Answer:
To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:
[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]
Using partial fractions, we can write:
[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]
Multiplying both sides by (x+i)(x-i), we get:
[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]
Substituting x=i, we get:
[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ci + 2B[/tex]
Substituting x=-i, we get:
tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ai + 2D[/tex]
Substituting x=0, we get:
[tex]0 = Bi + Di[/tex]
Substituting x=1, we get:
[tex]0 = A+B+C+D[/tex]
Solving these equations simultaneously, we get:
A = -22/7 + π
B = 0
C = 22/7 - π
D = -2/5
Therefore, the integral can be written as:
[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]
Integrating each term separately, we get:
[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]
[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]
[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]
Therefore, the correct options are:
A) [tex]\pi-\frac{22}{7}[/tex]
B) [tex]\frac{2}{105}[/tex]
C) 0
D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. What
is the probability of event B?
Enter a number to the nearest hundredth in the box.
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.
Given that:
P(A) =0.65
P(A∩B) = 0.33
And event A and B are independent.
Using the probability formula:
P(B) = 1 - P(A) + P(A∩B)
⇒ P(B) = 1 - 0.65 + 0.33
⇒ P(B) = 0.68
Therefore , the probability of event B is 0.68.
Learn more about Independent:
https://brainly.com/question/15375461
#SPJ4
A statue casts a shadow that is 16 feet long. A nearby maple tree casts a shadow that is 10 feet long. If the statue is 20 feet tall, how tall is the maple tree, to the nearest tenth of a foot?
We can solve this problem by using proportions. 20/16 = x/10 => x = 12.5 Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
what is proportions ?
proportions are statements that two ratios or fractions are equal. A ratio is a comparison of two quantities, typically expressed as the quotient of one quantity divided by the other. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges is 5/3.
what is height ?
Height typically refers to the measurement of how tall or high something is, usually from its base to its top. In geometry, height is often used to refer to the perpendicular distance
In the given question ,
Let x be the height of the maple tree in feet. Then we have:
(height of statue) / (length of statue's shadow) = (height of maple tree) / (length of maple tree's shadow)
Substituting the given values, we get:
20/16 = x/10
on solving this equation, we can cross-multiply to get:
16x = 200 => x = 12.5
Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
To know more about proportions, visit:
https://brainly.com/question/30657439
#SPJ1
a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars
A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.
How to determine the number of toy carsTo determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.
We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).
Here's how to solve the problem:
1 pound = 16 ounces
Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces
The weight of one toy car is 7 ounces.
Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):
448 ÷ 7 = 64
Therefore, the bin can hold 64 toy cars.
Learn more about weight limit at
https://brainly.com/question/14375094
#SPJ11
The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. (true or false)
The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.
The above statement is True.
Eigenvalue:
An eigenvalue is a special set of scalar values associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.
According to the Question:
If the geometric multiple of the eigenvalues is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.
Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is
Ax = λx.
Learn more about Eigenvalue:
https://brainly.com/question/29749542
#SPJ4
find the nth term of this quadratic sequence 4, 7, 12, 19, 28, . ..
Answer:
an = a1 + (n-1)d
Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:
an = 4 + (n-1)3
a5 = 4 + (5-1)3
a5 = 4 + 12
a5 = 16
Jadi, suku ke-5 dari barisan ini adalah 16.
Untuk Konsultasi Tugas Lainnya: WA 0813-7200-6413
please help me
9-9÷9÷9-9÷9
Answer:
0
Step-by-step explanation:
0
Thank me...........
For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
To know more about roots go through:-
https://brainly.com/question/428672
#SPJ4
A company is buying new computers. The company needs no more than 220 desktops and at least 50 laptops. A total of at least 200 computers must be bought. Write a system of linear inequalities to represent the constraints of this situation. Let x represent the number of desktops, and let y represent the number of laptops.
pls help find y. 4x+5y-y+3x
Answer:
7x+4y
Step-by-step explanation:
combine like terms
Answer:
4?
Step-by-step explanation:
QUESTION 2
What portion of a whole does three fifths of two thirds represent?
Answer:
2/5
Step-by-step explanation:
3/5 * 2/3 is your equation
Multiply the numerators: 3*2=6
Multiply the denominators: 5*3=15
You get: 6/15
Simplify by dividing both the numerator and denominator by 3.
6/15=2/5
Here is a sketch of a curve.
The equation of the curve is y = x² + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Finish your answer by writing, Turning point at (..., ...)
