Answers
Step-by-step explanation:
∫ 9 arctan(1/x) dx
If u = 9 arctan(1/x), then:
du = 9 / (1 + (1/x)²) (-1/x²) dx
du = -9 dx (1/x²) / (1 + (1/x²))
du = -9 dx / (x² + 1)
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ln(x² + 1)
Evaluate from x=1 to x=√3.
[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]
[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]
(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)
(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)
(6π√3 − 9π)/4 + 9/2 ln(2)
Answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Step-by-step explanation:
We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].
Now let's say that u = arctan(1/x). The value of 'du' would be as follows:
du = - x / (1 + x²) * dx
If we apply integration by parts, v = 1, and of course u = arctan(1/x):
=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]
Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':
=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx
=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du
=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du
=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )
=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |
So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;
[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]
Now computing the boundaries we have the following answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Related Questions
In a triangle, the sum of the measures of the first two angles is 12 less than the measure of the third angle. In addition, the measure of the first angle is twice as big as the measure of the second angle. Create and solve a system of linear equations to represent this situation. Then select the true statement.
А. The solution to this system is nonviable because it results in a negative angle measure.
B. The solution to this system is nonviable because it results in too large of an angle measure.
C. The solution to this system is viable.
D. The solution to this system is nonviable because it results in fractical values for the angle measures.
Answers
the sum of the internal angles of a triangle are equal to 180 degrees.
once i remembered that the problem became a lot easier.
let a, b, and c be the angles of the triangle.
-----
let a = 2*b
-----
let c = a+b-12
-----
the above two statements are given.
since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is
-----
a + b + c = 180
-----
we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.
-----
it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.
-----
since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.
that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.
looking at the equation c = a + b - 12, we solve for b as follows:
since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.
-----
the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.
we can substitute 3*b - 12 for c and the equation becomes
3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.
dividing both sides of the equation by 6 and we get b = 32 degrees.
-----
we have b = 32 degrees.
we have a = 2 * b so a = 64 degrees.
we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.
-----
substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.
-----
answer is:
a
Mickey used these calculations to find how much he would spend on 7 cartons of eggs, if 12 cartons of eggs cost $22.20. Describe his error.
12 cartons(÷22.20)
$22.22(÷22.20)
Unit price = $0.54
$0.54(7) = $3.78
Answer ; Mickey set up the equivalent rate wrong. The cartons of eggs should be in the denominator, because you need to find the unit price for 1 carton of eggs.
Answers
Answer: you would divide the total price of $22.20 by the amount of cartons, which is 12, giving you the unit rate of $1.85 per carton. the unit rate, $1.85 multiplied by 7 is $12.95, so it would cost $12.95 for 7 cartons of eggs
Step-by-step explanation:
Answer:
Step-by-step explanation:
the person up is right
1) Identify the volume of a rectangular pyramid with length 16 m, width 12 m, and height 17 m. 2) Identify the volume of a regular hexagonal pyramid with base edge length 8 in. and height 10 in. rounded to the nearest tenth. PLEASE HELP
Answers
Answer:
First problem: 1088 [tex]m^{3}[/tex]
Second problem: 554.3 [tex]m^{3}[/tex]
Step-by-step explanation: Please see the images below!
The volumes of both the pyramids are 1088 m³ and 554.3 in³.
What is volume?The volume of a shape or solid is the space occupied by it, which also includes its height or depth.
a) To find the volume of the pyramid, first calculate the area of the base.
B = lw
Substitute 16 for l and 12 for w.
B = 16 ⋅ 12
Simplify.
B = 192 m²
To find the volume of the pyramid, use the formula for the volume of a pyramid.
V = 1/3 Bh
Substitute 192 for B and 17 for h.
V = 1/3 ⋅ 192 ⋅ 17
Simplify.
V = 1088 m³
Therefore, the volume of the rectangular pyramid is 1088 m³.
b) Similarly for the volume of a regular hexagonal pyramid with base edge length 8 in. and height 10 in.
Base area = 96√3 in²
Volume = 1/3 × 96√3 in² × 10 in
= 554.3 in³
Hence, the volumes of both the pyramids are 1088 m³ and 554.3 in³.
