Answer:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int\left(\ln x\right)^2 \, dx[/tex]
We can use Integration by Parts. Rewriting the integral yields:
[tex]\displaystyle =\int 1\cdot (\ln(x))^2\, dx[/tex]
Recall that IBP is given by:
[tex]\displaystyle \int u\, dv = uv - \int v \, du[/tex]
Let u be (ln(x))². And let dv be (1) dx. Therefore:
[tex]\displaystyle du = 2\ln x \cdot \frac{1}{x}\, dx[/tex]
Simplify:
[tex]\displaystyle du=\frac{2\ln(x)}{x}\, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=\underbrace{\ln(x)^2}_{u}\underbrace{x}_{v}-\int\underbrace{x}_{v}\cdot \underbrace{\frac{2\ln(x)}{x}\, dx}_{du}[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2 \int\ln(x)\, dx[/tex]
We can perform IBP again. Let u = ln(x) and v = 1. Hence:
[tex]\displaystyle du = \frac{1}{x} \, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Thus:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (x)\frac{1}{x}\, dx\right)[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (1)\, dx\right)[/tex]
Evaluate:
[tex]=x\ln(x)^2-2(x\ln(x)-x)+C[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2x\ln(x)+2x[/tex]
Factor:
[tex]=x(\ln(x)^2-2\ln(x)+2)[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
If a car travels 10 ft due north and then 15 feet due west, how far is the car from it starting point? This is for homework and it’s on the Pythagorean theorem
The supplement of an angle is 42 degrees less than 3 times the complement of the angle. What is the measure of the angle?
Answer: 24°
Step-by-step explanation:
Given the following :
supplement of an angle is 42 degrees less than 3 times the complement of the angle
Let the angle = θ
Supplement of angle = 180° - θ
Complement of angle = 90° - θ
Supplement of angle is also said to be:
(3 × complement) - 42° = 3(90° - θ) - 42°
= 270° - 3θ - 42° = 228° - 3θ
Hence,
180° - θ = 228° - 3θ
Solve for θ
-θ + 3θ = 228° - 180°
2θ = 48°
θ = 48°/2
θ = 24°
If uw =6x-35, find uw
Answer:
The value of uw is 67
Step-by-step explanation:
Given that,
If uw= 6x-35...(I)
Line segment consists of points u,v,w
u to v is 19
v to w is 4x-20
We need to calculate the value of x
Using given data
[tex]uw=6x-35[/tex]
[tex]uv+vw=6x-35[/tex]
Put the value of u and w
[tex]19+4x-20=6x-35[/tex]
[tex]19+35-20=6x-4x[/tex]
[tex]34=2x[/tex]
[tex]x=\dfrac{34}{2}[/tex]
[tex]x=17[/tex]
We need to calculate the value of uw
Put the value of x in equation (I)
[tex]uw=6\times17-35[/tex]
[tex]uw=67[/tex]
Hence, The value of uw is 67
Find
(1) a + b,
(2) 2a + 3b,
(3) |a|, and |a − b|.
a = 5i + j, b = i − 2j
Answer:
Step-by-step explanation:
this problem is on vector
given the vectors
a = 5i + j, and
b = i − 2j
1. summation of vector a + b
[tex]= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\[/tex]
collect like terms
[tex]=5i+i+j-2j\\\\=6i-j\\\\[/tex]
2. 2a + 3b
[tex]= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\[/tex]
collecting like terms we have
[tex]=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j[/tex]
(3) |a|, and |a − b|.
|a|= |5i+j|
[tex]=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1[/tex]
also,
[tex]|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\[/tex]
[tex]|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25[/tex]
Apply the laws of probability and calculate the probability the offspring of the cousin marriage of 3 x 7 will have the trait. (enter a decimal fraction between 0.00 and 1.00)
Answer:
0.16
Step-by-step explanation:
The calculation of probability by applying the is shown below:-
It is evident from the pedigree that the mode of inheritance is recessive and the characteristic is recessive that's also phenotype of disease is only seen if the genotype is aa.
The genotype of 1. In pedigree Can be either AA or Aa.
The chance that the offspring of the [tex]3\times 7[/tex] cousin marriage will have the characteristic is
[tex]= \frac{1}{6}[/tex]
which gives results
= 0.16
Which of the following represents “ 10 times the sum of a number and 14 is equal 9 times the number”?
Answer:
The expressión is:
10(a+14) = 9a
and the number is:
-140
Step-by-step explanation:
The expression is:
10(a+14) = 9a
then:
10*a + 10*14 = 9a
10a + 140 = 9a
10a - 9a = -140
a = -140
Check:
10(-140+14) = 9*140
10*-126 = 1260
Slope intercept Functions
I want to bring my grade up so if anyone knows tell me
Answer:
no
Step-by-step explanation:
You will have more time to do it, but no, try extra credit
Sorry mate hope this helps<3
On Thursday, a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Thursday?