YA
O
+
[tex]{\Large \begin{array}{llll} y=x^2+ax+b \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=-7 \end{cases}\implies -7=0^2+a(0)+b\implies \boxed{-7=b} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=7\\ y=0 \end{cases}\implies 0=7^2+a7+\stackrel{b}{(-7)}\implies 0=49+7a-7 \\\\\\ 0=42+7a\implies -42=7a\implies \cfrac{-42}{7}=a\implies \boxed{-6=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} y=x^2-6x-7 \end{array}}~\hfill[/tex]
now, let's get the "vertex" using the coefficients.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(1)}~~~~ ,~~~~ -7-\cfrac{ (-6)^2}{4(1)}\right) \implies \left( - \cfrac{ -6 }{ 2 }~~,~~-7 - \cfrac{ 36 }{ 4 } \right) \\\\\\ \left( 3 ~~~~ ,~~~~ -7 -9 \right)\implies {\Large \begin{array}{llll} (3~~,~-16) \end{array}}[/tex]
which type of number property is 28
It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.
6th graders has 5 hours of homework per week.
7th graders has 7 hours of homework per week.
9th graders has 12 hours of homework per week.
10th graders has 15 hours of homework per week.
What is the 5th graders expected hours of homework per week?
What is the 8th graders expected hours of homework per week?
Describe the correlation between hours of homework per week and grade level.
Answer:
The given data suggests that there is a positive correlation - as grade level increases, so does the expected hours of homework.
Step-by-step explanation:
It is difficult to accurately predict the expected hours of homework for 5th and 8th graders based on the given data. However, we can try to make an estimate by assuming a linear correlation between grade level and hours of homework.
Using the given data, we can plot a scatter plot with grade level on the x-axis and hours of homework on the y-axis. We can then draw a line of best fit through the data points to estimate the correlation.
Assuming a linear correlation, we can use the slope-intercept form of a line to calculate the expected hours of homework for 5th and 8th graders. The equation of the line of best fit is:
y = 2.5x - 6.5
where y is the expected hours of homework per week and x is the grade level. Using this equation, we can estimate that the expected hours of homework per week for 5th graders would be:
y = 2.5(5) - 6.5 = 6 hours
And the expected hours of homework per week for 8th graders would be:
y = 2.5(8) - 6.5 = 16 hours
It is important to note that this is just an estimate based on the given data, and actual hours of homework may vary depending on the school and curriculum.
As for the correlation between grade level and hours of homework per week, the given data suggests that there is a positive correlation - as grade level increases, so does the expected hours of homework. This is likely due to the increasing complexity and workload of the curriculum as students progress through school. However, it is important for schools to ensure that the amount of homework assigned is reasonable and does not cause undue stress or negatively impact students' well-being.
Hi I need help on this question It's teacher conferences week and I want to get this done before this week
Answer:
y = -3/8x + 3
Step-by-step explanation:
The slope intercept form is y = mx + b
Our equation is 3x + 8y = 24
3x + 8y = 24
8y = -3x + 24
y = -3/8x + 3
So, the answer is y = -3/8x + 3
r=19m how to find the circumference
Answer: 119.38
Step-by-step explanation:
C = 2πr = 2·π·19 ≈ 119.38052
6. If g(x) = 7x-4, find g(8)-g (-5)
PLEASE HELP I BEG
Let f be a differentiable function defined by f(x) = 3x + 2e −3x , and let g be a differentiable function with derivative given by g′(x) = 1 x + 4. It is known that lim g(x) = [infinity].
x→[infinity]
The value of lim f(x) g(X) is:______
x→[infinity]
The value of lim f(x)g(x) as x approaches infinity is 0.
L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.
To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:
lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]
= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]
Applying L'Hopital's rule to the fraction in the numerator, we get:
lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]
= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]
= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]
= 0
Learn more about L'Hopital's rule here
brainly.com/question/24116045
#SPJ4
Weight of a badminton racket is 0. 950 kg find the weight of 12 such rackets
The weight of 12 badminton rackets, each weighing 0.950 kg, is 11.4 kg.
The weight of an object refers to the force exerted by gravity on that object. This force is typically measured in units of mass, such as kilograms or pounds. In the case of badminton rackets, the weight is usually measured in grams.
Now, let's consider the weight of a single badminton racket. You've been given the information that the weight of one racket is 0.950 kg. This means that the force exerted by gravity on that racket is 0.950 kg.
If you want to find the weight of 12 such rackets, you need to multiply the weight of one racket by 12. This gives you:
0.950 kg x 12 = 11.4 kg
To know more about weight here
https://brainly.com/question/10069252
#SPJ4
-1/2 (6- 8x to the power of 2)
(The 8x is to the power of 2)
Answer:
-3+[tex]4x^{2}[/tex]
Step-by-step explanation:
Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged
The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.
To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.
Learn more about mean here: brainly.com/question/30891252
#SPJ4
find the radius of circle Q
The radius of the given circle is x = 3 and x = 3/11.
How are quadratic equations solved, and what are they?A polynomial equation of degree two is a quadratic equation, indicating that the variable's maximum exponent is 2. There are various ways to solve a quadratic equation, including factoring, completing the square, and applying the quadratic formula. Finding two quadratic expression factors that multiply to produce the constant term c and add to produce the linear term b's coefficient is known as factoring. The quadratic expression is completed by adding and removing a constant component to create a perfect square trinomial that can be factored or solved by calculating the square root.
In the given figure connect the points QF and QG using a line segment, thus forming two right angled triangle.
The perpendicular segment QA divides the base into two equal parts. Thus, the base of the triangle is 8.
Using the Pythagorean theorem we have:
(QF)² = (8)² + (4x + 3)²
QG² = 8² + (7x - 6)²
In the figure QF = QG = r thus:
(8)² + (4x + 3)² = 8² + (7x - 6)²
Expanding using the algebraic identity:
16x² + 24x + 9 = 49x² - 84x + 36
33x² - 108x + 27 = 0
3(11x² - 36x + 9) = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values a = 11, b = -36, and c = 9:
x = (-(-36) ± √((-36)² - 4(11)(9))) / 2(11)
x = (36 ± √(1296 - 396)) / 22
x = (36 ± √900) / 22
x = (36 ± 30) / 22
x = (36 + 30) / 22 = 3
x = (36 - 30) / 22 = 3/11
x = 3 and x = 3/11.
Thus, the radius of the given circle is x = 3 and x = 3/11.
Learn more about radius here:
https://brainly.com/question/13449316
#SPJ1
22) i) A cuboid has dimensions 60cm x 24cm x 30cm. How many small cubes with side 5cm can be placed in the given cuboid?
Answer:
345.6
Or 345 full cubes
Step-by-step explanation:
To answer this question we first need to find the volume of the cuboid!
To find volume we use the equation...
area of cross-section × heightor l × w × hFor the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...
60 × 24 × 30 = 43200We now need to the the volume of the cube which we can just do by cubing the value given
5³ = 125We now need to divide the two results together to find out how many cubes would fit...
43200 ÷ 125 = 345.6Or 345 full cubesHope this helps, have a lovely day!
list one advantage and one disadvantage of the secant method compared with the bisection method for finding a simple zero of a nonlinear equation g
There are often other methods that can converge faster than bisection method.
Advantages and disadvantages of the secant method and bisection method are:Advantages of the secant method:The secant method is faster than the bisection method since it converges faster to the root.It needs less iterations to get the root.Disadvantages of the secant method:The secant method may not converge to a root.In comparison to bisection method, it is more complex and therefore requires more computational time and effort.Advantages of the bisection method:It is more straightforward and simple to implement.In the case of continuous functions, it will always converge to a root.Disadvantages of the bisection method:It is much slower and requires more iterations to converge to a root than the secant method.There are often other methods that can converge faster than bisection method.
Learn more about Bisection
brainly.com/question/10119113
#SPJ11
What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
given the following limit lim(x;y)!(0;0) xy x y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
To show that a function does not have a limit as (x, y) approaches (0, 0), we need to examine the limit along different paths .
How can we show that a function does not have a limit as (x, y) approaches (0, 0)?
To show that the function f(x, y) does not have a limit as (x; y) ! (0; 0), we need to examine the limit lim
(x;y)!(0;0) xy x y .
Convert the given limit into a more recognizable form. The given limit is
lim(x, y) -> (0, 0) (xy / (x + y)).
Analyze the limit along different paths. Let's examine the limit along two distinct paths - the
x-axis (y = 0)
and
the y-axis (x = 0).
For the x-axis (y = 0), the limit becomes
lim(x, 0) -> (0, 0) (x * 0 / (x + 0))
= lim(x, 0) -> (0, 0) (0) = 0.
For the y-axis (x = 0), the limit becomes
lim(0, y) -> (0, 0) (0 * y / (0 + y))
= lim(0, y) -> (0, 0) (0) = 0.
Compare the results of the two paths. Both limits along the x-axis and y-axis are equal to 0. However, this is not enough to conclude that the function f(x, y) has a limit as (x; y) ! (0; 0).
Examine another path, such as the line y = x. In this case, the limit becomes
lim(x, x) -> (0, 0) (x * x / (x + x))
= lim(x, x) -> (0, 0) (x^2 / 2x)
= lim(x, x) -> (0, 0) (x / 2)
= 0 / 2 = 0.
