The general solution of the nonhomogeneous differential equation [tex]2y""' + y" + 2y' + y = 2t^2 + 3[/tex] is [tex]y(t) = c_1 * e^(^-^t^) + c_2 * cos(t/\sqrt{2} ) + c_3 * sin(t/\sqrt{2} ) + (1/2)t^2 + (3/2)[/tex], where [tex]c_1[/tex], [tex]c_2[/tex], and [tex]c_3[/tex] are arbitrary constants.
To find the complementary solution, we first solve the associated homogeneous equation by setting the right-hand side equal to zero. The characteristic equation is [tex]2r^3 + r^2 + 2r + 1 = 0[/tex], which can be factored as [tex](r + 1)(2r^2 + 1) = 0[/tex]. Solving for the roots, we have r = -1 and r = ±i/√2. Therefore, the complementary solution is [tex]y_c(t) = c_1 * e^(^-^t^) + c_2 * cos(t/\sqrt{2}) + c_3 * sin(t/\sqrt{2} )[/tex], where [tex]c_1[/tex], [tex]c_2[/tex], and [tex]c_3[/tex] are arbitrary constants.
To find the particular solution, we consider the form [tex]y_p(t) = At^2 + Bt + C[/tex], where A, B, and C are constants to be determined. Substituting this into the original equation, we solve for the values of A, B, and C. After simplification, we find A = 1/2, B = 0, and C = 3/2. Hence, the particular solution is [tex]y_p(t) = (1/2)t^2 + (3/2)[/tex].
Therefore, the general solution of the nonhomogeneous differential equation is [tex]y(t) = y_c(t) + y_p(t) = c_1 * e^(^-^t^) + c_2 * cos(t/\sqrt{2}) + c3 * sin(t/\sqrt{2} ) + (1/2)t^2 + (3/2)[/tex], where [tex]c_1[/tex], [tex]c_2[/tex], and [tex]c_3[/tex] are arbitrary constants.
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let a be a countably infinite set. which of the following must be true?
a. there is a one-to-one function from set A to the set of rational numbers
b. the set of integers have the same cardinality as the set A
c. there can be no surjective function from the set of rational numbers
d. the open interval (0, 1) has the same cardinality as the set A
The set of integers has the same cardinality as the countably infinite set A. The correct option is b.
A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers (integers starting from 1). This means that we can establish a one-to-one function (bijection) between the countably infinite set A and the set of integers.
Options a, c, and d are not necessarily true.
Option a: There is no guarantee that there is a one-to-one function from the set A to the set of rational numbers. The set of rational numbers, also known as Q, is uncountably infinite, while A is only countably infinite.
Option c: It is possible to have a surjective function (onto) from the set of rational numbers to a countably infinite set. For example, a function that maps every rational number to its numerator can be surjective onto the set of integers.
Option d: The open interval (0, 1) has a higher cardinality (uncountable) than a countably infinite set. The interval (0, 1) contains an uncountably infinite number of real numbers between 0 and 1, whereas A is countably infinite.
The correct option is b.
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The data set below is a random sample of the heights (in meters) of women belonging to a certain ethnic subgroup. Assume the population is normally distributed 1.63 1.62 1.61 162 1.39 1.55 a) Find the mean and standard deviation of the data.
The mean of the data set is approximately 1.57 meters. The standard deviation of the data set is approximately 0.0968 meters, indicating the average deviation of data points from the mean.
To compute the mean and standard deviation of the data set, we'll use the following formulas:
Mean (μ) = (sum of all data values) / (total number of data values)
Standard Deviation (σ) = sqrt((sum of squared differences from the mean) / (total number of data values))
Let's calculate the mean and standard deviation for the given data set:
Data set: 1.63, 1.62, 1.61, 1.62, 1.39, 1.55
Mean (μ) = (1.63 + 1.62 + 1.61 + 1.62 + 1.39 + 1.55) / 6 = 9.42 / 6 ≈ 1.57
Next, we calculate the sum of squared differences from the mean:
(1.63 - 1.57)^2 + (1.62 - 1.57)^2 + (1.61 - 1.57)^2 + (1.62 - 1.57)^2 + (1.39 - 1.57)^2 + (1.55 - 1.57)^2 ≈ 0.0666
Finally, we calculate the standard deviation:
Standard Deviation (σ) = sqrt(0.0666 / 6) ≈ 0.0968
Therefore, the mean of the data set is approximately 1.57 meters and the standard deviation is approximately 0.0968 meters.
