Answer:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]
Required
Solve
Let
[tex]u = \frac{x^2}{4}[/tex]
Differentiate
[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]
[tex]du = 2 * \frac{x}{4}\ dx[/tex]
[tex]du = \frac{x}{2}\ dx[/tex]
Make dx the subject
[tex]dx = \frac{2}{x}\ du[/tex]
The given integral becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2= 4u[/tex]
Square both sides
[tex]x^4= (4u)^2[/tex]
[tex]x^4= 16u^2[/tex]
Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]
Simplify
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
In standard integration
[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]
So, the expression becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Meaning of part of a whole
Answer:
Step-by-step explanation:
a portion or division of a whole that is separate or distinct; piece, fragment, fraction, or section; constituent: the rear part of the house;to glue the two parts together.
Please thank me!
Help me please
Determine the ratio for COS C in the picture below
Answer:
Step-by-step explanation:
Cos=opposite/hypotenuse
Cos C=32/40 or 4:5
Cos C=0.8
Paul has a 40 ft. by 30 ft. pole barn on his farm that he wants to move. The southeast corner of the pole barn is currently located 50 ft. west and 25 ft. north of the stock tank where the cows get their water. Paul wants to move the pole barn so the southeast corner of the barn is located 80 feet east and 80 feet south of the stock tank
1. 1. Complete the transformation statement for moving Paul’s pole barn, (x,y) (x+ fill in the blank, y + fill in the blank)
2. Draw the new location of the pole barn on the graph below. Note that the stock tank is located at the origin
3. How far is it from the old location to the new location? (Hint: use the distance formula
Answer:
Step-by-step explanation:
(x,y) ↦ (x+130, y-105)
original position of SE corner: (-50,25)
new position of SE corner: (80,-80)
distance = [tex]\sqrt{(80-(-50))^{2}+(-80-25)^{2} }[/tex]≅167.1 ft
What is the solution of the equation 13 + b = 37?
b=
Answer:
13 + 24 = 37 the answer is 24
Step-by-step explanation:
Answer: 24
Step-by-step explanation: 37-13= 24
x = 6y – 14
-X + 9y = 17
after substitution :
-6y + 14+ 9y = 17
= 14 + 3y = 17
by subtracting 14 :
3y = 3
by dividing over 3 :
y = 1
after substitution:
x = 6 * 1 - 14 = 6 - 14 = -8
x = -8
1/9 ÷5/4 plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
0.8888888888
Step-by-step explanation:
that decimal just convert it to a fractoin
Select five numbers that have 7, 13, and 3 as prime factors.
А
1,092
B
897
с
2,093
D
819
483
F
1,365
G
273
H
546
Answer:
ADFGH
Step-by-step explanation:
Good luck on your test!
The numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.
What is a prime factor?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.
The numbers having the prime factors 7, 13 and 3 are 1,092,819,1,365,273, and 546. Because all the numbers are completely divisible by the numbers 7, 13, and 3.
Therefore, the numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.
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a doll maker puts a small bag of 5 hair ribbons inside each box with a doll how many bags of 5 hair ribbons can be made from 45 hair ribbons
Answer:
divide 45 by 5
you get 9
the answer is 9
Answer:
45 / 5 = 9
Step-by-step explanation:
this.is your answer it's quite simple if u need more help lmk
43=0.34x+19.5
What is x
Step-by-step explanation:
43=0.34x+19.5
=> 0.34x+19.5 = 43
=> 0.34x = 43 - 19.5
= 23.5
[tex] = > x = \frac{23.5}{0.34} [/tex]
=> x = 69.117 (Ans)
What operation should be done first to solve 6x + 5 = 35?
Answer:
Subtract 5
Step-by-step explanation:
Pemdas is done backwards in algebra
solve the equation (0°≤A≤360°)
a) √3sinA-cosA=√2
Step-by-step explanation:
√3sinA-cosA=√2
dividing both side by (√3²-1²=2 we get)
√3/2 sinA-1/2.cos A=√2/2
cos 30sinA-sin30cosA=√2/(√2×√2)
sinAcos30-cosAsin30=1/√2
sin(A-30)=sin45,sin(180-45)
therefore
A-30=45,135
A=45+30=75 or A=135+30=165
? points
Simplify completely :
5x - 20
9x - 36
Answer:
5/9
Step-by-step explanation:
How much should you invest at 5% annual interest rate to have the annual interest of $150?
Answer:
it is 7.5
Step-by-step explanation:
Answer:
It is 7.5
Step-by-step explanation:
Purple paint is made by mixing red paint and blue paint in the ratio 5:2
Yan has 30 litres of red paint and 9 litres of blue paint.
What is the maximum amount of purple paint he can make?
Find the given probabilities. If the probabilities or given in decimal then your answer should be in decimals. If the probabilities are a fraction then your answer should be in fraction.
a. If \large P\left(A\right)=\frac{1}{6} and \large P\left(B\right)=\frac{4}{9}, and events A and B are disjoint events, so \large P\left(A or B\right)=
b. If P(A)= .67 and P(B)= .13 and events A and B are disjoint events, so P(A or B)=
Answer:
B
Step-by-step explanation:
Help? I’ll give brainliest
9514 1404 393
Answer:
10,466.7 in^3
Step-by-step explanation:
The volume of a cone is given by ...