Hey there! I'm happy to help!
Let's call the hamburgers h and the cheeseburgers c.
h+c=234
c=2h
Let's plug this value of c into the first equation to solve for h.
h+2h=234
3h=234
Divide both sides by 3.
h=78
Therefore, 78 hamburgers were sold on Thursday.
Have a wonderful day! :D
Can you explain how to do these three problems?
Step-by-step explanation:
a) The distance is the integral of the velocity vs. time graph. We can approximate the distance using a left hand Riemann sum. That means for each interval, use the velocity at the beginning of the interval. Don't forget to convert mi/hr to mi/s.
d₁ = (10 s − 0 s) (183.9 mi/hr × 1 hr / 3600 s) = 0.5108 mi
d₂ = (20 s − 10 s) (169.0 mi/hr × 1 hr / 3600 s) = 0.4694 mi
d₃ = (30 s − 20 s) (105.6 mi/hr × 1 hr / 3600 s) = 0.2933 mi
d₄ = (40 s − 30 s) (99.8 mi/hr × 1 hr / 3600 s) = 0.2772 mi
d₅ = (50 s − 40 s) (124.5 mi/hr × 1 hr / 3600 s) = 0.3458 mi
d₆ = (60 s − 50 s) (177.1 mi/hr × 1 hr / 3600 s) = 0.4936 mi
d = 0.5108 + 0.4694 + 0.2933 + 0.2772 + 0.3458 + 0.4936
d = 2.390 miles
b) Do the same as part a, but this time, use a right hand Riemann sum. Instead of using the velocity at the beginning of the interval, use the velocity at the end of the interval.
d₁ = (10 s − 0 s) (169.0 mi/hr × 1 hr / 3600 s) = 0.4694 mi
d₂ = (20 s − 10 s) (105.6 mi/hr × 1 hr / 3600 s) = 0.2933 mi
d₃ = (30 s − 20 s) (99.8 mi/hr × 1 hr / 3600 s) = 0.2772 mi
d₄ = (40 s − 30 s) (124.5 mi/hr × 1 hr / 3600 s) = 0.3458 mi
d₅ = (50 s − 40 s) (177.1 mi/hr × 1 hr / 3600 s) = 0.4936 mi
d₆ = (60 s − 50 s) (175.6 mi/hr × 1 hr / 3600 s) = 0.4878 mi
d = 0.4694 + 0.2933 + 0.2772 + 0.3458 + 0.4936 + 0.4878
d = 2.367 miles
c) The velocity decreases from 0 s to 30 s, but then increases from 30 s to 50 s, and then decreases from 50 s to 60 s.
Since the velocity doesn't consistently increase or decrease, these Riemann sums are neither lower nor upper sums.
Solve for z - 9 = 27
Answer:
z = 36
Step-by-step explanation:
Add nine to each side, so it now looks like this: z = 36Answer:
36
Step-by-step explanation:
The manager of a restaurant found that the cost to produce 200 cups of coffee is $65.00 , while the cost to produce 250 cups is $77.50 . Assume the relationship between the cost y to produce x cups of coffee is linear. a. Write a linear equation that expresses the cost, y, in terms of the number of cups of coffee, x. b. How many cups of coffee are produced if the cost of production is $135.00 ?
Answer:
a). y = 0.25x + 15
b). x = 480 cups
Step-by-step explanation:
(a). Let the equation of the linear function passing through a point (x', y') is,
y - y' = m(x - x')
'm' = slope of the line
b = y-intercept
Two points lying on the linear function will be (200, 65) and (250, 77.5).
Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{77.5-65}{250-200}[/tex]
= [tex]\frac{12.5}{50}[/tex]
= 0.25
Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,
y - 65 = 0.25(x - 200)
y - 65 = 0.25x - 50
y = 0.25x + 15
(b). For y = $135 we have to calculate the number of cups of coffee produced.
135 = 0.25x + 15
0.25x = 135 - 15
0.25x = 120
x = 480 cups
Therefore, 480 cups of coffee will be produced.
NEED HELP ASAP!!! Solve 0 = (3x - 4) / 5
answer: 1.13622
Step by step explanation:
n:
0=(3x-4)/5
0=3x/5-4/5
x=1.3.....
Solve for x 40+5x>95-4x
Steps to solve:
40 + 5x > 95 - 4x
~Subtract 40 to both sides
5x > 55 - 4x
~Add 4x to both sides
9x > 55
~Divide 9 to both sides
x > 55/9
Best of Luck!