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A claim investigating company that investigates illegal claims suspects that the number of claims per major city filed is exceeding the past average of 70 claims, with standard deviation of 8.9. Suppose the company surveys 100 major cities and finds the average number of claims per city to be 71.8. At a significance level of = 0.05, test to determine if this sample data supports the company's suspicion?
The sample data does support the company's suspicion that the number of claims is exceeding the past average.
The company can use a "One-Sample T-Test" to determine if the sample data supports its suspicion. Under the null hypothesis, it is assumed that the mean number of claims per major city is still the previously established population mean of 70.
We can then calculate the test statistic:
T-test statistic = (71.8-70)/(8.9/√100)
= 1.8/0.8931
= 2.02
We can then compare this statistic to the critical value at an alpha level of 0.05. With n=100, and a two-sided test, this value is 1.645.
Because 2.02 > 1.645, we can reject the null hypothesis that the mean number of claims is still 70.
Therefore, the sample data does support the company's suspicion that the number of claims is exceeding the past average.
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Express the following complex numbers in the form atib (i) ei (it) bg (1+²) (iii) Senci) (iv) ezbg(-1)
(i) Express the complex number in the form a+bi:ei (it) bg
The complex number ei(it)bg can be expressed in the form a+bi, where a is the real part and b is the imaginary part of the complex number. In this case, we have:
ei(it)bg = cos(bg) + i sin(bg)
The real part of the complex number is cos(bg) and the imaginary part is sin(bg). Therefore, we can express the complex number as:
ei(it)bg = cos(bg) + i sin(bg)
(ii) Express the complex number in the form a+bi: 1+²
To express the complex number 1+² in the form a+bi, we need to recognize that i² = -1. Therefore, we have:
1+² = 1 - 1 = 0
Since the imaginary part of the complex number is zero, we can express it as:
1+² = 0 + i0
(iii) Express the complex number in the form a+bi: Sen(ci)
To express the complex number Sen(ci) in the form a+bi, we need to use the formula:
Sen(ci) = sin(c) cosh(i) + cos(c) sinh(i)
where sinh(i) = i sin(1) and cosh(i) = cos(1). Therefore, we have:
Sen(ci) = sin(c) cosh(i) + cos(c) sinh(i)
= sin(c) cos(1) + cos(c) i sin(1)
(iv) Express the complex number in the form a+bi: e^zbg(-1)
To express the complex number e^zbg(-1) in the form a+bi, we need to recognize that zbg(-1) is a complex number. Therefore, we have:
e^zbg(-1) = e^(a+bi)
= e^a e^(bi)
= e^a (cos(b) + i sin(b))
where a is the real part of zbg(-1) and b is the imaginary part. Therefore, we can express the complex number as:
e^zbg(-1) = e^a (cos(b) + i sin(b))
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Please help me guys!
Answer:
11+13+16 or 14x15x18
Step-by-step explanation:
HOPE IT HELPS! :)
1/2 x 240 im just too lazy to do it lol
Answer: 120
Step-by-step explanation:
A cup and saucer together cost N$ 20.50 . A cup and two saucer cost N$ 27.00 . Find the cost of the cup and the saucer.
Answer: Cup-$14, Saucer-$6.5
Step-by-step explanation:
Given
Cup and saucer costs $20.5
A cup and two saucer costs $27
Assume the price of cup and saucer are x and y
So, we can write
[tex]\Rightarrow x+y=20.5\quad \ldots(i)\\\\\Rightarrow x+2y=27\quad \ldots(ii)[/tex]
Solving [tex](i)\ \text{and}\ (ii)[/tex] we get
[tex]x=\$\ 14, y=\$\ 6.5[/tex]
Thus, the cost of the cup is $14 and that of the saucer is $6.5
What is the probability of selecting an orange candy
Answer:
how many colors are there and how many of each color?
Step-by-step explanation:
Probability of an event is the measurement of its chance of occurrence.
The probability of selecting an orange candy depends on how many candies are there. If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100%How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered random experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
How to convert percent to probability?Percent counts the number compared to 100 whereas probability counts it compare to 1.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in probability)
The probability of selecting an orange candy depends on how many candies are there.
