Answer:
[tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
Integrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {x \ln x} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = \ln x[/tex][u] Logarithmic Differentiation: [tex]\displaystyle du = \frac{1}{x} \ dx[/tex]Set dv: [tex]\displaystyle dv = x \ dx[/tex][dv] Integration Rule [Reverse Power Rule]: [tex]\displaystyle v = \frac{x^2}{2}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \int {\frac{x}{2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \frac{1}{2} \int {x} \, dx[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \int {x} \, dx \bigg)[/tex][Integral] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \frac{x^2}{2} \bigg) + C[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
29. The table shows the average annual salary in dollars based on the minimum level of education required for two occupations. Based on the average annual salaries in the table, how much more would an accountant eam than a tax preparer over a 30 year career? Occupations Occupation Average Annual Salary (dollars) Level of Education Required Accountant 71,040 41,700 Bachelor's degree High school diploma Tax preparer A $112,740 B. $3,382,200 C. $880,200 D. $1,251,000
Answer:
c. 880,200
Step-by-step explanation:
ur welcome
Solve each proportion 3/39= y/13
Answer:
[tex]y = 1[/tex]
Step-by-step explanation:
[tex] \frac{3}{39} = \frac{y}{13} [/tex]
Cross multiply
[tex]39 = 39y[/tex]
Divide by 39
[tex]y = 1[/tex]
Answer:
[tex]\boxed {\boxed {\sf y=1}}[/tex]
Step-by-step explanation:
To solve the proportion, we must solve for the variable. This is done by isolating the variable.
[tex]\frac {3}{39}= \frac {y}{13}[/tex]
The variable, y, is being divided by 13. The inverse of division is multiplication. Multiply both sides of the proportion by 13.
[tex]13*\frac {3}{39}= \frac {y}{13}*13[/tex]
[tex]13*\frac {3}{39}=y\\1=y[/tex]
Another way to solve is by cross multiplying. Multiply the 1st numerator by the 2nd denominator, then the 1st denominator and the 2nd numerator.
[tex]\frac {3}{39}= \frac {y}{13}[/tex]
[tex]3*13=39*y\\39=39y[/tex]
Divide both sides by 39 to isolate the variable.
[tex]39/39=39y/39 \\1=y[/tex]
In this proportion, y is equal to 1.
What is the circumference in centimeters of the circle? Use 3.14 for 7. Enter your answer in the box
24 cm
cm
Answer:
75.36
Step-by-step explanation:
24 cm x 3.14 = 75.36
Which is the cost of the minimum spanning tree of the weighted graph using Kruskal's Algorithm?
28
30
31
40
9514 1404 393
Answer:
(a) 28
Step-by-step explanation:
Kruskal's algorithm has you identify the shortest edge at each stage, including in the tree any identified edge that does not form a cycle. Here, we can start with AB, then add DF, EH, HG, BG, AC, CD and that covers the entire graph.
Starting at E, the node list is EHGBACDF. The cost is ...
3 +4 +5 +1 +6 +7 +2 = 28
__
In the attached, the minimum-cost spanning tree is highlighted in red.
The Lazy River has a current of 2 miles per hour. A motorboat can travel 15 miles
down the river in the same amount of time it takes to travel 9 miles up the river.
What is the speed of the boat in still water? Please show your work and use table to
relate time, speed, distance.
Answer:
8mph
Step-by-step explanation:
I just answered the question
The diagonals of square ABCD intersect at point E. If BE = 2x + 1, and AC = 3(6x - 4), find BD.
Answer:
Step-by-step explanation:
5
-27 +2+ 23р - Зр
Hurry please
Answer:
20p - 25
Step-by-step explanation:
-27 +2+ 23р - Зр
20p - 25
Answer:
-25+20p
Step-by-step explanation:
Add -27 and 2
-25+23p-3p
Subtract 3p from 23 p
-25+20p
Hope this helps! If so brainiest, please?
Thanks!!!
A scale drawing of an NFL god post uses a
scale of 2 inches = 5 feet. If the actual width
of the goal post is 182 feet, what is the width
of the goal post on the drawing?
help me plssssssssss
9514 1404 393
Answer:
a, c, d
Step-by-step explanation:
b is NOT equivalent, because the content of parentheses is evaluated first. That makes the expression equal to 2/15, which is not equal to the given expression.
[tex]\dfrac{2}{(5\times 3}=\dfrac{2}{15}\ne\dfrac{2}{5}\times3=\dfrac{6}{5}[/tex]
__
Expressions (a) and (d) are exactly the same thing, written using different symbols for division. Expression (c) is the equivalent.
I WILL NAME BRAINSLEST WHI EVER ANSWRS FIRST AND DOESNT MAKE ME READ A LOT
The lengths of the three sides are 4 centimeters, 2 centimeters, and 7 centimeters.
The measures of two angles are 30 and 60 and the length of the included side is 12 inches.
The measures of the three angles are 45, 75, and 60"
Number of
Triangles
Glven Conditions
0
1
infinitely
many
Answer:
60? Maybe could be wrong
Step-by-step explanation:
0 Sides 4 cm, 2 cm, 7 cm
1 ASA = 30°, 12 in, 30 cm
∞ Angles 25°, 75°, 60 °
FOUND THIS IN BRAINLY
Answer:
0 matches with 4,2, and 7 centimeters.
1 matches with 30, 60, and 12
infinitely many matches with 45, 75, and 60!
A building in a city has a rectangular base. The length of the base measures 70 ft less than twice the width. The perimeter of this base is 820 ft. What are the dimensions of the base?
