The t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46
How to calculate the valueUsing Critical value calculator we calculate the values.
a) at n = 10
Therefore degrees of freedom is = n - 1= 9, So therefore at 9 degrees of freedom and 0.01 level of significance, t critical value is 2.82
b) at n= 20
Degrees of freedom is 19.
The t critical value at 19 degrees of freedom and 0.01 level of significance is 2.54
c) at n = 30
Degrees of freedom is 29.
So therefore t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46
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An angle measures 11.4° more than the measure of its complementary angle. What is the measure of each angle?
The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.
What is the measure of each angle?Let x be the measure of the angle and y be the measure of its complementary angle.
Then we have:
x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)
x + y = 90 (since the two angles are complementary)
Substituting the first equation into the second equation, we get:
(y + 11.4) + y = 90
2y + 11.4 = 90
2y = 78.6
y = 39.3
Substituting y = 39.3 into the first equation, we get:
x = y + 11.4 = 50.7
So, we have
x = 50.7
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Scott has a rectangular garage that has a length of 234 inches. The width is 1. 5 times shorter than the length. What is the area of his garage?
The area of garage is 36,504 square inches.
The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).
so width = 234/1.5
=> 156
To find the area, we multiply the length by the width:
=> 234 inches x 156 inches
=> 36,504 square inches.
To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.
To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.
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The value of car depreciates by 15% every year. if its present value is rs.80000 what is its value after 3 years.
A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.
A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.
To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Identify the longest side. In this case, it's the side with length 7 cm.
Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²
Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²
Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²
Compare the results:
49 cm² = 49 cm²
Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.
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Qn2. Two functions f and g are defined as follows: f(x) = 2x – 1 and g(x) = x +4. Determine: i) fg(x) ii) value of x such that fg(x) = 20
The value of x such that fg(x) = 20 is 6.5.
Find the value of f(x)g(x) by substituting g(x) into f(x):f(x)g(x) = f(x)(x+4) = 2x(x+4) - 1(x+4) = 2x^2 + 8x - 4To find the composite function fg(x), we need to substitute the expression for g(x) into f(x), as follows:
fg(x) = f(g(x)) = f(x + 4) = 2(x + 4) - 1 = 2x + 7
So, fg(x) = 2x + 7
ii) To find the value of x such that fg(x) = 20, we can substitute fg(x) into the equation and solve for x, as follows:
fg(x) = 2x + 7 = 20
2x = 13
x = 6.5
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Solve: 5x + 6 > 3x + 15
Answer:
Subtract the smaller amount of [tex]x[/tex] → [tex]2x+6 > 15[/tex]
Then subtract 6 from 15 as it is a plus you do the opposite → [tex]2x > 9[/tex]
Now divide 9 by 2 to isolate [tex]x[/tex] → [tex]x > 4.5[/tex]
Please help... 100 points promised!
Answer:
Step-by-step explanation:
The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:
There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.
After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.
To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:
(26/52) * (25/51) = 0.245 or approximately 24.5%
Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.
A table titled inequality symbols contains the symbols for less-than and greater-than.
Check all that are inequalities.
-3 = y
t > 0
-4. 3 < a
g = 5 and one-half
k less-than Negative Start Fraction 5 Over 7 End Fraction
x = 1
The inequalities in the given table are "t > 0" and "3 < a."
To identify the inequalities from the provided options, we need to understand the meaning of the symbols and check if they represent a comparison between two values.
-3 = y: This is not an inequality symbol but rather an equality symbol. It represents that -3 is equal to y, not greater or less than.
t > 0: This is an inequality symbol. The symbol ">" represents "greater than." Therefore, t is greater than 0.
-4. 3 < a: This is another inequality symbol. The symbol "<" represents "less than." Hence, 3 is less than a.
g = 5 and one-half: This is an equality symbol. The symbol "=" denotes equality, indicating that g is equal to 5 and one-half, not greater or less than.
k less-than Negative Start Fraction 5 Over 7 End Fraction: This is also an inequality symbol. The phrase "less than" indicates a comparison. The fraction "Negative Start Fraction 5 Over 7 End Fraction" represents -5/7. Therefore, k is less than -5/7.
x = 1: This is an equality symbol. The symbol "=" indicates that x is equal to 1, not greater or less than.
In summary, the inequalities in the table are "t > 0" and "3 < a."
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Una carretera recta forma un angulo de 22° con la horizontal dde cierto punto Q en ella el angulo de elevacion del avion en el punto A 57 en el mismo instante dde otro punto Q a 100 m adelante del primero el angulo de elevacion 63 los puntos P Q A quedan en el plano vertical calcule la distancia de P al avion
The distance from P to the airplane is y = x + 100 ≈ 628.38 m.
