Answers
Answer:
-ln(| x - 1 |) + -ln(| x - 2 |) + C
Step-by-step explanation:
[tex]\displaystyle \int \dfrac{1}{x^2 -3x +2} dx\\\\\\=\displaystyle \int \dfrac{dx}{x^2 -3\cdot \dfrac 32 \cdot x + \left(\dfrac 32 \right)^2 -\left( \dfrac 32 \right)^2 +2}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x- \dfrac 32 \right)^2 +2- \dfrac 94}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x - \dfrac 32 \right)^2-\dfrac 14 }\\\\\\=\displaystyle \int \dfrac{du}{u^2-\left( \dfrac 12 \right)^2} ~~~~~~~~~~~~~~~~~~;\left[u = x - \dfrac32\implies du= dx\right]\\[/tex]
[tex]=\dfrac{1}{2\cdot\tfrac 12} \ln \left| \dfrac{u-\dfrac 12 }{u+\dfrac 12 } \right|+C~~~~~~~~~~:\left[ \displaystyle \int \dfrac {dx}{x^2 -a^2} = \dfrac 1{2a} \ln \left| \dfrac{x-a}{x+a} \right| +C\right]\\\\\\=\ln\left|\dfrac{x- \dfrac 32 - \dfrac 12}{x-\dfrac3 2 + \dfrac 12 } \right|+C~~~~~~~~~~~~;\left[\text{Substitute back}~u =x- \dfrac 32 \right]\\\\\\=\ln\left|\dfrac{x-2}{x-1} \right|+C[/tex]
Related Questions
Solve the following system of equations using the elimination method.
5x + y = 9
–10x + 7y = 18
Answers
x = 1
The first step is to multiply such that one variable is the negation of that same variable in the opposite equation:
10x + 2y = 18
-10x + 7y =18
Next, combine the equations:
9y = 36
Divide:
y = 4
Then, to solve for x, just put the value of y into the original equation.
5x + 4 = 9
Subtract 4 from 9:
5x = 5
Divide:
x = 1
And then, to check your answers, insert your variables into the other equations:
-10(1) + 7(4) = 18
Multiply your variables:
-10 + 28 = 18
Add 10 to 18:
28 = 28
And there you go!
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
5x + y = 9
- 10x + 7y = 18 [tex]\rightarrow[/tex] (ii)
Now, multiplying "5x + y = 9" by 2 we get,
10x + 2y = 18[tex]\rightarrow[/tex] (i)
Now, using Elimination method.
So, we gotta subtract Equation (i) from Equation (ii)
Equation (i) - (ii)
[tex](10x + 2y) - ( - 10x + 7y) = 18 - 18 \\ \\ \implies \: 10x + 2y + 10x - 7y = 0 \\ \\ \implies \: \cancel{10x} + 2y + \cancel{10x} - 7y = 0 \\ \\ \implies - 5y = 0 \\ \\ \implies \: y = 5[/tex]
So, the value of "y" is 5. Now we gonna put the value of "y" in Equation (i).
[tex]10x + 2y = 18 \\ \\ \implies \: 10x + 2 \times 5 = 18 \\ \\ \implies10x + 10 = 18 \\ \\ \implies10x = 18 - 10 \\ \\ \implies10x = 8 \\ \\ \implies \: x = \frac{8}{10} \\ \\ \implies \: x = \cancel{ \frac{8}{10}} \\ \\ \implies \: x = \frac{4}{5} \\ \\ \implies \: x = 0.8[/tex]
So, at the we've found the values of "x" and "y".
x = 0.8 and y = 5
[tex] \boxed{ \frak \pink{Be \: Brainly}}[/tex]
I need help with question number one and an explanation.
Answers
Answer:
4π
Step-by-step explanation:
Formula for length of an arc is 2πr(θ/360) with r being the radius and θ being the angle of the arc
2πr is the circumference of the circle and (θ/360) is the fraction of the circle the arc is
The angle of arc AB is 120° and the radius is 6
Now we can use substitution in the formula
2πr(θ/360)
2π(6)(120/360)
12π(1/3)
4π
That is the answer goodbye
- Kan Academy Advanced
Please help with this easy problem for 30 points!!!
