Answer:
[tex]\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Step-by-step explanation:
Perform the partial fraction decomposition
[tex]\int{\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)} } \, dx\\ \\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\ \\7x^3+5x^2+49x+5=(x^2+7)(Ax+B)+(x^2+1)(Cx+D)\\\\7x^3+5x^2+49x+5=Ax^3+Bx^2+7Ax+7B+Cx^3+Dx^2+Cx+D\\\\7x^3+5x^2+49x+5=Ax^3+Cx^3+Bx^2+Dx^2+7Ax+Cx+7B+D\\\\7x^3+5x^2+49x+5=x^3(A+C)+x^2(B+D)+x(7A+C)+7B+D[/tex]
Set up a system of equations and solve for each constant
[tex]\begin{cases} A + C = 7\\B + D = 5\\7 A + C = 49\\7 B + D = 5 \end{cases}[/tex]
[tex]A+C=7\\A=7-C[/tex]
[tex]7A+C=49\\7(7-C)+C=49\\49-7C+C=49\\49-6C=49\\-6C=0\\C=0[/tex]
[tex]A=7-C\\A=7-0\\A=7[/tex]
[tex]B+D=5\\B=5-D[/tex]
[tex]7B+D=5\\7(5-D)+D=5\\35-7D+D=5\\35-6D=5\\-6D=-30\\D=5[/tex]
[tex]B=5-D\\B=5-5\\B=0[/tex]
Plug solved constants in and evaluate
[tex]\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x+0}{x^2+1}+\frac{0x+5}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x}{x^2+1}+\frac{5}{x^2+7}[/tex]
Break up integral
[tex]\int {\bigr(\frac{7x}{x^2+1}+\frac{5}{x^2+7}\bigr) } \, dx[/tex]
[tex]\int {\frac{7x}{x^2+1} } \, dx +\int {\frac{5}{x^2+7}} \, dx\\\\\int {\frac{7x}{x^2+1} } \, dx +5\int {\frac{1}{x^2+7}} \, dx[/tex]
Solve first integral
Let [tex]u=x^2+1[/tex] and [tex]du=2xdx[/tex] for the first integral. Thus, [tex]\frac{7}{2}du=7xdx[/tex]:
[tex]\frac{7}{2}\int {\frac{du}{u}}\\\\\frac{7}{2}ln(|u|)+C\\ \\\frac{7}{2}ln(|x^2+1|)+C[/tex]
Solve second integral
Since [tex]5\int {\frac{1}{x^2+7} } \, dx[/tex] is in the form of [tex]\int{\frac{1}{x^2+a^2} } \, dx[/tex], its formula is [tex]\frac{1}{a}arctan(\frac{x}{a})+C[/tex]:
[tex]5\int {\frac{1}{x^2+7} } \, dx\\\\5\bigr(\frac{1}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\bigr)\\\\\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Combine integrals
[tex]\biggr[\frac{7}{2}ln(|x^2+1|)+C\biggr]+\biggr[\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\biggr]\\ \\\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. This problem is an example of a _____. a. multinomial population b. normally distributed variable c. uniformly distributed variable
Answer:
A. Multinomial population
Explanation:
A multinomial population has categorical data. In other words data in this form has different classes in which data is grouped into. These classes do not overlap and are more than two as opposed to binomial populations that have just two outcome variables or data categories. For example in the above data, we see that data is grouped into three categories:students in business college, students in liberal art college and students in education college
This figure represents a small glass container.
What is the volume of the container?
270 in³
264 in³
240 in³
216 in³
Answer:
The answer is D. 216 [tex]in^{3}[/tex]
Step-by-step explanation:
I took the test. Hope this helps.
The volume of the container is 216 inches³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given a container.
A triangular prism consists of two triangular bases and three rectangular faces.
The given container is a right triangular prism.
Volume of a triangular prism = Base area × Length of the prism.
Base area = Area of right triangle
= [tex]\frac{1}{2}[/tex] × 6 × 8
= 24 inches²
Length of the prism = length between the base triangles = 9 inches
Volume = 24 × 9 = 216 inches³
Hence the required volume of the container is 216 inches³.
Learn more about Volume here :
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PLEASE HELP! GIVING BRAINLIEST!
You have a piece of canvas that you want to paint. You have enough paint to cover
252 square inches. You know you want one side to be 14 inches. How long should
the other side be if you want to use up all the paint?
show your work
Answer:
18 inStep-by-step explanation:
The area = 252 in²
One side = 14 in
The other side = x
The area of a rectangle is a product of 2 sides
14x = 252x = 252/14x = 18 inAnswer:
h = 18 in.Step-by-step explanation:
Area of a rectangular canvas = base x height (A = b*h)
where A = 252 in²
b = 14 in
find: height (h)
solution:
just plugin the values into the formula:
252 = 14 * h
h = 252 / 14
h = 18 in
Can someone please help with this?
