After integrating the expression [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex] we will get the value as: [tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]
Integration by parts, also known as partial integration, is a technique used in calculus and more widely in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.
The integration of the result of two functions is the integration by parts. Typically, the two functions are shown as f(x) and g. (x). The first function, f(x), is chosen from the two functions in such a way that its derivative formula exists, while the second function, g(x), is chosen in such a way that its integral formula exists.
∫ f(x).g(x).dx = f(x) ∫ g(x).dx - ∫(f'(x) ∫g(x).dx).dx + C
We have, [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]
We know that
[tex]\frac{1}{x}=arccot(x) \\I=5 \int_1^{\sqrt{3}} arccot(x) dx[/tex]
Integrating by parts
[tex]$$\int f g^{\prime}=f g-\int f^{\prime} g$$[/tex]
let us assume that,
[tex]$\quad f=\cot ^{-1}(x) \quad g^{\prime}=1$[/tex]
[tex]$I=5 \int_1^{\sqrt{3}} \cot ^{-1}(x) d x$[/tex]
[tex]$I=5\left[x \cot ^{-1}(x)-\int \frac{-x}{x^2+1} d x\right]$[/tex]
[tex]$I=5\left[x \cot ^{-1}(x)+\frac{1}{2} \ln \left|x^2+1\right|\right]_1^{\sqrt{3}}$[/tex]
[tex]$I=5\left[\left(\sqrt{3} \cot ^{-1}(\sqrt{3})+\frac{1}{2} \ln |4|\right)-\left(\cot ^{-1}(1)+\frac{1}{2} \ln |2|\right)\right]$[/tex]
[tex]$I=5\left[\frac{\sqrt{3} \pi}{6}+\ln 2-\frac{\pi}{4}-\frac{1}{2} \ln |2|\right]$[/tex]
[tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]
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The correct question should be:
Evaluate the integral [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]
A can of soup has the shape of a cylinder.
The diameter of the base of the can is
3.4 inches, and the height of the can is
4.5 inches. What is the volume of the can
rounded to the nearest tenth of a cubic
inch?
Answer:
Step-by-step explanation:
Height h = 4.5 inches
Radius r = 3.4/2 = 1.7 inches
Area of base = πr² = 2.89π square inches
Volume of cylinder = πr²h = 2.89π4.5 = 13.0 cubic inches
Answer:
The answer is 40.8
Step-by-step explanation:
The volume of a cone equals the area of a circle multiplied by the height
[tex]v = \pi \times {r}^{2} \times h \\ = 3.14 \times 1.7 \times 1.7 \times 4.5 \\ = 40.8[/tex]
Is A PQR-AXYZ? If so, name which similarity postulate or
theorem applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
D. Cannot be determined
Step-by-step explanation:
Similarly between given triangles can not be determined because given information are insufficient.
The correct option for the given triangles is D. Cannot be determined
What are similar triangles?Any two triangles will be considered as similar as they have congruent corresponding angles and the corresponding sides are in equal ratios.
Two shapes are Similar when one can become the other after a resize, flip, slide or turn.
Given are two triangle PWR and XYZ we need to determine whether they are similar or not,
So, we only have measurement of a pair of sides and measurement of an angle,
We have some similarity rules by which we can prove two triangles to be similar, they are :-
AA rule, Side Angle Side (SAS), Side Side Side (SSS) and Right-angle Hypotenuse Side (RHS)
Since, we do not enough information to conclude our discussion.
Hence, the correct option is D. Cannot be determined
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Verify that the given segments are parallel.
Answer:
Step-by-step explanation:
M and N and QR
Find the solution of y = –2x + 3 for x = 2.
A. (7, 2)
B. (2, [tex]\frac{1}{2}[/tex])
C. (2, –1)
D. (2, –10)
Write an integer for this situation: 5 feet below sea level
Given A=
What is the value of matrix B if A + B = C
Answer:
A
Step-by-step explanation:
We know that 8+3x= x
solve for x
8= -2x
-4 =x
The only answer that has -4 is A
A store pays $11 for a set of spoons and marks the price up by 30%. What is the amount of the markup?