If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100% because then n(E) = 1 and n(S) = 1 where
E is event of selecting one orange candy from only 1 candy availablen(E) = count of ways E can be done = 1n(S) = number of ways 1 candy can be selected from only 1 candy availableThus, the probability of selecting an orange candy depends on how many candies are there. If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100%
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The most efficient first step in the process to factor the trinomial 3x³-24x² + 36x is :
O A. factor out 3
O B. factor out 3x
O C. factor out (x - 2)
O D. factor out-1
Answer:
B
Step-by-step explanation:
Factor the Expression= -3x + 12
Answer:
-3(x-4)
Step-by-step explanation:
to factor, you have to find the gcf of both numbers. the gcf is -3
Answer:
-3 (x-4)
Step-by-step explanation:
Take a negative three out of each part of the problem.
Assume that the U.S. Mint manufactures dollar coins so that the standard deviation is 0.0390 g. The accompanying list contains weights (grams) of dollar coins manufactured with a new process designed to decrease the standard deviation so that it is less than 0.0390 g. This sample has these summary statistics: n=16, x = 8,068 9. s=0.02 g. A significance level is used to test the claim that the sample is from a population with a standard deviation less than 0.0390 g. 11 we want to use a 0.05 significance level and a parametric method to test the claim that the sample is from a population with a standard deviation less than 0.0390 g, what requirements must be satisfied? How does the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test of a claim about a mean? Click the icon to view the weights of dollar coins manufactured with the new process, What requirements must be satisfied? Select all that apply. A. Either or both of these conditions are satisfied:
A. the population is normally distributed or the sample size is greater than 30. B. The population has a chi-square distribution C. The sample is a simple random sample. D. The sample size is greater than 30. E. The population has a normal distribution F. No requirements must be satisfied.
To test the claim that the sample is from a population with a standard deviation less than 0.0390 g, and using a 0.05 significance level and a parametric method, certain requirements must be satisfied. The requirements include:
A. Either or both of these conditions are satisfied:
A. the population is normally distributed or the sample size is greater than 30.
C. The sample is a simple random sample.
The normality requirement for a hypothesis test of a claim about a standard deviation differs from the normality requirement for a hypothesis test of a claim about a mean. For a hypothesis test of a claim about a standard deviation, it is not necessary for the population to be normally distributed. Instead, either the population should be normally distributed or the sample size should be sufficiently large (typically greater than 30) for the Central Limit Theorem to apply. In this case, the requirement is satisfied if either the population is normally distributed or the sample size is greater than 30. However, the sample should still be a simple random sample, which ensures that the observations are independent and representative of the population.
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The vectors a and b represent two forces acting at the same point, and 0 is the smallest positive angle between a and b_ Approximate the magnitude of the resultant force Irll: (Round your answer to one decimal place:) Ila |l 5.3b, Ilb |I 6,9 Ib; 60" Irll'
The magnitude of the resultant force, given two forces represented by vectors a and b with magnitudes 5.3 N and 6.9 N, respectively, and an angle of 60 degrees between them, can be approximated to 8.5 N.
To find the magnitude of the resultant force, we can use the law of cosines. According to the law of cosines, the magnitude of the resultant force (Ir) can be calculated using the formula: [tex](Ir)^2 = |a|^2 + |b|^2[/tex] - [tex]2|a||b|cos(theta)[/tex], where |a| and |b| represent the magnitudes of vectors a and b, and theta is the angle between them.
Given that |a| = 5.3 N, |b| = 6.9 N, and theta = 60 degrees, we can substitute these values into the formula and solve for Ir. Plugging in the values, we have [tex]Ir^2 = (5.3)^2 + (6.9)^2[/tex]- 2(5.3)(6.9)cos(60).
Simplifying the equation, we get [tex]Ir^2[/tex] = 28.09 + 47.61 - 36.66. Combining the terms, we have [tex]Ir^2[/tex] = 39.04.
Taking the square root of both sides, we find Ir ≈ √39.04 ≈ 6.2 N. Rounded to one decimal place, the magnitude of the resultant force is approximately 8.5 N.
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this ladybird is rotated. choose the correct word to complete eachsentence. this ladybird made a __ turn clockwise this ladybird made a -__ anticlockwise
We can see here that when the ladybird is rotated:
This ladybird made a 90° turn clockwise.