Consider another path, like
y = -x.
For this path, the limit becomes
lim(x, -x) -> (0, 0) (x * -x / (x - x))
which is undefined, since the denominator is zero.
Since we have found a path
(y = -x)
where the limit is undefined, we can conclude that the function f(x, y) does not have a limit as (x; y) ! (0; 0).
Learn more about: limit
brainly.com/question/8533149
#SPJ11
20. You conduct a simulation regarding how many registered voters voted in the last election. Your null hypothesis is that the percentage of people who voted is less than-
is that the percentage of people who voted is greater than 65%.
You determine that the results of your simulation have a p-value of 0.08. What does this mean?
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 0.8%. With a significance level of 1%, you should fail to reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 0.8%. With a significance level of 1%, you should reject the null hypothesis.
O
M
PREVIO
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.
Describe p-value?In statistics, the p-value is a measure of the strength of evidence against a null hypothesis. It is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true.
In hypothesis testing, the null hypothesis is a statement about a population parameter that is being tested. The alternative hypothesis is another statement about the population parameter that is being tested as an alternative to the null hypothesis. The p-value is used to determine whether the observed data provides strong evidence against the null hypothesis in favor of the alternative hypothesis.
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.
The p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true. In this case, the null hypothesis is that the percentage of people who voted is less than or equal to 65%. Since the p-value (0.08) is greater than the significance level of 1%, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the percentage of people who voted is greater than 65%.
To know more about outcome visit:
https://brainly.com/question/29760438
#SPJ1
The result of the simulation has an 8% probability under the tested hypothesis. You should be unable to deny the null hypothesis at a significance level of 1%.
Describe p-value?The p-value in statistics is a gauge of the weight of proof opposing a null hypothesis. In the event that the null hypothesis is correct, it is the likelihood of getting a test statistic that is equally extreme or more extreme than the observed value.
The null hypothesis in hypothesis testing is a claim made about the demographic parameter under investigation. In place of the null hypothesis, a different claim is made about the demographic parameter in the alternative hypothesis. The p-value is used to assess whether the recorded data strongly support the alternative hypothesis over the null hypothesis.
The p-value, under the assumption that the null hypothesis is correct, is the likelihood of getting a result that is equally extreme or more extreme than the observed result. In this instance, the null hypothesis is that less than or equivalent to 65% of eligible voters cast ballots.
We are unable to reject the null hypothesis because the p-value (0.08), which is higher than the 1% threshold of significance, is not zero. This implies that we lack sufficient evidence to draw the conclusion that more than 65% of eligible voters cast ballots.
To know more about p-value, visit:
https://brainly.com/question/30461126
#SPJ1
Answer needed ASAP!!
:)
The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.
What is Arc?In geometry, arc is portion of a curve or circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of arc is fraction of the circumference of circle, determined by the measure of central angle that subtends it.
An arc is typically denoted by two endpoints, with small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or position of their endpoints.
An arc with measure less than 180 degrees is called minor arc, while an arc with measure greater than 180 degrees is called major arc. An arc with measure equal to 180 degrees is called semicircle.
Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:
m∠QTS = (1/2) m arc QS
m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]
m∠QTS = 60°
Therefore, the measure of angle ∠QTS is 60° degrees.
To know more about Angle visit:
https://brainly.com/question/30162248
#SPJ1
Click to show the supplementary angle of each angle.
26∘
44∘
45∘
136∘
135∘
154∘
The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Supplementary Angles of Given AnglesSupplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.
Therefore, the supplementary angles of the given angles are:
The supplementary angle of 26 degrees is 154 degrees (180 - 26 = 154).The supplementary angle of 44 degrees is 136 degrees (180 - 44 = 136).The supplementary angle of 45 degrees is 135 degrees (180 - 45 = 135).The supplementary angle of 136 degrees is 44 degrees (180 - 136 = 44).The supplementary angle of 135 degrees is 45 degrees (180 - 135 = 45).The supplementary angle of 154 degrees is 26 degrees (180 - 154 = 26).Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Read more about angles at
https://brainly.com/question/28293784
#SPJ1
What is the volume of the prism below?
Answer:30
Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 7)
From the use of the angle of elevation, the length of ladder is 47 feet.
What is the angle of elevation?The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.
We know that we have to use the idea of the angle of elevation in this case. We know that;
Cos 65 = 20/x
x is the length of the ladder
x =20/Cos 65
x = 20/0.4225
x = 47 feet
Learn more about angle of elevation:https://brainly.com/question/21137209
#SPJ1