What is the triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
From a certain point Q on a straight road, which forms an angle of 22° with the horizontal, the angle of elevation of an airplane at point A is 57°. At the same instant from another point Q, 100 meters ahead of the first point, the angle of elevation of the airplane is 63°. The points P, Q, and A are in the same vertical plane. Find the distance from P to the airplane.
To solve the problem, we can use the concept of similar triangles. Let's call H the height of the airplane and x the distance from Q to the airplane. Then, the distance from P to the airplane is given by y = x + 100.
From triangle QA1H, we have:
tan(57°) = H / x
From triangle QA2H, we have:
tan(63°) = H / (x + 100)
Dividing these two equations, we get:
tan(57°) / tan(63°) = x / (x + 100)
Solving for x, we get:
x = 100 * tan(63°) / (tan(63°) - tan(57°)) ≈ 528.38 m
Therefore, the distance from P to the airplane is:
y = x + 100 ≈ 628.38 m.
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WILL GIVE BRAINLIEST!!!
A team of scientists is studying the animals at a nature reserve. They capture the animals, mark them so they can identify each animal, and then release them back into the park. The table gives the number of animals they’ve identified. Use this information to complete the two tasks that follow.
Animal Total in Park Number Marked
elk 5,625 225
wolf 928 232
cougar 865 173
bear 1,940 679
mountain goat 328 164
deer 350 105
moose 215 86
What is the probability of the next elk caught in the park being unmarked? Write the probability as a fraction, a decimal number, and a percentage
The probability of the next elk caught in the park being unmarked can be calculated as follows:
There are a total of 5,625 elks in the park, out of which 225 have been marked.This means that the number of unmarked elks is 5,625 - 225 = 5,400.Therefore, the probability of the next elk caught in the park being unmarked is 5,400/5,625 = 0.96 or 96%.What is the probability of capturing an unmarked elk at the park?The probability of capturing an unmarked elk in a nature reserve park can be calculated by dividing the number of unmarked elks by the total number of elks.
In this case, the number of unmarked elks is 5,400 out of a total of 5,625 elks. This gives a probability of 96% or 0.96 in decimal form. Marking and tracking animals is a common method used by scientists to study animal populations in nature reserves.
This data is crucial for designing conservation strategies that promote the survival of endangered species. Nature reserves play a crucial role in preserving and protecting wildlife and their habitats, given the significant threats they face from habitat loss, poaching, and climate change.
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If a ball is dropped on the ground from a height of h m, then the ball reaches the ground with the
velocity V=4.43√h m/sec. Find the velocity with which a ball reaches the ground when it is dropped
from a height of 64 m.
The velocity with which a ball reaches the ground when it is dropped
from a height of 64 m is 35.44m/sec
How to determine the valueFrom the information given, we have that the equation representing the velocity of the ball is expressed as;
V = 4.43√h
Given that the parameters of the formula are;
V is the velocity of the ball from he ground.h is the height of the ball.Since the height of the ball from the ground is 64m, we have to substitute the value, we have;
V = 4.43√64
Find the square root of the value
V= 4.43(8)
Now, multiply both the values to determine the velocity, we get;
V = 35.44m/sec
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If a, b and c are distinct real numbers, prove that the equation(x−a)(x−b)+(x−b)(x−c)+(x−c)(x−a=0has real and distinct roots.
Answer:
Step-by-step explanation:
skating Dinero broke 1p revision yahoo d10
If a photo measures 4 inches by 6 inches is places in a frame that measure 2 inches wide all around what percent of the fear is the photo itsel
The photo takes up 30% of the framed area.
To calculate the percentage of the frame that is taken up by the photo, we first need to calculate the dimensions of the framed photo. If the photo measures 4 inches by 6 inches, the dimensions of the framed photo will be 8 inches by 10 inches (adding 2 inches to each side).
To calculate the area of the frame, we need to subtract the area of the photo from the area of the framed photo. The area of the photo is 4 inches x 6 inches = 24 square inches. The area of the framed photo is 8 inches x 10 inches = 80 square inches. So, the area of the frame is 80 square inches - 24 square inches = 56 square inches.
To calculate the percentage of the frame that is taken up by the photo, we divide the area of the photo by the area of the framed photo and multiply by 100.
24 square inches / 80 square inches x 100 = 30%
Therefore, the photo takes up 30% of the framed area.