Answer:
∠K = 80°
∠M = 100°
Step-by-step explanation:
Angles along a line total 180°. So, your equation for ∠K is ...
60° +40° +∠K = 180°
∠K = 180° -100° = 80°
Similarly, ...
∠M = 180° -∠K = 100°
_____
Additional comment
Together, the 60° and 40° angles make a 100° angle that is vertical to (and congruent with) ∠M. Recognizing that, you know ∠M = 100°. ∠P is a vertical angle with ∠K, so will have the same measure, 80°.
Round this answer (1,417.4) to the nearest tenth of a gram. can someone please so very kindly help me with this ASAP!
Answer:
1417.4 if they are looking for a whole number the answer is 1417
Step-by-step explanation:
Hope this helped :)
P.S. If this is wrong please let me know
Given f (x) = 5x + 1, find f(0).
Answer:
1
Step-by-step explanation:
5(0)+1=1 because 5x0=0 then add the 1
The value of the function f (x) = 5x + 1 at x equal to zero will be 1.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given function is f (x) = 5x + 1. The value of the function at x equal to 0 will be calculated as below:-
f (x) = 5x + 1
f (0) = 5 x 0 + 1
f (0) = 0 + 1
f (0) = 1
Therefore, the value of the function f (x) = 5x + 1 at x equal to zero will be 1.
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Find the distance between points (4,-9) and (-2,6)
Answer:
16.1555
Step-by-step explanation:
Five-sevenths of the T-shirts in a T-shirt shop are blue. Seven-ninths of those T-shirts are on sale. One-fifth of the blue T-shirts that are on sale are size medium. What fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium? Explain
Answer:
2/5
Step-by-step explanation:
If you take 5/7//9+82+23=2-5
find the distance from the point (6,4) to the line y=x+4
9514 1404 393
Answer:
3√2
Step-by-step explanation:
The distance from point (x, y) to the line ax+by+c=0 is given by ...
d = |ax +by +c|/√(a²+b²)
In general for, the equation of the line is ...
x -y +4 = 0
so the distance formula is ...
d = |x -y +4|/√(1² +(-1)²) = |x -y +4|/√2
For the given point, the distance is ...
d = |6 -4 +4|/√2 = 6/√2
d = 3√2 . . . . distance from the point to the line
the diagonals of a rectangle is 25in. The width is 15 inches. What is the length ? ( Pythagorean theorem c^2 = a^2 + b^2)
Answer:
20
Step-by-step explanation:
(You could also use 3-4-5 method, 15, 20 , 25)
[tex]15^{2} +x^{2} =25^{2}\\225+x^{2}=625\\-225 -225\\x^{2}=\sqrt{400}\\x = 20\\Length = 20 \\\\\\[/tex]
The ____ of two or more sets is the set that contains all elements of the set.
Answer:
Union
Step-by-step explanation:
The UNION of two or more sets is the set that contains all elements of the set.
8.25 halfway to the nearest tenth
Answer:
10
Step-by-step explanation:
Find the equation of the line passing through (-4,-2) and having a slope of 0.
Using the point-slope form:
⇒ [tex](y-y0) = m(x-x0)[/tex]
Which require one point (x0,y0) on the line and the slope (m)
(x0,y0) --> (-4,-2)m --> 0Thus let us plug int the value
[tex](y + 2) = 0(x + 4)\\y + 2 = 0\\y = -2[/tex]
Thus the equation of the line is y = -2
Hope that helps!
HELP will mark brainlesest
Answer:
the angles and side length will stay the same
Step-by-step explanation:
it's a rigid translation, meaning that the shape doesn't change
I need help with this question real quick.
Answer:
The answer is D
Step-by-step explanation:
Alonzo used 5.3 in his model instead of .53
Practice Exercise 1:
1. Given the polynomial functionp(x) = 12 + 4x - 3x2 – x3, find
(a) The degree of the polynomial
(b) The leading coefficient
(c) The constant term
(d) The number of zeroes
Answer:
Step-by-step explanation:
A
pls help :((
i rlly appreciate it ^_^
FALSE
7Y= 1 --> Y= ⅐ NOT 7
so it can't be it's solution
12 (2 -2)+32 = (x +6) +2
Answer: x = 24
Step-by-step explanation:
Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.
Step 1: Remove parentheses.
12 (2 − 2) + 32 = [tex]x[/tex] + 6 + 2
Step 2: Simplify 2 − 2 to 0.
12 × 0 + 32 = [tex]x[/tex] + 6 + 2
Step 3: Simplify 12 × 0 to 0.