Answer:
[tex]\$3.3[/tex]
Step-by-step explanation:
Given:
Amount paid by a store for a set of spoons = $11
Percentage increase in price = 30%
To find: amount of the mark up
Solution:
To find amount of the mark up, find 30% of (amount paid by a store for a set of spoons)
Amount of the mark up = [tex]\frac{30}{100} (11)=\$3.3[/tex]
5 examples of theorems in math. :")
Madison is starting her own sewing business. Madison has calculated that she needs to earn $840 per week to support her family. If she knows she will only be able to work 75 hours per week, what is the minimum amount of dollars per hour that she will need to charge her customers?
Answer:
$11.20 per hour
Explanation:
x = dollars per hour
75x = 840
x = 11.20
three times the cost is 24$.
Answer:
72
Step-by-step explanation:
24 x 3 = 72
20 x 3 = 60
4 x 3 = 12
60+12= 72
You are going on an expedition to dig for dinosaur fossils. In digging you come across a small trunk left by another archeologist. In the trunk is a paper that lists how deep you need to dig to reach dinosaur fossils. Unfortunately, something spilled on part of the paper and it is damaged.
Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.
If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.
Answer:
200,000 feet to dig
Step-by-step explanation:
We use a ratio for this problem
30,000 200,000,000
----------- = ---------------------
30 x
200,000,000 * 30
---------------------------- = 200,000 feet to dig
30,000
This answer is reasonable because 200,000,000 years ago was a long time ago so then the person must dig a reasonable amount of dirt. So then 200,000 feet is reasonable.
What is 73 x 4 + 13?
Answer:
73 x 4 + 13 is 305
Answer:
305
explaination:
73 x 4 = 292
292 + 13 = 305
what is the distance between-2 and -5 on the number line?
Answer:
3
Step-by-step explanation:
on a number line, we use the absolute values to find the difference.
the absolute value of -2 is 2
the absolute value of -5 is 5
5-2=3
so, the distance between -2 and -5 on a number line is 3
3/10 divided by 2/5?
Answer:
3/4 is your answer
Step-by-step explanation:
‘Find the value and figure of B’
Answer:
b = 12 in
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + b^2 = c^2
b^2 + 9^2 = 15^2
b^2 = 225 - 81
b^2 = 144
b = 12
Answer: b = 12 in
1. Does the system of linear equations shown below have a solution? Explain.
Answer:
hb Step-by-step explanation:
The student council is selling carnations for Valentine's Day. Two different shops can provide these flowers. . Gracie's Flowers charges a $5.00 fee per order plus $0.75 per carnation Ben's Blooms charges a $10.00 fee per order plus $0.25 per carnation for an order. Gracie tells you the equation that would work with her shop: Using c to represent the total cost for an order of carnations and n to represent the number of carnations in the order, her equation is c=0.75n + 5.00 Ben is not sure how to write the equation for his shop. Fill in the following blanks to help him: C = nt
9514 1404 393
Answer:
c = 0.25n +10.00
Step-by-step explanation:
The form of the equation is ...
c = <cost per carnation>n + <fixed fee>
For Ben's shop, the equation would be ...
c = 0.25n + 10.00
A newsstand seller sold a total of 68 magazines and newspapers, which brought in a total of $199 on a certain day. Newspapers sell for $2 per copy and magazines sold for $5 per copy. How many magazines were sold on that day?
Answer:
21
Step-by-step explanation:
Using inequality to solve this question, we say
Let the total number of newspapers sold be x
Let the total number of magazines sold by y
x + y = 68
Suppose 1x = $2 and 1y = $5, then
2x + 5y = $199
Solving both as a simultaneous equation, we get that
2(68 - y) + 5y = $199
136 - 2y + 5y = $199
136 + 3y = $199
3y = 199 - 136
3y = 63
y = 63/3
y = 21
Then solving for x, we have
x + 21 = 68
x = 68 - 21
x = 47
Therefore, a total of 21 magazines were sold that day
15 POINTS! PLEASE HELP ASAP! WILL GIVE BRAINLIEST!
Determine a series of transformations that would map Figure G onto Figure H. I need help ASAPPP PLEASEEE
Answer:
A translation followed by a rotation would do it if they are congruent, which they should be.