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In right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (s)
In right triangle RST, the value of tan (s) is 12/5.
To find tan(s), we first need to determine which side is opposite angle S and which side is adjacent to angle S.
In this case, RT is the side opposite angle S, and ST is the side adjacent to angle S. Since tangent (x) or tan(x) is defined as the ratio of the length of the opposite side to the length of the adjacent side, we can write the formula for tan(s) as follows:
tan(s) = (opposite side) / (adjacent side)
Now we can plug in the given side lengths to calculate the value of tan(s):
tan(s) = RT / ST
tan(s) = 12 / 5
Thus, tan(s) = 12 / 5.
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What is the solution for 11\31×38\33
Answer:
38/93
Step-by-step explanation:
11/31 x 38/33
11 x 38 = 418
31 x 33 = 1023
= 418/1023
Simplifying
The simplified form of 418/1023 is 38/93.
38/93 is your final answer.
Find the measure of each arc of ⊙ p, where rt is a diameter.
When rt is a diameter of circle p, it divides the circle into two equal halves. Since the sum of angles in a circle is 360 degrees, each half of circle p measures 180 degrees.
Thus, each arc of circle p that is intersected by diameter rt measures half of the circle or 90 degrees.
Therefore, each arc of circle p measures 90 degrees when rt is a diameter.
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Aimie is looking for a golf ball that he hit into the air towards a fence surrounding the golf course. The fence has a height of 2 yards and is located at a distance of 120 yards from where Jaimie hit the ball. Jaimie wants to determine if his golf ball landed inside or outside of the fence.
The golf ball's height, h, in yards with respect to time, t, in seconds, can be modeled by the quadratic function h=−0. 6t2+3t. Jaimie's golf ball reached its maximum height at the fence.
What is the maximum height, in yards, the golf ball reached before landing back on the ground?
_____yards
The maximum height the golf ball reached before landing back on the ground is 3.75 yards.
To find the maximum height the golf ball reached before landing back on the ground, we need to find the vertex of the quadratic function[tex]h(t) = -0.6t^2 + 3t.[/tex] The vertex of a quadratic function in the form of[tex]f(x) = ax^2 + bx + c[/tex] is given by the formula x = -b/(2a).
In this case, a = -0.6 and b = 3. Plugging these values into the formula:
t = -3 / (2 * -0.6) = 3 / 1.2 = 2.5
Now that we have the time at which the ball reaches its maximum height, we can plug this value back into the height function to find the maximum height:
[tex]h(2.5) = -0.6(2.5)^2 + 3(2.5) = -0.6(6.25) + 7.5 = -3.75 + 7.5 = 3.75[/tex]
So, the maximum height the golf ball reached before landing back on the ground is 3.75 yards.
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Help me please I need the answer to the value of x
celine ordered a set of beads. she received 10,000 beads in all, 9,100 of the beads were brown. what percentage of the beads were brown?
Answer:
91%
Step-by-step explanation:
the asq (american society for quality) regularly conducts a salary survey of its membership, primarily quality management professionals. based on the most recently published mean and standard deviation, a quality control specialist calculated the z-score associated with his own salary and found it was -2.50. this tells him that his salary is
This tells him that his salary is significantly below the average salary of quality management professionals surveyed by the ASQ, and that he is in the bottom percentile of salaries in this group.
The z-score is a statistical measure that indicates the number of standard deviations that a data point is from the mean of a distribution. A negative z-score indicates that the data point is below the mean.
In this case, the quality control specialist's z-score of -2.50 indicates that his salary is 2.50 standard deviations below the mean salary of the quality management professionals surveyed by the ASQ.
Without knowing the specific mean and standard deviation provided by the survey, it is difficult to determine the exact value of the specialist's salary. However, we can use the z-score to estimate the percentile rank of his salary compared to the rest of the survey respondents.
Using a standard normal distribution table, we can see that a z-score of -2.50 corresponds to a percentile rank of approximately 0.0062 or 0.62%. This means that only about 0.62% of quality management professionals surveyed by the ASQ earn a salary lower than that of the quality control specialist.
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Ralph has a cylindrical container of parmesan cheese. The diameter of the base of the container is 2. 75 inches, and the height is 6 inches. What is the area of a horizontal cross section of the cylinder to the nearest tenth of a square inch? Use 3. 14 for π
The area of a horizontal cross-section of the cylinder whose diameter is 2.75 inches and height is 6 inches is 5.9 inch².
Diameter of the base of the container = 2.75 inch
Height of the cylinder = 6 inch
Area of a horizontal cross-section of the cylinder = πr²
Here, r = radius of the container
Radius = Diameter/2
Radius = 2.75/2
Radius = 1.375
Area of the horizontal cross-section of the cylinder = 3.14 × 1.375 × 1.375
Area = 5.9365625
Area of the horizontal cross- section of the cylinder to the nearest tenth is 5.9
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PLEASE HELP ASAP 3 PART QUESTION
Answer:
that is really hard but im pretty sure one of the answers to the first one is -16? for the second x
Step-by-step explanation:
A punch recipe calls for 1 1/2
quarts of sparkling water and
3/4 of a quart of grape juice.How much grape juice would you need to mix with
3 3/4 quarts of sparkling water?
Therefore, we need 3/4 of a quart of grape juice to mix with 3 3/4 quarts of sparkling water.
What is fraction?In mathematics, a fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator and a denominator, separated by a horizontal or diagonal line. The numerator is the number above the line and the denominator is the number below the line. The numerator and denominator can be any real numbers, including integers, decimals, or even other fractions.
Here,
The punch recipe requires a ratio of 1 1/2 quarts of sparkling water to 3/4 of a quart of grape juice. To determine how much grape juice is needed to mix with 3 3/4 quarts of sparkling water, we can set up a proportion:
1 1/2 quarts of sparkling water : 3/4 quart of grape juice = 3 3/4 quarts of sparkling water : x
To solve for x, we can cross-multiply and simplify:
(1 1/2) / (3/4) = (15/4) / (3/4)
= 15/3
= 5
3 3/4 * 1 / 5 = 15/20
= 3/4
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What is the sum of the series?
Σ (2k2 – 4)
k=1
The sum of the series Σ (2k² - 4) from k = 1 to n can be found using the following formula:
Σ (2k² - 4) = [2(1²) - 4] + [2(2²) - 4] + [2(3²) - 4] + ... + [2(n²) - 4]
= 2(1² + 2² + 3² + ... + n²) - 4n
The sum of squares of the first n natural numbers can be calculated using the formula:
1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6
Substituting this value in the above equation, we get:
Σ (2k² - 4) = 2[(n(n + 1)(2n + 1)) / 6] - 4n
= (n(n + 1)(2n + 1)) / 3 - 4n
Therefore, the sum of the series Σ (2k² - 4) from k = 1 to n is (n(n + 1)(2n + 1)) / 3 - 4n.
Manuel types at a rate of 34 words per minute. How many words does he type in 2 minutes?
Manuel can type 68 words in two minutes at a rate of 34 words per minute.
What is the number of words typed in the given time?Given that; Manuel types at a rate of 34 words per minute.
To determine how many words Manuel can type in two minutes, we simply need to multiply his typing rate by the number of minutes he is typing.
Since Manuel is typing for two minutes
Hence;
Number of words = Typing rate × Time
Plugging in the values we have from the problem.
Number of words = 34 words/minute × 2 minutes
Simplifying
Number of words = 34 words × 2
Number of words = 68 words
Therefore, he can type 68 words in two minutes.
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A two digit number is 11 times its units digit. The sum of the digits is 12. Find the number
According to the given condition the two-digit number is 66.
To find the two-digit number that is 11 times its units digit and has a sum of digits equal to 12, we can use the following steps:
1. Let's represent the two-digit number as XY, where X is the tens digit and Y is the units digit.
2. The number is 11 times its units digit, so we can write the equation: 10X + Y = 11Y.
3. The sum of the digits is 12, which means X + Y = 12.
4. Now, we have two equations with two variables:
- 10X + Y = 11Y
- X + Y = 12
5. We can solve for X from the second equation: X = 12 - Y.
6. Substitute the value of X in the first equation: 10(12 - Y) + Y = 11Y.
7. Simplify and solve for Y: 120 - 10Y + Y = 11Y.
8. Combine the Y terms: 120 - 9Y = 11Y.
9. Move all the Y terms to one side: 120 = 20Y.
10. Divide by 20 to get Y: Y = 6.
11. Now, substitute the value of Y back into the X equation: X = 12 - 6.
12. Solve for X: X = 6.
So, the two-digit number is 66.
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Which choice correctly compares two decimals?
A 2.17 > 2.0172.17 > 2.017
B 2.018 > 2.172.018 > 2.17
C 2.16 < 2.0172.16 < 2.017
D 2.17 = 2.017
Answer:
A
Step-by-step explanation:
2.17 > 2.017
because
2.017 = 2 + 17/1000
while
2.17 = 2 + 17/100 = 2 + 170/1000
170/1000 is larger than 17/1000.
for that reason D is wrong, of course.