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The rule (x, y) → (-X, -y) maps A RST to A R'S'T',
Which statement correctly describes the relationship between ARST and A R'S'T'?
The triangles are congruent because AR'S'T' is a rotation of ARST, and a rotation is a rigid motion.
The triangles are congruent because AR'S'T' is a translation of ARST and a translation is a rigid
motion
The triangles are not congruent because AR'S'T' is a translation of ARST, and a translation is not a
rigid motion
The triangles are not congruent because AR'S'T' is a rotation of A RST, and a rotation is not a rigid
motion
Answers
Answer:
A
Step-by-step explanation:
These triangles are first off congruent, because the only value that is changing, is the negative sign in front.
This negative sign means that the triangle is being rotated to a different quadrant of the graph, so the answer is A.
I need help on this assignment
Answers
Answer:
11. X'( 1 , 6 )
12. Y'( 5 , 1 )
13. Z'( 6 , 4 )
14. X"( -1 , -6 )
15. Y"( -5 , -1 )
16. Z"( -6 , -4 )
Only had time for the coordinates-!
1. What percent of 29 is 3?
Answers
Answer:
0.34%
Step-by-step explanation:
1. Start by representing the percentage with the variable, x %. Using x%, create an algebraic expression.
29% X x = 3
2. Solve for x by dividing both sides by 29.
29x divided by 29 =3 divided by 29.
x=0.1034
3.Convert 0.1034 into a percentage by multiplying the decimal by 100%
X =0.1034 x 100%
x=10.34%
Identify the domain and range of the function. Enter your answers as numbers in the boxes; do not include units. Enter the range values in ascending order separated by commas inside the curly brackets. Age Admission Price under 5 free 5-17 $25 18-64 $40 65 and over $35 What is the range?
Answers
Answer:
When we have a function y = f(x)
The set of the possible values of x is called the domain, and the set of the possible values of y is called the range.
In this case, we have:
x = age, and y = price.
x y
< 5 $0
5 - 17 $25
18 - 64 $40
≥ 65 $35
Then the range is the possible age of the customer, and it goes for all the possible ages (as whole numbers)
So the domain will be the set of all the positive integers:
D = {1, 2, 3, 4, 5, ...}
(of course, we can not have an age equal to 1300 or infinity, but we really can not cap the domain)
The range is the possible values of y, in this case is discrete, because we have only 4 possible prices, so the range is:
R = {$0, $25, $40, $35}
Can someone rewrite the expression x^2 * x^-12 in the form of x^n. Pleasee
Answers
Answer:
x^ -10 or 1/x^10
Step-by-step explanation:
Anders has a total of 7 yards of ribbon. He cuts the ribbon into 4 pieces of equal length. What is the length, in yards, of each piece of
ribbon?
NY
Answers
Help quickly please hurry i am almost done
Answers
Answer:
Might be wrong but i got c( NOPE NOT C ITS A
Step-by-step explanation:
Solve inequalities 5x>2x+6
Answers
Answer:
x>2
Step-by-step explanation:
5x>2x+6 Subtract 2x from 5x
3x>6 Divide 3 by 6
x>2
Answer:
B. April
Step-by-step explanation:
In a certain field, the ratio of pigs to sheep is 8 3 . If there are 165 pigs and sheep altogether in a field, how many sheep are there?
Answers
Answer:
440 I think haven't done these questions in a while.
Line q passes through points (9, 9) and (1, 2). Line r is perpendicular to q. What is the slope of line r?
Answers
Answer:
y=mx+b
Step-by-step explanation:
Here is the question 20 points and brainlest but I want a detailed answer
Answers
Answer:
18.75 sq.feet
Step-by-step explanation:
According to the question
1 card = 18 sq.in
150 cards = 150 * 18
= 2700 sq.in
= 18.75 sq.feet
a preschool student finds a big bag of cookies and begins to take the cookies from the bag and hide them in her cubbyhole. after hiding 3 cookies, she decides to keep count of how many cookies are actually in her cubbyhole. first there are 3 cookies. after pulling out more cookies, she then has 5 cookies, then 7 cookies, and then 9 cookies. however, she only knows how to count to 10! assuming she continues to pull cookies from the bag at the same rate indicated by the sequence of cookies above, how would the preschool student continue the pattern? describe the arithmetic sequence in this context.
