Tried doing it myself multiple times , multi choice question, not getting any availabile answer.
Answers
Answer: The given integral is impossible to solve.
Step-by-step explanation: I tried solving it right now with integration by parts and trigonometric substitution, and I was unable to solve it.
So I looked at two math solvers and tried inputting the question, and it either says "There is nothing more you can do with this problem," or "We are unable to solve this problem."
First, let's substitute [tex]x=\frac w4[/tex] and [tex]dx=\frac{dw}4[/tex] to get rid of the fraction.
[tex]\displaystyle \int \csc^6\left(\dfrac w4\right) \cot^4\left(\dfrac w4\right) \, dw = 4 \int \csc^6(x) \cot^4(x) \, dx[/tex]
Recall that
[tex]\cot^2(x) + 1 = \csc^2(x)[/tex]
[tex]\dfrac{d}{dx} \cot(x) = -\csc^2(x)[/tex]
We can the rewrite the integrand as
[tex]\displaystyle 4 \int \csc^6(x) \cot^4(x) \, dx = 4 \int \left(\cot^2(x) + 1\right)^2 \cot^4(x) \csc^2(x) \, dx[/tex]
then substitute [tex]y=\cot(x)[/tex] and [tex]dy=-\csc^2(x)\,dx[/tex] to get
[tex]\displaystyle -4 \int (y^2 + 1)^2 y^4 \, dy[/tex]
Expand the integrand.
[tex]\displaystyle -4 \int (y^4 + 2y^2 + 1) y^4 \, dy = -4 \int (y^8 + 2y^6 + y^4) \, dy[/tex]
Now integrate with the power rule.
[tex]\displaystyle -4 \left(\frac{y^9}9 + \frac{2y^7}7 + \frac{y^5}5\right) + C[/tex]
[tex]\displaystyle -\frac{4y^9}9 - \frac{8y^7}7 - \frac{4y^5}5 + C[/tex]
Put everything back in terms of [tex]x[/tex], then [tex]w[/tex].
[tex]\displaystyle -\frac{4\cot^9(x)}9 - \frac{8\cot^7(x)}7 - \frac{4\cot^5(x)}5 + C[/tex]
[tex]\displaystyle \boxed{-\frac49 \cot^9\left(\dfrac w4\right) - \frac87 \cot^7\left(\dfrac w4\right) - \frac45 \cot^5\left(\dfrac w4\right) + C}[/tex]
Related Questions
Neil emptied his change jar and noticed he only had pennies, nickels, and quarters. He had coins for a total of . He had fewer quarters than nickels. How many pennies did Neil have? The solution is
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Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.
Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)
Hence:
0.1x + 0.05y + 0.25z = 4.6 (1)
Also:
x = 3y (2)
And:
z = y + 4 (3)
From the equations:
x = 18, y = 6, z = 10
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
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GEOMETRY
Surface area of a cube or a rectangular prism
There is a rectangular prism with a length of 8 yd, a width of 6 yd, and a height of 5 yd.
Find the surface area of this rectangular prism.
Be sure to include the correct unit in your answer.
Answers
SA = 2[8(6) + 6(5) + 8(5)]
SA = 2(48 + 30 + 40)
SA = 2(118)
SA = 236 square yards
Solve:
55) A pool is filling at 3 pts per min. How many gallons per hour is that?
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2 pints = 1 quart
4 quarts = 1 gallon
60 minutes = 1 hour
15 pints/minute x 60 minutes/hour x 1 quart/2 pints x 1 gallon/4 quarts = 112.5 gallons/hour
If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
OA) 3 blocks
OB) 4.4 blocks
OC) 5.4 blocks
OD) 15 blocks
Answers
Answer: C. 5.4 Blocks
Step-by-step explanation:
Given information
5 bags = 3 blocks
Set variable
Let x be the number of blocks
Constructure proportional equation
[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]
Cross multiply the fraction
[tex](3)~*~(9)~=~(5)~*~(x)[/tex]
[tex]27~=~5x[/tex]
Divide 5 on both sides
[tex]27~/~5~=~5x~/~5[/tex]
[tex]\Large\boxed{x=5.4~blocks}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
oc
Step-by-step explanation:
5 times .6 equals 3
9 times .6 equals 5.4
Write 80.54 as a mixed number.