Answers
Answer:
x^3 + 3x^2 - 10x
Step-by-step explanation:
(x - 0)(x - 2)(x + 5)
= (x^2 - 2x)(x + 5)
= x^3 + 5x^2 - 2x^2 - 10x
= x^3 + 3x^2 - 10x
Suppose a plumber charges $80 for a house call and $60 for each hour it takes him to complete the repair. Write an equation in slope-intercept form to represent this situation.
Answers
Answer:
80 + 60x
Step-by-step explanation:
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 30-49 years old is chosen at random, what is the probability that they have completed a master's degree? Round your answer to the nearest thousandth.
Answers
Answer:
The required Probability =0.433
Step-by-step explanation:
number of residents who has master degree =2078
number of residents who has master degree and age group 30-49years= 455+ 445=900
900/2078
=450/1039
=0.43310
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
a 120 degree angle is 90 (right angle) + 30 (an acute angle)
Gunner is racing his motorcycle. He has raced for 45 minutes. If he has completed 15% of his race, how many minutes will he race in all?
Answers
Answer:
300
Step-by-step explanation:
45 minutes is 15% of x
45 = 0.15x
0.15x = 45
x = 45/0.15
x = 300
Answer: 300
Tanika drew a line of best fit on a scatter plot as shown below
Answers
Answer:
C. she forgot the minus sign for the first term on the right side of the equation.
Step-by-step explanation:
Tanika's work: 1.02(0.5)+7.09 = y
y = 7.6
She's missing the negative sign before 1.02. Her equation should have been -1.02(0.5)+7.09 = y
y = 6.58
Tess says this shape is a rhombus. Jack says the shape is a square. Who is correct? Use the drop-down menus to explain who is correct.
Click the arrows to choose an answer from each menu.
Answers
The above shape is a quadrilateral and its a square. Therefore, Jack is correct.
What is a quadrilateral?A quadrilateral is a 2 dimensional figure with 4 sides.
Examples of quadrilaterals are rhombus , square, rectangle, parallelogram etc.
A rhombus is a quadrilateral with 4 sides same length. The angles of rhombus are not right angles.
A square is a quadrilateral with 4 sides same length and 4 square corners that a right angles.
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A store donated 2 1/4 cases of crayons to a daycare. Each case holds 24 boxes of crayons; each box holds eight crayons. How many crayons did the center receive?
Answers
Answer:
432 crayons
Step-by-step explanation:
24/4=6
24+24+6=54
54*8=432
Find a1 when S7=5465, r=3, n=7 using geometric series
Answers
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ n=7\\ r=3 \end{cases} \\\\\\ S_7=a_1\left( \cfrac{1-r^7}{1-r} \right)\implies 5465=a_1\left( \cfrac{1-3^7}{1-3}\right)\implies 5465=a_1(1093) \\\\\\ \cfrac{5465}{1093}=a_1\implies \boxed{5=a_1}[/tex]
A basketball player made 70 out of 100 attempted free throws. What percent of free throws was made?
Answers
Answer:
70%
Step-by-step explanation:
To find the percent you put the part (70) out of the whole (100) and then multiply it by 100%. Like this:
[tex]\frac{70}{100} *100[/tex] = 70%
You can also look at it like this, it is already out of 100, so he made 70% of free throws because he made 70 free throws!
I hope this helps! Good luck and if you have any questions please let me know in the comments!
what is the volume of a cylinder, in cubic with a height of 2 inches and a base diameter of 18 inches Round to the nearest place
Answers
Answer:
V = 508.938 [tex]in^{3}[/tex]
Step-by-step explanation:
The equation to find the volume of a cylinder is:
[tex]V = \pi r^{2} h[/tex]
r = radius
h = height
In the question it gives us the height (2 inches) and the diameter (18 inches).
We need to find the radius from the diameter. To do this, divide the diameter by 2:
r = 18/2 = 9
Now, plug everything into the equation and solve:
[tex]V = \pi (9)^{2} (2)[/tex]
Use a calculator to get the answer:
V = 508.938 [tex]in^{3}[/tex]
(Side note: I don't know what place to round to because in the question it says to "round to the nearest place" but doesn't say tenth, hundred, etc. If the question on your homework says tenth then the answer would be 508.9, hundredth = 508.94, thousandth = 508.938)
Hope this helps!! If you have questions please comment them under this!
Customers at the restaurant have to wait an average of 25 minutes before they receive their meal
from the time their order was placed. Assume these waiting times are normally distributed with a
standard deviation of 5 minutes.
Question: What is the maximum waiting time for a customer to receive her meal if she is in the 10% of
customers who receive their meals in the fastest time from when the order was placed?
Answers
Answer: the required time is 18.6 minutes.
Step-by-step explanation:
It typically takes 10–15 mins in most of the restaurants however, it also depends on the type of food you've ordered + the time you're visiting (peak time, weekends, etc).
The time may go high if the quantity ordered is more & different variety of food is ordered. 10–15 mins is typically for 2 people visiting a restaurant for lunch or dinner.
Restaurants which have high focus on customer service ensures they have sufficient staff & ingredients available during their peak hours so that wait time is minimal.
Small restaurants where customer only comes for tasty food (because they're famous) & have high number of customers visiting may at times take a longer time to deliver as they have many customers to attend and usually have less staff.
Hope this is helpful.
The US Mint charges $25 for a limited edition coin, plus a $6 shipping charge. The
cost, c, of purchasing n coins can be found using the function c = 25n+6. There is a
limit of 5 coins per purchase. What is a reasonable domain for this function?
a. {5}
b. {1, 2, 3, 4, 5}
c. {25, 50, 75, 100, 125}
d. {31, 56, 81, 106, 131}
Answers
Answer:
b. {1, 2, 3, 4, 5}
Step-by-step explanation:
Given function:
c = 25n + 6
(where c is the total purchase cost and n is the number of coins)
Domain: input values → n-values
If there is a limit of 5 coins per purchase, this means that you can purchase up to and including 5 coins at any one time.
Therefore, the domain is: {1, 2, 3, 4, 5}
{1, 2, 3, 4, 5} is a reasonable domain for this function.
So, the correct answer is:
b. {1, 2, 3, 4, 5}.
The cost function for purchasing n coins is given by c = 25n + 6.
However, there is a limit of 5 coins per purchase.
This means that the number of coins (n) should not exceed 5,
as it is not possible to purchase more than 5 coins in a single purchase.
Therefore, a reasonable domain for this function would be the set of numbers from 1 to 5,
since n can take any value between 1 and 5, inclusive.
Hence, {1, 2, 3, 4, 5} is a reasonable domain for this function.
So, the correct answer is:
b. {1, 2, 3, 4, 5}.
To learn more on function click:
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Help me please. I need the answer and method of how you got your answer asap.
Answers
Answer:
60 degrees
Step-by-step explanation:
a straight line is equal to 180 degrees. 180 - 120 = 60 degrees for x
Answer:
60 degrees
Step-by-step explanation:
both big angles are 120. 12x2=240, 360-240=120, half 120= 60.
PLEASEEEEEE HELP ASAP
Answers
Answer:
27% is the answer
And goodluck
What’s the answer????
Answers
ANSWER FOR A BRAINLY plEASE
Answers
Answer:
91 I believe. 7x4 is 28, divide by 2, you get 14. there is two triangles that have the same area so multiply by two to get 28 for the top half. then 7x9 is 63, divided by 2 times 2 is 63. add 63 and 28 to get 91
Use Statistics to make an argument to the court on behalf of your client. Structure your essay as a paragraph that contains the following:
Your Honor,
Explain why random sampling in this situation of juror selection relates the expected sample proportion to the population proportion.
Compare the expected value to the actual sample proportion.
Show that the requirements for a binomial experiment are met in this situation, implying that the binomial distribution can be used.
Identify the values for n,p, and x for this situation
Interpret the answers to parts c. and d. and submit them as evidence.
Use this to argue that the juror selection was likely to be random or not likely to be random (depending on your answer to part c).
Request a new jury be selected or accept the selected jury (depending on your answer to part c)
Respectfully,
[Your Name]
Answers
In explaining of the random sampling situation, you tell the jury that Random sampling is a kind of sampling technique where all sample has an equal right or probability to be chosen.
What is random sampling example?An example of a simple random sample would be the names of 30 employees were chosen out of a box from a company of 300 employees. In this above scenario, the population is all 300 employees, and the sample is random based on the fact that each employee do possess an equal chance of been selected.
By using the example of the argument given above to convince the juror about why the selection is said to be likely to be random.