Answers
Answer:She will count the cookies by 2's
Step-by-step explanation:
What is the range?
8,10, 60, 3, 5, 13, 12, 40, 8
Answers
explanation: to find the range you subtract the smallest value from the largest value in the set
How do
You Write 67 in expanded form
Answers
Answer:
sixty seven
Step-by-step explanation: i think
Answer:
60+7
Step-by-step explanation:
Solve the equation for the specified variable
S=gr-5gk*3, for g
Answers
Answer:
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
Step-by-step explanation:
Given
[tex]S=gr^{-5}gk*3[/tex]
Required
Solve for g
[tex]S=gr^{-5}gk*3[/tex]
Split into different entities
[tex]S=g * r^{-5}*g*k*3[/tex]
Reorder in terms of like terms
[tex]S=g*g * r^{-5}*k*3[/tex]
[tex]S=g^2 * r^{-5}*k*3[/tex]
[tex]S=g^2 * 3kr^{-5}[/tex]
Solve for [tex]g^2[/tex]
[tex]g^2 = \frac{S}{3kr^{-5}}[/tex]
Take square root of both sides
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
Solve the equation 1/4 (x+2)+5=-x
Answers
Answer:
Exact Form:
x=−225
Decimal Form:
x=−4.4
Mixed Number Form:
x=−4 2/5
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
1/4 (x-2) + 5 = x
1/4 (x-2) = x - 5
x - 2 = 4(x-5)
x-2 = 4*x + 4*-5
x-2 = 4x - 20
x - 4x = 2 - 20
-3x = -18
x = -18/-3
x = 6
Check:
1/4(6-2) + 5 = 6
1/4(4) + 5 = 6
1 + 5 = 6
Solve the equation. 25=9x+4-6x
Answers
Step-by-step explanation:
[tex]25 = 9x + 4 - 6x[/tex]
[tex]25 - 4 = 9x - 6x \\ [/tex]
[tex]21 = 3x[/tex]
[tex] \frac{21}{3} = x[/tex]
[tex]7 = x[/tex]
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:
[tex] \star{ \tt{ \: 25 = 9x + 4 - 6x}}[/tex]
[tex] \sf{Step \: 1 \: }[/tex] : Collect like terms
Like terms are those which have same base
[tex] \longmapsto{ \sf{25 = 3x + 4}}[/tex]
[tex] \tt{Step \: 2 \: }[/tex] : Swap the sides of the equation
[tex] \longmapsto{ \sf{3x + 4 = 25}}[/tex]
[tex] \tt{Step \: 3 \: }[/tex] : Move 4 to right hand side and change it's sign
[tex] \longmapsto{ \sf{3x = 25 - 4}}[/tex]
[tex] \tt{Step \: 4}[/tex] : Subtract 4 from 25
[tex] \longmapsto{ \sf{3x = 21}}[/tex]
[tex] \tt{Step \: 5}[/tex] : Divide both sides by 3
[tex] \longmapsto{ \sf{ \frac{3x}{3} = \frac{21}{3}}} [/tex]
[tex] \tt{Step \: 6}[/tex] : Calculate
[tex] \longmapsto{ \sf{x = 7}}[/tex]
The value of x is 7
Hope I helped!
Best regards! :D
~TheAnimeGirl
if there are 91 seats in 7 rows how many seats are in 4 rows
Answers
Answer:
It would be 52
Step-by-step explanation:
You divide 91 by 7 and u get 13 so u multiply that by 4 and u get your answer
In Seattle, WA, it is said to rain 66% of the time. Since there are 365 days in a year, approximately how many days is it expected To rain?
Answers
xdays is 66%
66x365 =24090
24090/100= 240,9
it’s expected to rain approximately 241 days
In a year with 365 days, it should rain for about 240 of those days for the given condition.