Answers
Answer:
Step-by-step explanation:
[tex]80.54=80+0.54=80+\frac{54}{100} =80+\frac{27}{50} =80\frac{27}{50}[/tex]
The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?
The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
-----------------------------------------------------------------------------------------------
Answer on Edmentum is:
The y-intercept of the graph of y = x2 is shifted up 3 units.
Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.
Answers
The y-intercept of the graph of y = x2 is shifted up 3 units.
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the parent function f(x) = x^2
If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;
g(x) = f(x) + 3
g(x) = x^2 + 3
Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3
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The question is attached
Answers
Answer:
We call the denominator rational.
Step-by-step explanation:
For example:
[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]
It's clear that the denominator is now a rational number, not an irrational one anymore.
at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of the students participate in either sports or drama, what is the probability that a student participates in both sports and drama?
Answers
P( A Student participates in Both sports and Drama) =0.07
What is the probability?The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
To find the probability that a student participates in both sports and drama:
Let
A =Student participate in Sport
B = Student participate in Drama
Thus we have:
P(A) = 0.42
P(B) = 0.25
and
P(Ac and B or A and Bc) =0.53
P(Ac and B ) + P( A and Bc) =0.53
P(B) - P(A and B) + P(A) - P(A and B) = 0.53
0.25 - P(A and B ) + 0.42 - P(A and B) = 0.53
0.25+0.42 - 2 * P( A and B) = 0.53
0.67 - 2 * P(A and B) = 0.53
0.67 - 0.53 = 2* P(A and B)
0.14 = 2 * P(A and B)
0.14 / 2 = P( A and B)
0.07 = P( A and B)
that is:
P( A and B) = 0.07
P( A Student participate in Both sports and Drama) =0.07.
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The probability that a student participates in both sports and drama is [tex]0.14[/tex].
What is the formula for P(AUB), where A and B are any two events?If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.
Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].
We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].
By the above formula, we obtain:
[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]
Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].
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flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet-stream, the same jet travels 5360 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the jet stream?
Answers
Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:
In still air = 1,170 mphRate of wind = 170 mphWhat is the speed of the jet?The speed of the jet flying against the wind is:
= 3,000 / 3
= 1,000 mph
The speed with the jet stream is:
= 5,360 / 4
= 1,340 mph
Assuming the speed of the jet is x and the rate of wind is y, the formulas are:
x - y = 1,000
x + y = 1,340
Solving gives:
2x = 2,340
x = 1,170 mph
The rate of jet stream is:
x - y = 1,000
1,170 - y = 1,000
y = 170 mph
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ill give you brainliest :)
Answers
Following the instructions for the inequalities gives the following results:
1. 4<7, both sides multiplied by 7
= 28<49, both sides multiplied by 6
= 168<294, both sides multiplied by 3
= 504<882, both sides multiplied by 10
= 5,040<8,820
2. 11>2, add 5 to both sides
= 16>3, add 3 to both sides
= 19>9, add -4
= 15>5
3. -4<-2, subtract 6
= -10<-8, subtract 8
= -18<-16, subtract 2
= -20<-18
4. -8<8, divide by -4
= 2>-2, divide by -2
= -1<1
5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.
What are inequalities?Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.
Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.
Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.
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Select the correct answer.
Which statement is true about function f, which is shown in the graph?
ƒ(x) = -8x5 + 4x³ + 5x
Answers
Answer:
I think its A
Step-by-step explanation:
b) The diameter of a circular coin is 1.14 cm. How many coins of the same size are required to place in a straight row to cover 2.85 m length (without leaving any gap between each coin)
Answers
Answer:
250.
Step-by-step explanation:
if one coin covers 1.14 cm, then the required number can be calculated according the equality:
required_number=(given_length/given_diameter);
Then:
[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]
P.S. note, the given length is in [meter], the diameter is in [cm].
express 350 as a product of prime factors
Answers
Answer:
2^1 × 5^2 × 7^1 = 350
Step-by-step explanation:
2, 5, 7 are prime
first step is to divide the number 350 with the prime factor 2
continue dividing the number 175 by the next smallest prime factor
stop until you can't divide anymore
https://www.cuemath.com/numbers/factors-of-350/
URGENT!!!!!!
Use arrow notation to describe the translation of point P(–5, –4) to point P′(–8, –7).
Answers
The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:
(x,y) -> (x - 3, y - 3).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:
(x,y) -> (x - 3, y - 3).
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A bookstore carries 48 magazines. 75% of the magazines are women's magazines. How many women's magazines does the bookstore carry?
Answers
Answer:
36
Step-by-step explanation:
75/100
75/100=0.75
0.75*48 =36
(1 point) Find y as a function of x if
y" - 12y" + 32y' = 0,
y(0) = 5, y'(0) = 2, y" (0) = 1.
0
y(x) =
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y’(x)= 3x^2 + x + 2
y(x)= x^3 + 1/2x^2 + 2x + 5
which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle
Answers
Answer:
A, C
Step-by-step explanation:
See attached image.
Can u guys please give me the correct answe
Answers
Answer:
90°(the figure is poorly drawn)
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°120 ° and y are in a straight line, so 120° + y = 180 °
find y
180 - 120 = 60°
find x
180 - 60 - 30 = 90°
Which of the following are polynomials?
A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2
Answers
Answer: C, E
Step-by-step explanation:
These are polynomials by the definition of a polynomial.
Any helppppppp??????
Answers
First find volume of both the cylinders:
Cylinder Volume Formula: πr²h
(r => radius, h => height)
*Container A:
r = 8
h = 15
πr²h = π(8)²(15) = 960π³
*Container B:
r = 11
h = 13
πr²h = π(11)²(13) = 1573π³
What % of container B is empty after the pumping is complete?
The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:
[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)
Hope it helps!
Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350
Answers
Answer:
5,526
Step-by-step explanation:
Mean of scores = Total Value of Scores / Number of Values
= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]
= 5,526
Answer:5526
Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers
According to indical equation solve 3×=1\81
Answers
Answer:
x = - 4
Step-by-step explanation:
using the rule of indices
[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then
[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is
[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus
x = - 4
ALOT KF POINTS PLEASE HELP The measures of two exterior angles are given in the figure below.
Choose an equation that could be used to represent one of the exterior
angles and a logical conjecture about the exterior angles of a triangle.
Answers
An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
What is a triangle?The term triangle refers to a figure that has three sides. There are several types of triangles such as the;
Isosceles triangleScalene triangleRight angled triangleDespite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.
Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
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4. Simple Interest: An investment earned 4% simple interest for 8 years. At its maturity, it was worth $5000. What amount was invested? (3
Answers
Answer:
To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.
need heeeelp please
Answers
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
imageGiven: a = 2, b = 3, and c = 4. What is m measured angle C degree to the nearest tenth?
Answers
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
What is the measured angle C?From the law of cosines;
cosC = ( a² + b² - c² ) / 2ab
Where C is the angle C and a, b, and c are the three sides of the triangle.
Given the data in the question;
Side a = 2Side b = 3Side c = 4Angle C = ?Using law of cosine;
cosC = ( a² + b² - c² ) / 2ab
We substitute the values into the equation.
cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )
cosC = ( 4 + 9 - 16 ) / ( 12 )
cosC = -3 / 12
cosC = -0.25
We find the inverse of cosine.
C = cos⁻¹( -0.25 )
C = 104.477°
C = 104.5°
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
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A data set has a mean of x = 75 and a standard deviation of 11.4. Find the z-score for each of the following.
Answers
Part (a)
[tex]z=\frac{85-75}{11.4} \approx \boxed{0.88}[/tex]
By similar logic, the answers to the other parts are
(b) 1.75
(c) -2.19
(d) 0
What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT
Answers
Answer:
-1
Step-by-step explanation:
0.35 - 0.8 = -0.45
-0.1 - 0.35 = -0.45
-0.55 - 0.45 = -1
Ms. Oshiro teaches her 27 students to make folded-paper birds. Each student can make about 2 birds in 1 minute. About how many birds can all the students make in 55 minutes? A 3,000 B 1,500 C 100 D 60
Answers
Answer:
The answer is 2970
Step-by-step explanation:
Collectively, all the students can make about 54 books rds per minute (27 * 2)
Therefore in 55 minutes there should be 2970
(54*55) :)
One circle has a circumference of 12x cm. Another circle has a circumference of 32x cm. What is the ratio of the
radius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1
Answers
Answer:
3 :8
Step-by-step explanation:
12 : 32 = 3:8
I believe that is right.