(6+2)-15divided5*2. How can I add all this up
Answer
2
Step-by-step explanation:
6+2=8 15/5*2=6 8-6=2
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. a 11.5 and 23.6
Answer:
[tex]12.1 < Y < 35.1[/tex]
Step-by-step explanation:
Given
Sides: 11.5 and 23.6
Required
Determine the range of the third side
Let the third side with Y
Two of the following conditions must be satisfied to calculate the range of the third side
[tex]11.5 + Y > 23.6[/tex]
[tex]23.6+ Y > 11.5[/tex]
[tex]11.5 + 23.6 > Y[/tex]
We'll solve one after other
1. [tex]11.5 + Y > 23.6[/tex]
[tex]Y > 23.6 - 11.5[/tex]
[tex]Y > 12.1[/tex]
2. [tex]23.6+ Y > 11.5[/tex]
[tex]Y > 11.5- 23.6[/tex]
[tex]Y > -12.1[/tex]
3. [tex]11.5 + 23.6 > Y[/tex]
[tex]35.1 > Y[/tex]
[tex]Y < 35.1[/tex]
Inequalities with negative can't be used' So, we have
[tex]Y > 12.1[/tex] and [tex]Y < 35.1[/tex]
Rewrite inequality
[tex]12.1 < Y[/tex] and [tex]Y < 35.1[/tex]
Combine inequality
[tex]12.1 < Y < 35.1[/tex]
Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (4, −5, 2) and parallel to the line x + 5 = y 2 = z − 3
Answer:
Step-by-step explanation:
From the given information, the symmetric equations for the line pass through(4, -5, 2) i.e ([tex]x_o, y_o, z_o[/tex]) and are parallel to [tex]\dfrac{x+5}{1} = \dfrac{y}{2}= \dfrac{z-3}{1}[/tex]
The parallel vector to the line i + zj+k = ai + bj + ck
Hence, the equation for the line is :
[tex]x = x_o + at \\ \\ x = y_o + bt \\ \\ x = z_o + ct[/tex]
x = 4 + t
y = -5 + 2t
z = 2 + t
Thus, x, y, z = ( 4+t, -5+2t, 2+t )
The symmetric equation can now be as follows:
[tex]\begin {vmatrix} x = 4+ t \\ \\ \dfrac{x-4}{1} = t \begin {vmatirx} \end {vmatrix}[/tex][tex]\begin {vmatrix} y = - 5+2t \\ \\ \dfrac{y+5}{2} =t \end {vmatrix}[/tex][tex]\begin {vmatrix} z =2+t \\ \\ \dfrac{z-2}{1} =t \end {vmatrix}[/tex]
∴
[tex]\dfrac{x-4}{1}= \dfrac{y+5}{2}=\dfrac{z-2}{1}[/tex]
Write an equation in slope-intercept form (y = mx + b).
Parallel to 3x + 5y = 18 passing through (-10, -4).
Answer:
y= [tex]\frac{-3}{5}x -2[/tex]
Step-by-step explanation:
find the gradient by rearranging the equation, y= [tex]\frac{-3}{5}x[/tex] +[tex]\frac{18}{5}[/tex]
from here we can see that the slope or gradient is [tex]\frac{-3}{5}x[/tex]
now using the equation y-y2 = f'(x1)(x-1) we find the equation by subbing
= y- (-4) = [tex]\frac{-3}{5}[/tex] (x - [-10])
= y + 4 = [tex]\frac{-3}{5}x -6[/tex]
= y= [tex]\frac{-3}{5}x -2[/tex]
The sum of any two consecutive prime numbers is also prime true or false
Answer:
True
Step-by-step explanation:
how do you turn 372800 into scientific notation
Answer:
3.78x10^5
Step-by-step explanation:
11. What is the difference between the weights of planes C and D? Explain how to use mental math to solve. - C: 56,984 D: 79,473 - The difference in weights is ______ pounds. The difference in weights is given by the expression _______ - _______. Compensation can be used to rewrite this so that the second number is the next greater multiple of 1,000. Doing this gives the new expression ______ - ______. The value of this new expression is _____________. (Type whole numbers.)
Answer:
22,48979,473 - 56,98479,489 - 57,00022,489Step-by-step explanation:
Based on the clues in the problem wording, we assume the numbers given for C and D are the weights of planes, in pounds. For whatever reason, we seem to be interested in the difference of those weights.
The difference in weights is 22,489 pounds.
The difference in weights is given by the expression 79,473 - 56,984.
We can add 16 to both numbers to make the second number a multiple of 1000. To compensate, we also add 16 to the first number.
Doing this gives the new expression 79,489 - 57,000.
The value of this expression is 22,489.
_____
Additional comments
A number of thinking processes are taught for mental math. In this process, you recognize that 984 is near 1000, so you can add a small number to make all the rightmost digits be zeros. That number will have the digits that "make a ten" working from right to left. 4 needs 6 added to make a 10. Adding 6 to 84 makes it 90. Then the 9 needs 1 added to make a 10. Now, we have 984 with 16 added, which makes 1000. Adding that 16 to 79473 to make 79489 completes the transformation we're looking for: 79489 -57000.
i need help i only got 30 min... 40 points i will give brainliest
Questions 1, 2, and 5 are correct.