This ladybird made a 180° anticlockwise.
What is rotation?In mathematics, rotation refers to a transformation that turns or rotates an object around a fixed point called the center of rotation. It is a fundamental concept in geometry and is used to describe the movement of points, shapes, or figures in the plane or in three-dimensional space.
A rotation involves specifying the center of rotation, the angle of rotation, and the direction of rotation (clockwise or counterclockwise).
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Grayson is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $2 per mile driven. Company B charges an initial fee of $100 for the rental plus $1 per mile driven. Let A represent the amount
Company A would charge if Grayson drives x miles, and let B represent the amount
Company B would charge if Grayson drives a miles. Write an equation for each situation, in terms of x, and determine which company would be cheaper if Grayson needs to drive 45 miles with the rented truck.
A=
B=
_______ is $_____ cheaper than _____ when driving 45 miles.
Plz before in 10mins.
Answer:
A is 10 dollar cheaper than B
Step-by-step explanation:
A : 40 dollars plus 45*2=90
90+40= 130 dollars
B:100 dollars 45*1=45
100+45= 145 dollars
Answer:
A is 15$ cheaper than b
Step-by-step explanation:
A= 40+(45*2) = 40+90=130$
b= 100+45 =145$
A doctor is measuring body temperature for patients visiting the office. The doctor believes the average body temperature is less than 98.6 degrees Fahrenheit and would like to test this claim. During the process of hypothesis testing, the doctor computes a value from the sample data, which will be used to compare the sample data to the population parameter. What value did the doctor compute?
Answer:
Test statistic
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth.
15
25
Answer:
20.
Step-by-step explanation:
x^2 = 25^2 - 15^2
x^2 = 400
x = 20
PLEASE HELP ME :(
The questions and answer choices are in the picture.
It would also reallyyyyy help me if you explain how you solved it. At least just show the steps.
Thank you!
Hi army! I found the answer!
Answer:
F. An 18-month loan with an annual simple interest rate of 4.75%
Step-by-step explanation:
I just used a credit card payoff calculator to solve this problem. You can use that calculator to solve other problems like this too!
Also, stream BTS Film Out for clear skin and good grades ;)
Have a great day!
suzy randomly picks marbles from a bag containing 12 identical marbles. how many possible outcomes are there if she selects 9 marbles?
There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.
The problem asks how many possible outcomes there are.
To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.
In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).
So, plugging in our numbers:
12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220
Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.
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Solve the equation 4x-12=(11-3x)
Answer:
Step-by-step explanation:
4x - 12 = 11 - 3x
Bringing like terms on one side
4x + 3x = 11 + 12
7x = 23
x = 23/7
Factor the expression using the GCF.
42 – 12 =
Answer:
30
Step-by-step explanation:
Well 42
-
12
30
2) Check to see if x = 2 is the solution to this equation Explain your
reasoning with words and work. Be clear and completel
- 4x - 12 = 2x -8
The money spent on gym classes is proportional to the number of gym classes taken. Max spent $45.90 to take 6 gym classes.
What is the amount of money, in dollars, spent per gym class?
Answer:
$7.65
Step-by-step explanation:
its the right answer, TRUST ME!!!!
A sequence can be generated by using an=an−1+4, where a1=5 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
5, 20, 80, 320, 1280
4, 9, 14, 19, 24
4, 20, 100, 500, 2500
5, 9, 13, 17, 21
The first 5 terms of the arithmetic sequence are: 5, 9, 13, 17, 21.
How to find the first 5 terms?Here we have an arithmetic sequence, such that the recursive formula is:
[tex]a_n = a_{n- 1} + 4[/tex]
Such that:
a₁ = 5.
Using that formula we can get the next 4 terms. For the second term we use n = 2, so we get:
[tex]a_2 = a_1 + 4 = 5 + 4 = 9[/tex]
For the third term we have:
[tex]a_3 = a_2 + 4 = 9 + 4 = 13[/tex]
For the fourth term we have:
[tex]a_4 = a_3 + 4 = 13 + 4 = 17[/tex]
For the fifth term we have:
[tex]a_5 = a_4 + 4 = 17 + 4 = 21[/tex]
Then the first 5 terms of the sequence are:
5, 9, 13, 17, 21.
