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90 degrees and right angle
Related Questions
Calculate the integral ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x^2]dx.
Answers
The solution of the integral (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C.
We have the following integral to solve.∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²2)]dx
Let's begin by using the substitution u = arctan(3x).
We need to convert this integral into a U-form. By substituting the above expression, we have the following new expression.
∫ [(1+cos u)+u⁵]/[1+9(3tanu)²] *(1/3) du=∫ [(1+cos u)+u⁵]/(9tan²u+1) *(1/3) du
Let's now consider the numerator.
We have 1+cosu+u⁵ in the numerator. Let's break down the integral into 3 parts. The first part is ∫(1)/(9tan²u+1) *(1/3) du.
We can convert the denominator to a perfect square of the form 3²tan²u+1 which simplifies to (3tanu+1)(3tanu-1)+2.
Let's now factorize
= ∫(1)/(9tan²u+1) *(1/3) du
=∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
Now let's perform partial fraction decomposition. We have 1/[(3tanu+1)(3tanu-1)+2] which we can write as
= A/(3tanu+1)+B/(3tanu-1)+C/(3tan²u+1) where A, B, and C are constants to be determined.
We now have 1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1).
Let's now set up the system of equations.
The first equation is
1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1)
Putting u=0, we get
A = 1/4
Putting u =pi/3, we get
B=1/4 Putting
u = arctan(1/√(3)), we get C=1/2. Now that we have A, B, and C, let's substitute them back to our integral.
We have
= ∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
= (1/4)∫(1)/(3tanu+1) du + (1/4)∫(1)/(3tanu-1) du +(1/2)∫(1)/(3tan²u+1) du
Let's now solve the integral and simplify.
= ∫(1)/(3tanu+1) du
= (1/6)ln|3tanu+1|- (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
Similarly,
= ∫(1)/(3tanu-1) du
= (-1/6)ln|3tanu+1|+ (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
The third integral we can solve by substitution
v = √(3)tanu.
We then get
= ∫(1)/(3tan²u+1) du= (1/√(3))∫(1)/(v²+3) dv
= (1/sqrt(3))arctan(v/√(3))
= (1/√(3))arctan((√(3)tanu)/√(3)).
We can now put back all the values to get the solution.
= ∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²)]dx
= (1/3)∫ [(1+cos u)+u⁵]/(9tan²u+1) du
=(1/3)[(1/4)(ln|3tanu+1|- ln|3tanu-1|+ 2arctan (3tanu))+(1/4)(-ln|3tanu+1|+ ln|3tanu-1|+ 2arctan (3tanu))+(1/2)(1/√(3))(arctan((sqrt(3)tanu)/√(3)))]+ C
We can simplify the above expression to get
=- ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x²)]dx
= (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C
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These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
5 cm
Surface Area = [? ] cm2 Surface Area = 111 cm?
Answers
9514 1404 393
Answer:
17.8 cm²
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of the linear dimensions. The small/large linear dimension ratio is 2/5, so the surface area of the smaller cone is ...
A = (2/5)²(111 cm²) = 17.76 cm²
The area of the smaller cone is about 17.8 cm².
Answer: [tex]17.8 cm^{2}[/tex]
How do I solve for the missing side lengths. My sender has to be as a radical in simplest form.
Answers
Answer: 6√6
Step-by-step explanation: When an angle is 45 degrees in a triangle it is actually half a square (I know right!!!), so, therefore, the other side length will also be 6, and then using the Pythagorean theorem we get the hypotenuse to be 6√2. Now, when an angle is 60 degrees in a triangle it is actually half an equilateral triangle (I know right!!!), so, therefore, the other side length will be double the length, 12√2, and using the Pythagorean theorem we get the side length x to be 6√6! Hope this helps!