What is the percentage?It is the ratio of two integers expressed as a decimal fraction of a whole number. It is a statistic for contrasting two sets of data, and the % sign is used to describe it as a percentage. Percentages are often and creatively used. For instance, a lot of data is published as percentages in the media, including bank interest rates, retail discounts, and inflation rates.
It is supposed to rain 66% of the time in Seattle, Washington. Considering that there are 365 days in a year,
Suppose the number of days is it expected to rain obtained be x,
x=66% of 365
x=66/100 × 365
x=240,9 ≈ 240
Thus, it should rain for about 240 days.
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PLEASE HELP!! BEST ANSWER WILL BE MARKED BRAINIEST! The stadium is at (-2,3) and the high schools (1,8). What is the shortest driving distance (in blocks) between these two locations? Can you figure this out without looking a the grid
Answers
Answer:
Shortest distance is 5 blocks.
Answer:
5.8
Step-by-step explanation:
I'm not 100% on this as the decimal in the answer makes me doubt myself. Here's the explanation anyways
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points? It takes Aaron about 1 hour to mow 2 acres. Aaron’s rate for mowing lawns is 0.5 acres per hour. The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre.
Answers
Answer: Aaron’s rate for mowing lawns is 0.5 acres per hour
Step-by-step explanation:
Hope this helps!!
The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.
We have,
To determine the slope of the line passing through the points (3, 1.5) and (5, 2.5), we can use the slope formula:
Slope = (change in y) / (change in x)
Given the two points, we can calculate the change in y and the change in x:
Change in y = 2.5 - 1.5 = 1
Change in x = 5 - 3 = 2
Plugging these values into the slope formula:
Slope = 1 / 2 = 0.5
The slope represents the rate of change of the y-coordinate (area) with respect to the x-coordinate (time).
In this case, a slope of 0.5 means that for every hour it takes Aaron to mow a lawn (change in x), the area mowed (change in y) increases by 0.5 acres.
Therefore,
The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.
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31-X + (2 x + 1)] = x - 1.
X =
Answers
Answer:
answer is X= 2/1 ×5+2 ok
12. At noon the temperature was 30 degrees Celsius. At night it becomes 25 degrees Celsius. How
many degrees warmer or colder did it get?*
(10
Answers
Answer:
5 degrees colder
Step-by-step explanation:
You take the starting point then subract the ending point and you get your answer. But in order to know if its colder or warmer is to know that the higher the number, the hotter, and the lower the number, the colder.
=5
so 5 is your answer
MATH please heeeeeeeeeeeeeelp
Answers
Answer:
0, they all equal 0
Basic Math - the property of 0:
The multiplication property of zero says that zero times any number is equal to zero.
Step-by-step explanation:
Solution:
6(1/6)-2+1+12x0 = anything times 0 = 0
6(1/6)-2+1+0 = 0
6(1/6)-2+1 = 0
1-2+1 = 0
-1+1 = 0
=0
translate this phrase into algebraic expression 23 increased by twice gali’s score use variable g represent gali’s score
Answers
Hey there! I'm happy to help!
We have twice Gali's score, which is 2 multiplied by g, which we can write as 2g.
We increase 23 by 2g, which means, we add.
23+2g.
Have a wonderful day! :D
Answer:
23+2g
Step-by-step explanation:
Let g = gali's score
[tex]twice \:gali\: score = 2\times g\\\\= 2g[/tex]
To increase = +
[tex]23 +2g[/tex]
Last week, Benjamin spent $82.80 on groceries and $132.48 on bills. The amount he spent on groceries
was 15% of his paycheck. What percent of his paycheck did Benjamin spend on bills?
Answers
Answer:
amount spend on groceries = 82.80
percent spend in groceries = 15%
let total paycheck be x
15%of x= 82.80
x=552
percent spend on bills = 132.48/552 = 24%
Step-by-step explanation:
what value of x the given expression is undefined x+4/x-4
Answers
Answer:
At x= 4 the given expression is undefined.
Step-by-step explanation:
In a given function , if the denominator becomes zero then the function is undefined.
Here, denominator is x-4 so at x = 4 it will become zero. So we can say that at x=4 , the function is undefined