Question 3:
To find the common difference, we can subtract the last two numbers.
60 - 47 = 13
So, the common difference is 13
We can add 13 to each term to get the next term.
8 + 13 = 21
21 + 13 = 34
So, 8, 21, 34, 47, 60
Question 4:
To find the common difference, we can subtract the last two numbers.
8/3 - 2 = 2/3
So, the common difference is 2/3
We can add 2/3 to each term to get the next term.
0 + 2/3 = 2/3
2/3 + 2/3 = 4/3
So, 0, 2/3, 4/3, 2, 8/3
Question 4:
Since we are only given the first and last number, we need to find a number we can subtract that we get -13 at the end. The distance between 3 and -13 is 16. We can divide this by 4 since there are 4 numbers before -13.
16 / 4 = 4
Since the number is going down, the common difference is going to be -4.
Subtract find the next terms.
3 - 4 = -1
-1 - 4 = -5
-5 - 4 = -9
-9 - 4 = -13
So, 3, -1, -5, -9, -13
Best of Luck!
If two angles form a linear pair, they are
Answer:
If two angles form a linear pair, they are supplementary.
Step-by-step explanation:
A linear pair is two angles that are adjacent and the non-common sides form a straight line.
Answer:
They are supplementary
Step-by-step explanation:
A linear pair is two angles ajacent. The non - common side forms a straight line. So the angles added together are equal to 180 degrees.
A triangle has a base of 3 feet and an area of 15 square feet. Find the triangle's height
Answer:
10 ft
Step-by-step explanation:
The formula for the area of a triangle can be used. Put the known values into the formula and solve for the unknown.
A = (1/2)bh
15 = (1/2)(3)h
h = 15/1.5 = 10
The triangle's height is 10 feet.
Answer:
10
Step-by-step explanation:
A=1/2*b*h
15=1/2*3*h
15=3/2*h
15=3/2h
h=15/(3/2)
h=(15/1)(2/3)
h=30/3
simplify
h=10
If the aspect ratio in width to height (width: height) of a chalkboard is 46:30 and the width is 170 inches, what is the height of the chalkboard? 5,100 in 30 in 46 in 260.6 in
Answer:
110.7 inches
Step-by-step explanation:
Width : Height ( 46:30 )
Width is 46 and Height is 30
So 46 = 170 inches
1 = ?
1 = 170/46
=3.69 inches.
To know the height, multiply that(3.69) with 30. And you will get the inches of the height which is "110.7 inches"
Describe the relationship among the four terms
Choose the correct solution to the equation.
-3+w=
a. 2
b. Ž
ch
d. None of the Above
Оа
Ob
Ос
Od
Answer:
Step-by-step explanation: I have no clue
Find the distance from the point (0, 4, 3) to the plane 5x +1y +2z
Answer:
distance =
[tex] \sqrt{ \frac{10}{3} } [/tex]
Step-by-step explanation:
Without going through and deriving this (my blackboard doesn't have space and a textbook, teacher, or online tutorial is probably better for that), the equation for the distance from some point on the plane to some point in space is as follows:
[tex]distance = \frac{ax + by + cz - d }{ \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } } [/tex]
•Note that the d in the equation should actually be D but Brainly doesn't allow me to do uppercase letters on mobile it seems... Anyway, d in the equation represents the value which the equation of the plane is equal to. You only gave the plane equation so I assumed d=0 in my calculations.
•x, y, and z all come from the point which you want to find the distance to. So (x,y,z)=(0,4,3) here.
•a, b, and c all come from the components of the vector normal to the surface. For planes, it simply somes to be the coefficients in front of each part. So (a,b,c)=(5,1,2) here.
With that you just need to plug the information in and simplify for your answer. My work is in the attachment, comment with questions or if anything seems off.
Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home. Question 11 options: A) c = 25 – 10p – 5h B) c = 25 + 10p + 5h C) c + 25 = 10p + 5h D) c = 25 + 10 + 5
Answer:
B) c=25 +10p +5h
id expect 25 per night with the n variable next to it but i guessed not
, but one night would cost 25 but with the addition of 10 per person and 5 for every hour of a late checkout
Answer:
A
Step-by-step explanation:
C=25
25= How much she was Paid
p=People
1person is 10$
10$Was given in
10+
Late fee 5$
Then by there she gets Her 25
C=25-10p-5h
If x=y and y=z, which statement must be true ? DUE SOON PLEASE HELP
I cannot see the statements you are given as options, but if x = y, and y = z, you can write that as x = y = z, which means that x = z also.
I hope this helps!
Answer:
Step-by-step explanation:
If x=y and y=z, then x=z.