1 Consider a tournament between N teams, each team playing each of the other teams. We can represent the results of this tournament by a directed graph: node i represents team i, and an edge exists i+jif team i beat team j. The above problem suggests that it may be impossible to declare an absolute winner, as everyone may be beaten by somebody. We could relax this slightly in the following way: let's call team i a k-winner if there is a group of k-many teams that were each beaten by team i. Other teams may have beaten team i, but there is at least a group of size k that was roundly beaten by i. 3) If the results of each game are decided by fair coin flip, what is the probability that a given team i is a k-winner? (5 points) 4) Using result 3.0, bound the probability that there exists a k-winner in a tournament of size N? Write it nicely as you can but don't beat yourself up too much with it. (5 points) 5) For N = 100, what is the smallest k that 3.4 indicates the probability of having k-winners is less than 1? Code or Mathematica to evaluate your answer in 3.4 is fine. (5 points) 6) For N = 100 and k as in 3.5, argue that there exist possible tournaments with no k-winners. (5 points) Bonus: Using the Chernoff bound to bound the relevant probabilities, show that for a > 1/2 the probability of there being any oN-winners goes to 0 as No. Conclude therefore that there erist tournaments without a N-winners, for all sufficiently large N. (10 points)
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The analysis involves calculating probabilities, bounding the probabilities based on worst-case scenarios, and considering the implications of the Chernoff bound to demonstrate the existence of tournaments without a certain number of winners.
In a tournament between N teams, where each team plays each other, the concept of a k-winner is introduced. A team i is considered a k-winner if there is a group of k teams that were each beaten by team i. The probability that a given team i is a k-winner can be calculated when the results of each game are decided by a fair coin flip. This probability depends on the number of teams and the specific value of k.
Using this probability for a given team, we can bound the probability that there exists a k-winner in a tournament of size N. This bound takes into account the probabilities of individual teams being k-winners and considers the worst-case scenario.
For a specific value of N, such as N = 100, we can determine the smallest k for which the probability of having k-winners is less than 1. This can be done by evaluating the probabilities for different values of k until the desired condition is met.
When N = 100 and k is determined as in the previous step, it can be argued that there exist possible tournaments with no k-winners. This can be demonstrated by constructing specific scenarios or by analyzing the probabilities of different outcomes.
Using the Chernoff bound, it can be shown that for a value a greater than 1/2, the probability of having any oN-winners (where oN is an arbitrary constant) goes to 0 as N approaches infinity. This conclusion implies that there exist tournaments without N-winners for sufficiently large values of N.
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plz answer I will mark brainlest
Answers
Since you know y = -2x-6, you can easily plug into the other equation
2(-2x-6) = - 4x - 12
-4x - 12 = -4x - 12
True
Infinitely many solutions
Answer:
(-3,0)
Step-by-step explanation:
y=-2x-6 and 2y=-4x-12
=-2x-6
Solution is
(-3,0)
Find the volume of the cylinder. Use 3.14 for T.
height of 3 radius of 3
Answers
Answer:
84.82
Step-by-step explanation:
π·32·3≈84.823
Answer:
The volume of a cylinder with a height of 3 and a radius of 3 is 84.823 or you could say 84.8.
Step-by-step explanation:
Figure 222 is a scaled copy of Figure 111.
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
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Answer:
if im corect the anwser is 3.14 (Side note) this is the wrong question i was anwsering to
Jasmine bought four potted plants. Two of the plants cost $6.65, and the others cost $4 and $7.15. How much money did jasmine spend in all?
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Answer:
$24.45
Step-by-step explanation:
6.65 + 4 + 7.15 + 6.65 = 24.45
Can someone plzzz helppp meee!!!
Answers
Answer:
Step-by-step explanation:
Find the general solution to the homogeneous system of DE: -11 x' = Ax where A = [-26 41 Hint: Write your answer x(t) in the form of eat [cos(ht) + sin(bt)].
Answers
The general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
To find the general solution to the homogeneous system of differential equations -11x' = Ax, where A = [-26 4; 1 1], we first need to find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| -26-λ 4 |
| 1 1-λ |
Expanding the determinant, we have:
(-26-λ)(1-λ) - 4 = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -7
λ₂ = -20
Next, let's find the corresponding eigenvectors.
For λ₁ = -7:
(A + 7I)v₁ = 0
| -19 4 |
| 1 8 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 4 |
|-1 |
For λ₂ = -20:
(A + 20I)v₂ = 0
| -6 4 |
| 1 21 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 2 |
|-1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
Substituting the values of the eigenvalues and eigenvectors, we get:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
Simplifying this expression, we get:
x(t) = | 4c₁ * [tex]e^{(-7t)[/tex] + 2c₂ * [tex]e^{(-20t)[/tex] |
|-c₁ * [tex]e^{(-7t)[/tex] - c₂ * [tex]e^{(-20t)[/tex]) |
Therefore, the general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
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Tema: valor numérico de expresiones algebraicas
A= 2
B= 1
X= 3
Y= 5
Z= -3
Answers
Answer:
1. 61
2. -8
3. 731
4. -16
5. -5
Step-by-step explanation:
Solve.
t
8.4=
1.5
=
Help plzzzz
Answers
Answer:
t = 12.6
Step-by-step explanation:
8.4 x 1.5 = 12.6
to check it, do 12.6 ÷ 1.5 = 8.4
find the area of the triangle
Answers
six and fifty-three hundredths as a decimal-
Yes, I'm D-U-M-B!
Answers
Answer:
6.58
Step-by-step explanation:
ahahahaha lol
Answer:
6.58
i hope this helps:)
Step-by-step explanation:
brainliest please?
the area is ___ square units
Answers
Answer:
12 units²
Step-by-step explanation:
The height is 2, and the width is 12.
Now multiply and that gives us 24. But that's not the full answer.
Since a triangle's area is half of a square, we divide by 2, leaving us with 12. (plus the label which is units²)
Please help !
50 points !
Use the quadratic regression feature of a graphing calculator to find a quadratic model. Round to the nearest hundredths place.
A. Y=0.06x^2+0.31+4
B. Y=-4.03x^2+0.32x+8.19
C. Y=0.06x^2-0.31x-4
D. Y=4.03x^2-0.32x-8.19
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Answer:
It is A
Step-by-step explanation:
Answer:
its A he's right
Step-by-step explanation:
A concrete slab has the dimensions 4 yd by 2 yd by 1.2 yd. What is the volume of 40 of these concrete slabs
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The volume of 40 of the concrete slabs given the dimensions of one concrete slab is 384 yd³.
What is the volume of one concrete slab?The concrete slab has the shape of a rectangular prism. So, the volume of a rectangular prism would be used to determine the volume of the concrete slabs.
Volume of one concrete slab = length x width x height
4 x 2 x 1.2 = 9.6 yd³
Volume of 40 concrete slabs = 40 x 9.6 = 384 yd³
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How do you find the greatest common denominator, when comparing two numbers? Explain your thought process, in the example I provided. What is the greatest common Denominator for the numbers 20 and 40. Explain each step you do. Your answer will start with these words. "How to find the the greatest common denominator between 20 and 40?
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Answer:
20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.
3. A runner sprints 50 ft each day for 7 days. How many inches does she sprint during this week? (Again please hurry)
Answers
Answer: The runner will sprint 4,200 inches during this week
Step-by-step explanation:
50 * 7 = 350
350 * 12 = 4200
Answer:
It's 4200in
in feets its 350ft
Step-by-step explanation:
Please help, i need it done by today,
Answers
Answer:
x= 28
do i have to explain
Step-by-step explanation:
Can someone help me please ASAP? Correct answer gets brainliest!! :)
Answers
Answer:
Blank 1: 6
Blank 2: 30
1/2 = 6/12 = 30/60
Blank 3: 30
1/4 = 3/12 = 15/60
x-4.88=-5.78
solve for x
Answers
Answer:
-0.9
Step-by-step explanation:
Answer:
x =-.9
Step-by-step explanation:
x-4.88=-5.78
Add 4.88 to each side
x-4.88+4.88=-5.78+4.88
x =-.9
The proportion of students who fail the comprehensive statistics final had been 4%. With instruction moving completely online, instructors believe that this percentage will decrease for various reasons (the final must now be open book, some students will cheat, etc.). To test their claim, the appropriate test is
paired t test
z test for two proportions
t test for one mean
z test for one proportion
one-way ANOVA
Answers
The appropriate test to investigate whether the proportion of students failing the comprehensive statistics final has decreased with the shift to online instruction is the z test for two proportions.