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Write the equation in slope intercept form (y=mx+b):
Answer: Y=30x+120
Step-by-step explanation
The x stands for each week, the m stands for the money being added or subtracted. That is why the m and x are being multiplied together in the equation. The b stands for how much the person, Mike, already has. Hope this helps
use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 y2 and the sphere x2 y2 z2 = 162.
To find the volume of the solid enclosed by the cone and the sphere, we can use cylindrical coordinates. By expressing the equations in cylindrical coordinates and setting up the appropriate limits, we can integrate to calculate the volume of the solid.
In cylindrical coordinates, we have x = r cos θ, y = r sin θ, and z = z.
The equation of the cone, z = x^2y^2, can be expressed in cylindrical coordinates as z = (r^2 cos^2 θ)(r^2 sin^2 θ) = r^4 cos^2 θ sin^2 θ.The equation of the sphere, x^2 + y^2 + z^2 = 162, can be written in cylindrical coordinates as r^2 + z^2 = 162.
To find the limits for integration, we need to determine the intersection points of the cone and the sphere. Setting the equations equal to each other, we have r^4 cos^2 θ sin^2 θ = 162 - r^2.
Simplifying, we get r^4 cos^2 θ sin^2 θ + r^2 - 162 = 0.
We can solve this equation to find the values of r at the intersection points.
Once we have the limits for r, θ, and z, we can set up the triple integral to calculate the volume enclosed by the cone and the sphere.
By evaluating the integral with the appropriate limits, we can find the volume of the solid enclosed by the given cone and sphere equations using cylindrical coordinates.
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PLEASE HELP SOMEBODY
Answer:
24
Step-by-step explanation:
[tex]79-7=72[/tex]
[tex]\frac{72}{3} =24[/tex]
When blood cholesterol levels are tested, sometimes a cardiac risk ratio is calculated.
Cardiac risk ratio=total cholesterol level high-density lipoprotein level HDL
For women, a ratio between 3.0 and 4.5 is desirable.
A woman’s blood test yields an HDL cholesterol level of 60 mg/dL and a total cholesterol level of
225mg/dL. What is her cardiac risk ratio, expressed as a one-place decimal? Yes, Her ratio is in the normal range.
the answer is 3.8, yes.
please show the step of the solution.
The woman's cardiac risk ratio can be calculated by dividing her total cholesterol level by her high-density lipoprotein (HDL) level. With a total cholesterol level of 225 mg/dL and an HDL level of 60 mg/dL, her cardiac risk ratio is 3.8, which falls within the desirable range of 3.0 to 4.5 for women.
To calculate the cardiac risk ratio, we divide the total cholesterol level by the HDL level. In this case, the woman's total cholesterol level is 225 mg/dL, and her HDL level is 60 mg/dL. Thus, her cardiac risk ratio is given by 225 mg/dL / 60 mg/dL = 3.75.
The cardiac risk ratio is typically expressed as a one-place decimal. Rounding the ratio to one decimal place, we get 3.8. Since the desirable range for women's cardiac risk ratio is between 3.0 and 4.5, the woman's ratio of 3.8 falls within this range, indicating a desirable level.
Therefore, the woman's cardiac risk ratio, expressed as a one-place decimal, is 3.8, which indicates a normal and desirable range for her cholesterol levels.
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Carmen y Catalina comparan la nota que obtuvieron en su examen bimestral de Aritmética y mencionan lo siguiente: Nuestras notas juntas es igual a 34 puntos, pero se sabe que Carmen obtuvo 4 puntos más que Catalina. ¿Cuál es la nota de Catalina?
Answer:
La nota de Carolina es 15 puntos.
Step-by-step explanation:
Un sistema de ecuaciones lineales es un conjunto de ecuaciones lineales que tienen más de una incógnita, relacionadas mediante las ecuaciones.
En los sistemas de ecuaciones, se debe buscar los valores de las incógnitas. Al reemplazar en las ecuaciones, deben dar la solución planteada.
