
= 8 [-cos(x)] [0, π/4]
= 8 (1 - 1/√2)
= 8√2 - 8
Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:
A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx
Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:
A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx
= ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx (since cos(x - π/2) = sin(x))
= 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx
= 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]
= 4 (2/√2 + 2) - 4 (1 - 1/√2)
= 8√2
So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:
A = A1 + A2
A = 8√2 - 8 + 8√2
A = 16√2 - 8 squared units
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