2.17 is NOT equal to 2.017. 17/1000 is NOT equal to 170/1000.
2.018 = 2 + 18/1000
2.17 = 2 + 17/100 = 2 + 170/1000
also 18/1000 is NOT larger than 170/1000.
2.16 = 2 + 16/100 = 2 + 160/1000
2.017 = 2 + 17/1000
17/1000 are NOT larger than 160/1000.
5 Work out the volume of this prism. Write your answer
a in cm³
b in mm³.
20cm
120cm
30cm
10 cm
Answer:
a_48000cm^3
b_48000000mm^3
Step-by-step explanation:
first of all, let's find the base area:
Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2
then, to find the volume, we need to multiplicate the base area to the height of the prism:
V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3
(1 point) Use the method of undetermined coefficients to find a solution of a y" – 8y' + 297 = 48e4t cos(3t) + 80e4t sin(3t) + 3 - Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term. y = yh + yp = - = (1 point) Find y as a function of x if ' y" – 6y" + 8y' = 3e", - - = y(0) = 14, y'(0) = 29, y"(0) = 25. 33 4x y(x) = 37 91 e2x - tet 8 e 8 4
By using the method of undetermined coefficients, The general solution is y = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t). The solution to the initial value problem is y = 3e^(2x) + 14e^(4x) - 3e^(3x).
By using the method of undetermined coefficients, the associated homogeneous equation is y''-8y'+297=0, which has the characteristic equation r^2-8r+297=0. The roots of this equation are r=4+3i and r=4-3i, so the homogeneous solution is yh=a*e^(4x)cos(3x)+be^(4x)*sin(3x).
To find the particular solution, we make the ansatz yp = (Acos(3t) + Bsin(3t))e^(4t), where A and B are constants to be determined. Substituting this into the differential equation, we get
y" - 8y' + 297 = (16A - 18B)e^(4t)cos(3t) + (16B + 18A)e^(4t)sin(3t)
On the right-hand side, we have 48e^4tcos(3t) + 80e^4tsin(3t), which suggests setting
16A - 18B = 48, and
16B + 18A = 80
Solving these equations simultaneously, we get A = 7/2 and B = 5/2. Therefore, the particular solution is
yp = (7/2cos(3t) + 5/2sin(3t))e^(4t)
And the general solution is
y = yh + yp = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t)
For the second problem, the associated homogeneous equation is y''-6y'+8y=0, which has the characteristic equation r^2-6r+8=0. The roots of this equation are r=2 and r=4, so the homogeneous solution is yh=ae^(2x)+be^(4x).
To find the particular solution, we make the ansatz yp = Ce^3x, where C is a constant to be determined. Substituting this into the differential equation, we get
y" - 6y' + 8y = 9Ce^3x - 18Ce^3x + 8Ce^3x = (8C - 9C)e^3x = -C*e^3x
On the right-hand side, we have 3e^x, which suggests setting -C = 3. Therefore, the particular solution is
yp = -3e^(3x)
And the general solution is
y = yh + yp = ae^(2x) + be^(4x) - 3e^(3x)
To find the values of a and b, we use the initial conditions
y(0) = a + b - 3 = 14
y'(0) = 2a + 4b - 9 = 29
y''(0) = 2a + 8b = 25
Solving these equations simultaneously, we get a = 3 and b = 14. Therefore, the solution to the initial value problem is
y = 3e^(2x) + 14e^(4x) - 3e^(3x)
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--The given question is incomplete, the complete question is given
" (1 point) Use the method of undetermined coefficients to find a solution of a y" – 8y' + 297 = 48e4t cos(3t) + 80e4t sin(3t) + 3 - Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term. y = yh + yp = - = (1 point) Find y as a function of x if ' y" – 6y" + 8y' = 3e", - - = y(0) = 14, y'(0) = 29, y"(0) = 25."--
You invest ten thousand dollars in an account that pays eight percent APR compounded monthly. After how many years will the account have twenty thousand dollars.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
what is percentage ?As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.
given
With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.
When these values are added to the formula, we obtain:
[tex]20000 = 10000(1 + 0.08/12)^(12t) (12t)[/tex]
By multiplying both sides by 1000, we obtain:
[tex]2 = (1 + 0.08/12)^(12t) (12t)[/tex]
When we take the natural logarithm of both sides, we obtain:
ln(2) = 12t ln(1 + 0.08/12)
When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:
t = ln(2) / (12 ln(1 + 0.08/12))
Calculating the answer, we discover:
10.24 years is t.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
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