0 + 32 = [tex]x[/tex] + 6 + 2
Step 4: Simplify 0 + 32 to 32.
32 = [tex]x[/tex] + 6 + 2
Step 5: [tex]x[/tex] + 6 + 2 to [tex]x[/tex] + 8.
32 = [tex]x[/tex] + 8
Step 6: Subtract 8 from both sides.
32 − 8 = [tex]x[/tex]
Step 7: Simplify 32 − 8 to 24.
24 = [tex]x[/tex]
Step 8: Switch sides.
[tex]x[/tex] = 24
~I hope I helped you! :)~
hey can someone help me I pay you £50
Answer:
x= 31 degrees
Step-by-step explanation:
122x2=244
360-244 = 116
116/2 = 58
z= 91 degrees
so the inside next to corner b is 58 degrees
91 + 58 = 149
180 - 149 = 31
x = 31
Fernando's taxi company charges an initial fee of $3.35 to ride and $0.25 charge per mile. The
cost y in dollars of a taxi ride is a linear function of the distance x in miles traveled.
write the equation for the situation above.
PLEASE HELP❤️❤️❤️❤️❤️❤️❤️
Answer:
9.10938
Step-by-step explanation:
A replica of the Eiffel Tower has a scale factor of 100:1. If the Eiffel tower is 1063 feet tall, how tall is the replica?
Answer:
Height of replica = 10.63 feet
Step-by-step explanation:
Given :-
Scale factor = 100 : 1
Height of Eiffel Tower = 1063 feet
To Find :-
Height of replica (h)
Solving :-
100 = 1063 / x
x = 1063/100
x = 10.63
Solution :-
Height of replica = 10.63 feet
What is the measure of WXX, and why?
Answer:
B
Step-by-step explanation:
The vertical triangles are not congruent which eliminates A and D, the equvilant of Z is U which = y
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (−1, 4), (−1, −3)
Answer:
The slope is undefined.
Step-by-step explanation:
M = Y2 - Y1
X2 - X1
M = -3 - 4
-1 - (-1)
M = -7
0
M = Undefined
At 8:00 A.M., a train leaves a station and travels at a rate of 45 mph. At 9:00 A.M., a second train leaves the same station on the same track and travels in the direction of the first train at a speed of 61 mph. At 10:00 A.M., how far apart are the two trains?
a cylinder has a volume of 78 cm what is the volume of a cone with the same radius and height
Answer:
Volume of cylinder V= bh= 78 cm^3, where b is area of base(circle). Then volume of cone = 1/3bh =1/3*78 = 26 cm^3
Thanks!
Mark me brainliest!
Answer:
Volume (cone) = 26 cm³
Step-by-step explanation:
Given :-
Volume (cylinder) = 78 cm³
To Find :-
Volume (cone) with same height and radius
Solving :-
Find the equation for the volume of the cylinder.
πr²h = 78 cm³
But we know the volume of a cone is 1/3 of the volume of a cylinder.
=> Volume (cone) = 1/3 x 78
=> Volume (cone) = 26 cm³
4,5,6,6,7,7,8,8,8,8,8,9,9
What is the median of the set of numbers?
Answer:
8
Step-by-step explanation:
4,5,6,6,7,7,8,8,8,8,8,9,9
x x x x x x x x x x x x
19.5+24+7.5 =
19.5+__+24 =
___+24___=
Answer:
19.5+24+7.5 = 51
19.5+51+24 = 94.5
51+24+94.5=169.5
Step-by-step explanation: Basically for the blanks you insert the answer you got..
Answer:
19.5+24+7.5=51
19.5+7.5+24=51
19.5+24+7.5=51
Write 2350 million in standard form.
Answer:
2,350,000,000
Step-by-step explanation:
hope this helps
HOW MANY BRAINLIES POINTS SHOULD I MAKE THIS QUESTION???
PHOTO ATTACHED
a) Which country had the lowest number of overall medals among the ten countries?
b) Which country/countries competed in the least number of games?
c) What is the mode in the number of games countries participated in?
d) What is the range between the gold medals awarded to the 10 countries?
e) How many countries got more silver medals than bronze medals?
f) Apart from the United States, which country/countries got more gold medals, more silver medals and more bronze medals than Great Britain?
g) In comparing the number of games a country participated in and the overall number medals received, which country did the best (ie highest number of metals recived per game )? Show your work
h) Using the given Data, give TWO likely reasons why a country like Jamaica does not feature in the top 10 medals even though it does very well in athletics.
i) Using the given information, determine the medal category in which the United states far outperformed its closest competitor. Show your work.
j) Which 3 countries had the most evenly distributed number of goals. Silver and bronze medals (i.e. least smallest range)? Show your work.
Answer:
I think it should be 30-40 brain points, because there's too much questions.