En este caso se debe plantear un sistema de ecuaciones, donde las incógnitas son:
x: nota de Carolinay: nota de CarmenAmbas notas juntas es igual a 34 puntos. Expresado matemáticamente es:
x + y= 34
Se sabe que Carmen obtuvo 4 puntos más que Catalina. Esto es:
y= x + 4
Entonces el sistema de ecuaciones a resolver es:
[tex]\left \{ {{x+y=34} \atop {y=x+4}} \right.[/tex]
A través del método de sustitución debes despejar una de las incógnitas en una de las ecuaciones y sustituir su valor en la siguiente. En este caso, ya tienes despejada la incógnita y en la segunda ecuación. Por lo que sustituyes esta expresión en la primer ecuación:
x+ x+4=34
Resolviendo obtienes:
x + x= 34 - 4
2*x=30
x= 30÷ 2
x=15
Sustituyendo este valor en la segunda ecuación obtienes:
y= x+4
y= 15 +4
y= 19
Recordando que "x" representa la nota de Carolina e "y" la nota de Carmen, entonces la nota de Carolina es 15 puntos y la nota de Carmen es 19 puntos.
find the number of sides of a regular polygon in which the measure of 1 interior angle is 11 times the measure of the adjacent exterior angle
Let 'n' be the number of sides of a regular polygon, in which the measure of 1 interior angle is 11 times the measure of the adjacent exterior angle.
The formula to find the measure of an interior angle of a polygon is 180°(n - 2) / n. The formula to find the measure of an exterior angle of a polygon is 360° / n. We can use these formulas to form an equation that will help us find 'n'.According to the question, the measure of 1 interior angle is 11 times the measure of the adjacent exterior angle. Mathematically, we can express this as:180°(n - 2) / n = 11(360° / n - 180°(n - 2) / n)Simplifying this equation, we get:180°(n - 2) / n = 11(180° / n)Multiplying both sides by 'n', we get:180°(n - 2) = 11(180°)Simplifying further, we get:n - 2 = 11n = 13Therefore, the number of sides of the regular polygon is 13.Answer: 13
Let's denote the measure of the interior angle as x and the measure of the adjacent exterior angle as y. According to the given information, we have the equation:
x = 11y
In a regular polygon, all interior angles are congruent (have the same measure), and all exterior angles are congruent as well. The sum of the interior and exterior angles adjacent to each other forms a straight line, which measures 180 degrees. Therefore, we can write the equation:
x + y = 180
Substituting x = 11y into the equation, we get:
11y + y = 180
Combining like terms:
12y = 180
Dividing both sides by 12:
y = 15
Now, we can substitute this value back into the equation x = 11y:
x = 11 * 15 = 165
So, the measure of each interior angle is 165 degrees, and the measure of each exterior angle is 15 degrees.
In a regular polygon, the sum of the interior angles can be found using the formula:
Sum of interior angles = (n - 2) * 180
where n is the number of sides of the polygon.
Since each interior angle measures 165 degrees, we can set up the equation:
165n = (n - 2) * 180
Expanding the right side:
165n = 180n - 360
Subtracting 180n from both sides:
-15n = -360
Dividing both sides by -15:
n = 2
Therefore, the regular polygon has 24 sides.
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Let the measure of the adjacent exterior angle be x. Then the measure of the interior angle is 11x.
The number of sides of the regular polygon is given by: [tex]n = 3,960^{\circ} / x[/tex].
Since the polygon is regular, all interior angles and exterior angles have the same measure. Therefore, we can say that the sum of all the exterior angles of a polygon equals 360°.
This gives us an equation:
x + 11x + x + 11x + ...
= 360°,
where there are n terms in the sequence (since there are n sides in the polygon).
Simplifying this equation, we get:
[tex]360^{\circ}= nx[/tex]
Therefore, the number of sides of the polygon is:
[tex]n = 360^{\circ} / x[/tex]
Since the polygon is regular, each exterior angle must be congruent to x. Since the sum of all exterior angles in a polygon equals 360°, we can say that the measure of each exterior angle is:
[tex]x = 360^{\circ} / n[/tex]
Therefore, the measure of each interior angle is:
[tex]11x = 11(360^{\circ} / n)[/tex]
[tex]= 3,960^{\circ} / n[/tex]
Therefore, the number of sides of the regular polygon is given by:
[tex]n = 3,960^{\circ} / x[/tex]
Answer: The number of sides of the regular polygon is given by: [tex]n = 3,960^{\circ} / x[/tex].
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Factor as the product of two binomials.
x^2-3x+2=
Answer: (x - 2) (x - 1）
Step-by-step explanation:
x²-3x+2
= (x - 2) (x - 1）