Step-by-step explanation:
A transformation to move the corresponding points of each shape to the other, and a rotation to rotate the shape until the shapes map onto each other.
Can you conclude that these triangles are congruent?
Yes or no
Answer:
Yes
Step-by-step
If there flipped then they’re congruent
Answer:
Yes
Step-by-step explanation:
Here we get two triangles,
In triangle MNH. In triangle JKH
Can someone pls help me with this?? I’m in a rush it’s due at 11:59 pm..pls help! And show work pls and thx
Answer:
D. 4.5
Step-by-step explanation:
<3
Answer:the answer will be D)4.5
Step-by-step explanation:
AB, BC and CD are three sides of a regular polygon with centre o.
ABX is a straight line.
Angle BCD = 140°
0 Calculate the size of each of the angles marked v, w, x, y and z.
Pls help 10 points
Answer:
Step-by-step explanation:
Since, BC and DC are the sides of a regular polygon,
m(DC) = m(BC)
Opposite angles of these equal sides will be equal in measure.
m∠DBC = m∠CDB = v
By triangle sum theorem,
m∠DBC + m∠CDB + m∠DCB = 180°
v + v + 140° = 180°
2v = 40°
v = 20°
Since angle 'x' is an exterior angles of ΔBCD,
x = m∠BDC + m∠CBD [By the property of exterior angles]
x = v + v
x = 40°
Since, angles v, w and x are the linear angles,
v + w + x = 180°
20° + w + 40° = 180°
w = 120°
Since, measure of exterior angle = [tex]\frac{360}{n}[/tex]
n = Number of sides
40° = [tex]\frac{360}{n}[/tex]
n = 9
Sum of angles formed at the center by joining vertices of the polygon = 360°
Measure of each angle at the center of a polygon with 9 sides = [tex]\frac{360}{9}[/tex]
= 40°
Since, z = 3 × (Measure of central angle formed at the center)
= 3 × 40°
= 120°
In ΔOAB,
m∠OAB + m∠OBA + m∠AOB = 180°
y + y + 40° = 180° [m∠OAB = m∠OBA, Opposite angles of the equal sides OA and OB]
2y = 140°
y = 70°
The measure of an angle is 89. Find the measure of its supplement
Step-by-step explanation:
Supplementary angles are equal to 180°. To determine the supplement of any angle, subtract the given angle from 180°.
[tex] \text{Supplement \: of \: 89 \: \degree = 180 \degree - 89\degree = \boxed{ \bold{ \text{91\degree}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
# [tex] { \underbrace{ \text{Carry \: On \: Learning}}}[/tex] !! ✎
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6*10^5 is how many times as large as 3*10^3
So is 0.147 a rational number?
Answer:
Yes because it is a terminating decimal.
Step-by-step explanation:
The area of a rectangle is 2x^2-11x+15 square feet. The length of the rectangle
is 2x - 5 feet. What is the width of the rectangle?
A) W = x + 5
B) W = x-1
C) W = x-3
D) W = 2x-5
Answer:
A
Step-by-step explanation:
The perimeter of a rectangular plot of land is 250 meters if the. Length of one side of the plot is 40 meters what is the area of the plot in square meters?
Answer:
3400 meters squared
Step-by-step explanation:
So if you know that one side 40 another has to be to. So those 2 sides add up to 80. 250-80= 170. Next, you divide 170 by 2 and get 85. Then you just multiply 40 by 85.
Need help ASAP I’m on an exam there is a timer
Thankss + BRAINLIST only for correct answer
(question in the picture )
Answer:
it should be D
Step-by-step explanation:
Because shes going back home.
Which side lengths represent the sides of a right triangle?
A)
1, 1, 2
B)
2, 3,5
C)
5, 12, 13
D)
7, 23, 25
Answer: the answer is C
Step-by-step explanation:
My friend is a math teacher
Hope this helps