Answer:
160 ft, 250ft
Step-by-step explanation:
Rectangular base:
Width = w
length =2w - 70
Perimeter = 820 ft
2*(length + width) = 820
2*(2w - 70 + w ) = 820
2 *(2w + w - 70) = 820 {Combine like terms}
2* (3w - 70) = 820
3w*2 - 70*2 = 820
6w - 140 = 820
6w = 820 + 140 {Add 140 to both side}
6w = 960 {Divide both sides by 6}
w = 960/6
w = 160 ft
length = 2*160 - 70
= 320 - 70
= 250 ft
-12.3 + 7v = 10.1 solve for V
Answer:
v=3.2
Step-by-step explanation:
Let's solve your equation step-by-step.
−12.3+7v=10.1
Step 1: Simplify both sides of the equation.
7v−12.3=10.1
Step 2: Add 12.3 to both sides.
7v−12.3+12.3=10.1+12.3
7v=22.4
Step 3: Divide both sides by 7.
7v /7 = 22.4 /7
v=3.2
brainliest?
Accountants often use the median when studying salaries for various businesses. What is the median of the following salary list: $32,019; $21,971; $27,596; $43,715, $38,850, $25,963?
Answer
40.5
Step-by-step explanation
please answer asap! no scam links or scam comments or reported.
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
:))
HELP ON THIS QUESTION !!!!!!!!
Answer:
b
Step-by-step explanation:
i took the test
Ther *must* be an faster way of symplifying this expression. What could I have done differently?
Answer:
3x4
Step-by-step explanation:
You're gonna want to simplify that equation. We see the three and the four. Multiply that to get x^12
A garden is in the shape of a circle with a radius of 10 feet. Edging is place around the garden. How much edging, in feet, is needed to
go around the garden? Round your answer to the nearest whole number. Use 3. 14 for TT.
please!! I need it right jnow
Answer:
62.8 ft (of edging)
Step-by-step explanation:
We need to find the circumference of this circle, using C = 2(pi)r.
Here, C = 2(3.14)(10 ft) = 62.8 ft (of edging)
Answer:
63 feet is needed to go around the garden.
Approximately how long will it take a jet to travel 400 miles at a rate of 120
miles per hour?
A.) 3 1/3
B.)3 1/2
C.)4 1/2
D.)4 1/3
Answer:
3 1/3
Step-by-step explanation:
I'm stuck on this math problem. Please only answer if your 100% sure. ( Look at the picture for the problem) Will Mark Brainliest.
Answer:
-2x^4+10x^3-21x^2+19x-4
Step-by-step explanation:
Answer:
-2x^4+10x^3-21x^2+19x-4
Step-by-step explanation:
trust me bro
find the equation of the line use exact numbers
Answer:
y = -³/2x + 3
Step-by-step explanation:
To find the equation of the line in slope-intercept form, y = mx + b, we need to finder the slope (m) and the y-intercept (b).
✔️Slope (m) = ∆y/∆x
Using two points on the line, (0, 3) and (2, 0),
Slope = (0 - 3)/(2 - 0) = -3/2
Slope (m) = -³/2
✔️y-intercept (b) = 3 (this is the y-cooordinate of the point where the line intercepts the y-axis)
✔️To write the equation, substitute m = -³/2 and b = 3 into y = mx + b
This:
y = -³/2x + 3
28÷x=168
What is the value of "x"
If I invest $1,000 at an 8.5% interest rate, how much money will I earn over 6 years?
6,000$
if the answer is wrong i am sorry :(
Answer:
$510
Step-by-step explanation:
what is the value of x? Hiking trails oak trail 125 degrees. pine trail x degrees. ash trail.
HURRY! What is the circumference of the circle below? Use 3.14 for π.
Answer:
2.14 divided by 5 x 2 is the ansewer
Step-by-step explanation:
Invent measurements that would show triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
Answer:
The answer is that when you put the LMN. You can rotate it. Then we know it is similar.
Using the rotation method of the triangle LMN show triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
What is the similarity law for triangles?It is necessary to demonstrate compliance with the law to establish that two triangles are identical in both shape and size. The angles that correspond to those sides have the same congruence and the same ratio of sides.
It is given that the two triangles are triangle XYZ and triangle NLM.
Two triangles are said to be comparable if the ratio of one triangle's two sides to the two sides of another triangle is the same, and the angles that the two sides of both triangles inscribe are equal.
Thus, triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
Learn more about the similarity of triangles here:
brainly.com/question/8045819
#SPJ2
please help meeeeeeeeeeeeeeeee
Answer:
hi
Step-by-step explanation:
i think so...
[tex]\pi \times {r}^{2} \times \frac{h}{3} \\ 3.14 \times 3.5 \times \frac{9}{3} \\ = 32.97[/tex]
hope it helps
bye
1. In a fishing contest, the two largest bass weighed a total
of 22 pounds. The first-place bass weighed 8 pounds
more than the second-place bass. Find the weights of
the first-place and second-place bass.
Answer:
First place fish weights 15 pounds.
Second place fish weights 7 pounds.
Step-by-step explanation:
7+8=15
15+7=22
Hope this helped!
Pleaseeee helppppppppp
Answer:
5.616 x 10^6
Step-by-step explanation:
Im sure that it's right.
Someone please answer this
Answer:
Answer what?
Step-by-step explanation:
What is the answer to this
Answer:
The answer is x = 8
Step-by-step explanation:
