Answers
[tex]\displaystyle \int \dfrac{dx}{5x^2 -10x +15}\\\\\\=\displaystyle \int \dfrac{dx}{5(x^2-2x+3)}\\\\\\=\dfrac 1 5 \displaystyle \int \dfrac{dx}{x^2-2x+3}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{dx}{x^2 -2x +1^2 -1 +3}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{dx}{(x-1)^2+2}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{du}{u^2 +\left(\sqrt 2 \right)^2}~~~~~~~~~;[x-1 =u \implies dx = du]\\\\\\\\[/tex]
[tex]=\dfrac 1 {5\sqrt 2} \tan^{-1} \left( \dfrac u{\sqrt 2}\right)+C~~~~~~;\left[\displaystyle \int \dfrac{dx}{a^2 +x^2} = \dfrac 1a \tan^{-1} \left( \dfrac xa \right) +C\right]\\\\\\=\dfrac{1}{5\sqrt 2} \tan^{-1} \left( \dfrac{x-1}{\sqrt 2}\right)+C[/tex]
Related Questions
Write the expression represented by the following: 8 less than twice a number
Answers
Answer:
2x<8
Step-by-step explanation:
we don't know the number so let the number be x then 2*x=2x therefore 2x<8
The diagram shows a square pizza box with side lengths of 18 inches. In the box is a circular pizza with a radius of 8 inches. What is the difference between the area of box and the pizza?
Answers
18x18=324
pi8^2=201.0619
324-201=123
What is the mean for the set of data?
Rubric Test Score
xx. X. Xx. Xx. Xxx
1 2 3 4 5
Score
Answers
Steps: 1) 1+1+2+3+3+4+4+5+5+5=33
2) 33/10=3.3
Triangle ΔABC has side lengths of a = 18, b=[tex]18\sqrt{3}[/tex], and c = 36 inches.
Part A: Determine the measure of angle A.
Part B: Show how to use the unit circle to find tan A.
Part C: Calculate the area of ΔABC.
Answers
Answer:
Step-by-step explanation:
The Music Express has $72,000 to spend on the music bundles. If it buys
more pop bundles than rock bundles, how many bundles of each type of
music can The Music Express buy while getting closest to the budget of
$72,000? Explain.
Answers
Answer:
It Depend on how much the pop bundles/ rock bundles cost you need those numbers before you can dertermine the answer.
Step-by-step explanation:
HELP SOLVE THANK YOU!
Answers
Answer:
Solution 1: 1+1[tex]\sqrt{3}[/tex]
Solution 2: 1-[tex]1\sqrt{3}[/tex]
Step-by-step explanation:
x^2-2=2x
x^2-2x-2=0
Use quadratic equation.
(-b+-[tex]\sqrt{b^2-4ac}[/tex])/2a
(2+-[tex]\sqrt{(-2)^2-4*1*-2}[/tex])/2
(2+-[tex]\sqrt{(4+8})[/tex])/2
(2+-[tex]\sqrt{12}[/tex])/2
Solution 1: (2+2[tex]\sqrt{3}[/tex])/2=1+1[tex]\sqrt{3}[/tex]
Solution 2: 1-[tex]1\sqrt{3}[/tex]
Let's first move everything, the constants and variables to one side
[tex]x^2-2=2x[/tex] ⇒ [tex]x^2-2x-2=0[/tex]
The second form is in the general form of the quadratic equation:
⇒ [tex]ax^2+bx+c = 0[/tex]
a ⇒ 1b ⇒ -2c ⇒ -2To find the value of x, we can use the quadratic formula:
⇒ look at the diagram attached
[tex]x = \frac{-b-\sqrt{b^2-4ac} }{2a} =\frac{2-\sqrt{(-2)^2-4(1)(-2)} }{2*1} =\frac{2-\sqrt{4+8} }{2} =\frac{2-\sqrt{12} }{2} =\frac{2-2\sqrt{3}}{2} =1-\sqrt{3}[/tex]
[tex]x = \frac{-b+\sqrt{b^2-4ac} }{2a} =\frac{2+\sqrt{(-2)^2-4(1)(-2)} }{2*1} =\frac{2+\sqrt{4+8} }{2} =\frac{2+\sqrt{12} }{2} =\frac{2+2\sqrt{3}}{2} =1+\sqrt{3}[/tex]
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Answer
To answer the question, just answer in the order I solved it, because the question asks you to put the answer in ascending order which means from least to greatest.
Hope that helps!
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
x=19, y=[tex]19\sqrt{3}[/tex]
Step-by-step explanation:
This triangle is a 30-60-90 triangle.
This means the hypotenuse (38) is double the short leg (x)
x=19
Then use the pythagorean theorem
a^2+b^2=c^2
19^2+y^2=38^2
361+y^2=1444
Subtract 361 from both sides
y^2=1083
put it in square roots and simplify
[tex]\sqrt{1083} =19\sqrt{3}[/tex]
y=[tex]19\sqrt{3}[/tex]
To solve this problem:
⇒ need to use a special right triangle theorem:
Let's consider the information given:
⇒ one angle is 30 degrees
⇒ one angle marked with a little square signifies that it is 90
degrees
⇒ (all the angles added up are 180 degrees) so the last angle is
60 degrees
Therefore we have a '30-60-90' triangle which states:
the side opposite the 30-degree angle⇒ half the length of the hypotenuse (longest side of the triangle)
⇒ x = 38/2 = 19
the side adjacent to the 30-degree angle⇒ is the square root of 3 divided by 2 of the hypotenuse
⇒ y = [tex]\frac{\sqrt{3} }{2} *38=19\sqrt{3}[/tex]
Therefore:
x = 19
y = [tex]19\sqrt{3}[/tex]
Hope that helps!
Help urgently tired of post every 5 min
Answers
Answer:
A. 12.78
Step-by-step explanation:
4 shirts for 21.83 = 87.32
87.32 + 42.38 + 74.78 = 204.48
204.48 x 0.0625 = 12.78
The complete total of the items is $204.48.
And 6.25% of that would be $12.78. I hope this helped.
Find the error: 2(3x+4)=16
Answers
Answer:
6x+8=16
or,6x=16-8
or,6x=8
or,x=4 by 3
2. Given the system shown below do the following: y = 1/2x - 2 y = -3x + 5 solve this system graphically using the grid shown solve this system by substituting
Answers
Answer:
~Shoto todoroki here~
I think this would be your solved equation, -3x+5 making your X intercepts at: (5/3, 0) and your Y intercepts at: (0, 5)
The equation has Unique Solution.
What is solution of equation?The solution to a linear equation is the point at which the lines that represent the intersection of two linear equations are defined. In other words, the solution set for the system of linear equations is the set of all possible values for the variables that satisfy the given linear equation.
There are three ways to solve the set of linear equations.
Unique Solution, No Solution and Infinitely Many Solutions.
Given y = 1/2x - 2
x 0 4
y -2 0
y = -3x + 5
x 0 2
y 5 -1
the graph is attached
solving by substitution
y = 1/2x - 2
y = -3x + 5
both equations are equal for y
1/2x -2 = -3x + 5
1/2x + 3x = 5 + 2
7/2x = 7
x = 2
and at x =2 y = -1
equation intersect at (2, -1) and have unique solution.
Hence there is Unique Solution for equations.
Learn more about solution of equation;
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A training field is formed by joining a rectangle and 2 semicircles. The rectangle is 89 m long and 66 m wide. Find the area of the training field. Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Step 1: break the shape into 2, a rectangle and a circle and first find the area of the rectangle ( l x w or 89 x 66)
Step 2: now that we know that the area of the rectangle is 5874 we find the area of the circle (3.14 x radius^2), the diameter is 66, and the radius is 33 (diameter divided by 2)
Now that we know both the rectangle (5874 meters) and circles (1092.14 meters) we add them and get 6966.14
I hope this helps if I made a mistake pls let me know
The perimeter of a triangle is 104 units. The combined length of two of the sides of the triangle is 64 units.
What is the length of the third side of the triangle in units?
Answers
Answer:
Step-by-step explanation:
168
Write 2 as a complex number.
Answers
Answer:
2 + 0i
Step-by-step explanation:
Our real number in this scenario would be 2. And since we don't need an imaginary part because we are just converting 2 by itself, we plug in 0 for the imaginary number.
What is the value of x? Enter your answer in the box.
Answers
Answer: x = 4
Step-by-step explanation:
this is just easier to show work for so i hope this helps :)
This is a valid probability distribution because if you add together the probabilities their sum is 1
True
False
Answers
Answer:
True
Step-by-step explanation:
any value that is unknown or can change is a variable? true or false ?
Answers
Answer:
True
Step-by-step explanation:
I just know off the internet. Hope this helps lol.
A square pyramid is shown below: What is the surface area of the pyramid?
A: 11.69 square feet
B: 3.29 square feet
C: 7.49 square feet
D: 2.24 square feet
Answers
Answer:
A: 11.69 square feet.
Step-by-step explanation:
11.2 + 0.49
= 11.69
Write the following as an inequality (-1,43)
Answers
Answer:
-1<x<43
Step-by-step explanation:
Chapman's Cheese factory packs assorted cheese into 100-slice boxes.
The factory has 150 slices of cheddar, 309 slices of swiss, and 147 slices of
parmesan.
How many boxes of cheese can it make?
Answers
hello,
the answer would be 6 boxes
A function, f(x), has a domain of −10≤x≤20 and range −40≤f(x)≤−10.
f(1)=−13
f(−10)=−40
Select each statement that must be false about f(x).
f(5)= - 40
f(0)=0
f(−15)=−20
f(1)=13
f(−9)=88
Answers
Answer:
all of them are false
Step-by-step explanation:
i know
what is 10066×140 please help me and explain the answer
Answers
Your answer would be 1,409,240
you would mutpliy 0 and 9 first and keep mutpliying until you get your answer
Answer:
The answer is 1,409,240
Step-by-step explanation:
I asume you are doing this by hand so here are the steps:
1. set up the problem- whitch would look like this
10066
x 140
Now you have to mutiply the 1s place, by all the number places of the top number
Sence you have a zero in the 1s place you can just put a x, whitch would look like:
10066
x 140
x
Now you do that for all the places
2 2 * Make sure you rase the number to the next place
10066 4*6 = 24 24+4= 28 4*0=0
x 140
40284x
Now that you mutiplyed the 4 by everything and got the answer of 402840 (the x is just a zero) then you leave it aside and mutiply the 1s by everything whitch is much simpler.
10066 1*6= 6 1*0= 0 1*1 =1
x 140
10066xx (now you put 2 X's)
You get the answer of 1006600 and you add it with 402840
whitch is 1,409,240 (and that is your answer)
Match each expression on the left with its corresponding simplified form.
A) m + 5
B) m + 3
C) m + 4
D) m + 8
note: there is no single answer. every single answer has to get matched
Answers
The equivalent expressions are: (4 + m) + 1 = m + 5, (m + 3) + 1 = m + 4, (2 + m) + 6 = 2 + m + 6 and (1 + m) + 2 = m + 3
What are equivalent expressions?Equivalent expressions are expressions that have equal values when evaluated
Start by evaluating each expression.
(4 + m) + 1
Remove the bracket
(4 + m) + 1 = 4 + m + 1
Evaluate
(4 + m) + 1 = m + 5
(m + 3) + 1
Remove the bracket
(m + 3) + 1 = m + 3 + 1
Evaluate
(m + 3) + 1 = m + 4
(2 + m) + 6
Remove the bracket
(2 + m) + 6 = 2 + m + 6
Evaluate
(2 + m) + 6 = m + 8
(1 + m) + 2
Remove the bracket
(1 + m) + 2 = 1 + m + 2
Evaluate
(1 + m) + 2 = m + 3
Hence, the equivalent expressions are: (4 + m) + 1 = m + 5, (m + 3) + 1 = m + 4, (2 + m) + 6 = 2 + m + 6 and (1 + m) + 2 = m + 3
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Read more about equivalent expressions at:
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Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Jane trained for a total of 19 hours on Wednesday and 7 hours on Thursday. How does each plan last?
Answers
Answer:
they would be about an hour
Step-by-step explanation:
kathryn is x years old. if her mother is two years more than the square of kathryn's age, and the sum of their ages is 44 years. form an equation in x and solve it to find the ages of kathryn and her mother
Answers
Answer:
aaa
Step-by-step explanation:
Graph a line with a slope of 4 that contains the point (3, 0)
Answers
[tex]\text{view explanation pls}[/tex]
Calculation ↓The first step is to write the line's equation in point-slope form
y-y1=m(x-x1)
y-0=4(x-3)
use the distributive property
y-0=4x-12
y=4x-12
Now that we have the equation of the line, we need to determine it's graph. how do we actually graph the line?Well, let's start with the y-intercept, which is -12 or (0, -12)
After plotting the point (0, -12) move up 4, over 1, up 4, over 1, up 4, over 1.
Do the same on both sides of the y-intercept.
hope helpful ~
im not quite sure how to do this pls if anyone could help thanks
Answers
Answer:
a, 10% of 300 = 30 b, 300 - 30 = 270
Step-by-step explanation:
1. 300 x 10 = 3,000
2. Move decimal place 2 to the left = 30.00
3. Subtract 30 from 300 which is 270
25. Anthropologists use a linear model that relates human femur (thighbone) length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. Here we find the model by analyzing the data on femur length and height for the eight males given in the following table.
(c) An anthropologist finds a human femur of length [tex]53 \mathrm{~cm} .[/tex] How tall was the person?
Answers
The height of the person when an anthropologist finds a human femur of length will be 183.94cm.
How to calculate the height?In order to calculate the height, the expression to use will be:
h = 1.876l + 84.512
h = 1.876(53) + 84.512
h = 99.428 + 84.512
h = 183.94
Therefore, the height is 183.94cm.
Learn more about height on:
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PLEASE I NEED HELP!!!!!
Answers
Answer:
-5, -8, -4, -7, 0
Step-by-step explanation:
Is this correct?
Draw and label a triangle that is similar to the one pictured below.
Answers
(6,-1) slope= 2/3 in y=mx+b pls help