Learn more about random sampling from
https://brainly.com/question/24466382
Find the shortest length of 1/2-inch conduit from which the following pieces can be cut: 7 1/8 inches, 3 1/4 inches, 6 1/2 inches, 12 1/8 inches, and 24 3/16 inches. Allow 1/ 16 inch for each saw cut.
please break it down for me:)
Answers
Answer:
106 7/8 inches
Step-by-step explanation:
Simplifying the pieces
57/8 + 13/4 + 13/2 + 97/8 + 387/16114/16 + 52/16 + 104/16 + 194/16 + 387/16 + 4/16855/16855/16 x 2855/8106 7/8 inchesNeed help on question 17
Answers
Answer:
x = - 1 or 1 or -4 or 4
Step-by-step explanation:
x^4 - 17x^2 + 16 = 0
let y = x^2
y^2 -17y + 16 = 0
(y-16)(y-1) = 0
y = 16 or y = 1
x^2 = 16 or x^2 = 1
x^2 = 16: x = 4 or -4
x^2 = 1: x = 1 or -1
PLEASE HELP WILL GIVE BRAINLIEST 60 POINTS Given the triangle congruence statement ΔUVW≅ΔABC and the triangles below, mark each of the triangles appropriately for corresponding angles and sides. Then create a list of congruent sides and angles using the table.
Corresponding Sides Corresponding Angles
Answers
Congruent triangles are those triangles which have the same size and form.
What are congruent triangles?Congruent triangles are those triangles which have the same size and form. This signifies that the matching sides and angles are the same.
The two triangles ΔUVW≅ΔABC, therefore, the corresponding sides can be written as,
WU = BAUV = ACWV = BCThe corresponding angles will be,
∠W = ∠B∠U = ∠A∠V = ∠CLearn more about Congruent Triangles:
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The correlation coefficient quantifies the relationship between two variables. This relationship is determined by the degree at which the dependent variable is affected by the value of the independent variable. In real life, why is there a need to quantify relationships and a need to know how to quantify relationships?
Answers
Answer:
When biomedical engineers work within a hospital or clinic, they are more properly called clinical engineers.
Passes through the point (0,6) and has a slope of -2/3
Answers
Answer:
[tex]y=-\frac{2}{3}x + 6[/tex]
Step-by-step explanation:
We are given that a line has a slope of -2/3 and passes through the point (0,6)
We want to write the equation of this line; there are 3 forms of the line that we can use:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negativeSlope-point form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointAll though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.
As we are already given the slope, we can immediately substitute m with that value.
Replace m with -2/3:
y = -2/3x + b
Now we need to find b.
As the equation passes through the point (0, 6), we can use it to help solve for b.
Substitute 0 as x and 6 as y.
6 = -2/3(0) + b
Multiply
6 = 0 + b
Add
6 = b
Substitute 6 as b.
y = -2/3x + 6
Topic: finding the equation of the line
See more: https://brainly.com/question/27645158
(3x−4)(x+2)(3x−1) hurry pls
Answers
Answer:
Step-by-step explanation:
(3x - 1)(3x - 4) = 9x^2 - 15x + 4
(x + 2)(9x^2 - 15x + 4) = 9x^3 - 15x^2 + 4x + 18x^2 - 30x + 8
9x^3 + 3x^2 -26x + 8 is the solution
The wholesale price for a desk is $199. A certain furniture store marks up the wholesale price by 24%. Find the price of the desk in the furniture store.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
246.76$
Step-by-step explanation:
199 x .24 =
47.76
199 + 47.76 =
246.76
Five marbles labeled 1 through 5 are placed in a bag. A marble is randomly pulled and the number is recorded before the marble is placed back in the bag. The results of the simulation of 20 marble pulls are shown in a dot plot. Which dot plot models an unfair data generating process?
Answers
Answer:
C
Step-by-step explanation:
Since having 1 and 5 as the most likely result is highly unlikely, the answer being 7 points on both numbers would be unfair resulting in C being the answer.
Convert the following angle from degrees to radians. Express your answer in simplest form 345 ∘
Answers
well, since we know that there are 180° in π radians, how many degrees will it be in 345°?
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}[/tex]
Spencer tells you the repair will be $70.00 plus $32.50 per ½ hr. or
part of an hour. Calculate the cost for Spencer's repair job
Answers
Answer:
If it doesn't tell you how long Spencer's repair took, it would just be 70+32.50 which equals $102.50