Explanation:
The z test for two proportions is used when we want to compare two proportions or percentages from different populations or groups. In this case, we want to compare the proportion of students who fail the statistics final before and after the instruction moved online.
To conduct the z test for two proportions, we follow these steps:
1. Define the null hypothesis (H₀) and alternative hypothesis (H₁). In this case, the null hypothesis would be that the proportion of students failing the final is the same before and after the instruction moved online, while the alternative hypothesis would be that the proportion has decreased after the shift to online instruction.
2. Collect data on the number of students who fail the statistics final before and after the shift to online instruction.
3. Calculate the sample proportions for each group. Let's denote the proportion before the shift as p₁ and after the shift as p₂.
4. Calculate the standard error (SE) of the difference between two proportions using the formula:
SE = sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))
where n₁ and n₂ are the sample sizes for the two groups.
5. Calculate the test statistic (z) using the formula:
z = (p₁ - p₂) / SE
6. Determine the critical value for the desired significance level (e.g., 0.05) and compare it to the calculated test statistic. If the calculated test statistic falls within the critical region, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
7. Interpret the results and draw conclusions about whether there is sufficient evidence to support the claim that the proportion of students failing the statistics final has decreased after the shift to online instruction.
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The quotient of a number more than 1 and 3 is 5
Answers
Answer:
https://brainly.com/question/13518166
Step-by-step explanation:
how do you find the radius when given the volume and height?
Answers
Answer:
Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume. SOO just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation.
Step-by-step explanation:
brainliest?
what is the value of x ?
Answers
Step-by-step explanation:
The line JK is tangent to the circle h so <KJH is a right angle.
[tex]a^2+b^2=c^2[/tex]
[tex]15^2+20^2=x^2[/tex]
[tex]625=x^2\\x=25[/tex]
Hope that helps :)
сть
b
d
a
If mza = 2.m2b, mzc = 60', and the right angles are labeled in the figure, which of the following
produce an acute angle? Select all that apply
Answers
Answer:
a and c
Step-by-step explanation:
Please help me in it! It's very difficult, i'm in 6th and I still don't understand this. Please, help me in this!!!
Answers
Answer:
40
where the line starts (75) and ends (115)
115-75=40
thats the quick way to solve... hope this helps!
Step-by-step explanation:
Brainliest?
Find the formula for the nth term in this arithmetic sequence a1=0 a2=.5 a3=1 a4=1.5
Answers
Answer:
Step-by-step explanation:
The arithmetic sequence usually write as [tex]a_{n}=a_{1} +(n-1)d[/tex], where a1 is the first term and d is a common difference.
[tex]a_{n} = a_{1}+(n-1)d\\a_{n} = 0+(n-1)0.5\\[/tex]
An element with a mass of 700 grams decays by 6.1% per minute. To the nearest
tenth of a minute, how long will it be until there are 220 grams of the element
remaining?
Answers
Answer:
11.2 minutes
Step-by-step explanation:
If the element decreases by 6.1, every minute, it means that the mass lost every minute = 0.061 x 700g = 42.7g
The mass remaining after a minute = 657.30g
The equation that can be used to solve this question is :
700 - 42.7m = 220
m = minutes
Collect like terms
700 - 220 = 42.7m
480 = 42.7m
divide both sides of the equation by 42.7
m = 11.241218 minutes
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Here, the hundredth is less than 5, so zero would be added to 2. the answer is 11.2 minutes
Answer:
18.4
Step-by-step explanation:
I answered the question