V = (1/3)πr^2·h
where r is the radius and h is the height. Using your numbers, we have ...
V = (1/3)(3.14)(20 in)^2·(25 in) = 10,466.7 in^3
_____
A more accurate value of π will give a different result.
. You got 46 out of 65 questions right on your exam. What's your grade?
Answer:
about like 8 /10
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
You apply the
{Select)
operation
[ Select ]
-for multiplication equations and
[ Select ]
for division equations
-to
[ Select ]
of the equation.
Answer:
ndhduejcijgisjcidjcjzjfjidjicjdici djcojzifcjdjcu
Step-by-step explanation:
no se weydgfds
Find the equation (in terms of x) of the line through the points ( − 1 , − 1 ) and( 4 , − 4 )
Answer:
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-1,-1)[/tex]
[tex](x_2,y_2) = (4,-4)[/tex]
Required
Determine the line equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-1)}{4 - (-1)}[/tex]
[tex]m = \frac{-4 +1}{4 +1}[/tex]
[tex]m = \frac{-3}{5}[/tex]
[tex]m = -\frac{3}{5}[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-1) = -\frac{3}{5}(x - (-1))[/tex]
[tex]y + 1 = -\frac{3}{5}(x +1))[/tex]
Open bracket
[tex]y + 1 = -\frac{3}{5}x -\frac{3}{5}[/tex]
Make y the subject
[tex]y = -\frac{3}{5}x -\frac{3}{5}-1[/tex]
[tex]y = -\frac{3}{5}x +\frac{-3-5}{5}[/tex]
[tex]y = -\frac{3}{5}x +\frac{-8}{5}[/tex]
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
After dinner, Mirna had a second serving of her chocolate bar, eating 3
more pieces. Which equation shows how much she has left of the
whole candy bar after this second serving ?
A.) 5/8 - 3/8 = 2/8
B.) 8/8 - 3/8 = 5/8
C.) 8/8 - 5/8 = 3/8
D.) 3/8 - 2/8 = 1/8
The answer is c because 8 - 5 is 3.
expand and simplify (x-3) (x+5)
Answer:
x^2 + 2x - 15
Step-by-step explanation:
(x-3)(x+5)
x^2 + 5x - 3x - 15
x^2 + 2x - 15
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\mathsf{(x - 3) (x + 5)}}\\\\\large\text{DISTRIBUTE}\\\\\large\boxed{\mathsf{x(x) + 5(x) - 3(x) - 3(5)}}\\\\\large\boxed{\mathsf{x^2 + 2x - 15}}\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x^2+ 2x - 15}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]PLEASE HELP!! WILL MARK BRAINLIEST!! DONT GUESS :)
Answer:
x=9
Step-by-step explanation:
180-108=72 so the equation using x has to equal 72
(15x-63)=72
+63
15x=135
divide by 15
x=9
Simplify p^-8/7^-2q^-9
Answer:
[tex]\frac{7^2}{p^8 \cdot q^9}[/tex]
Step-by-step explanation:
[tex]\frac{p^{-8}}{7^{-2}} \cdot q^{-9} = \frac{\frac{1}{p^8}}{\frac{1}{7^2}} \cdot \frac{1}{q^9} = \frac{7^2}{p^8 \cdot q^9}[/tex] by the definition of negative exponents: [tex]a^{-b} = \frac{1}{a^b}[/tex] for all [tex]a,b[/tex] so long as [tex]a\ne 0[/tex].
The value of the exponential equation is A = 7²q⁹ / p⁸
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = p⁻⁸ / 7⁻² ( q ) ⁻⁹ be equation (1)
On simplifying the equation , we get
A = 7² ( q ) ⁹ / p⁸
Therefore , the value of A is 7²q⁹ / p⁸
Hence , the exponential equation is A = 7²q⁹ / p⁸
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A screening test for a newly discovered disease is being evaluated for its performance as a screening test. In order to determine the effectiveness of the new test, it was administered to 270 workers. A total of 42 individuals who had been diagnosed with the disease tested positive for it. Results showed a negative test for an additional 25 people with the disease. A total of 51 people without the disease tested positive. What is the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of the test
Answer:
- Sensitivity = 62.7 %
- specificity = 74.9 %
- positive predictive value = 45.2 %
- negative predictive value = 85.9 %
- Accuracy of the test = 71.9 %
Step-by-step explanation:
Given the data in th question;
CONDITION POSITIVE CONDITION NEGATIVE TOTAL
TEST POSITIVE 42 51 93
TEST NEGATIVE 25 152 177
TOTAL 67 203 270
so; A=42, B=51, C=25 and D=152
Sensitivity = [A / ( A + C) ]×100= [42 /( 42 + 25)]×100 = [42 / 67] 100=
Sensitivity = 62.7 %
specificity = [D / ( D + B) ]×100= [152 /( 152 + 51)]×100 = [152 / 203] 100=
specificity = 74.9 %
positive predictive value = [A / ( A + B) ]×100 = [42 /( 42 + 51)]×100 =[42/93] 100
positive predictive value = 45.2 %
negative predictive value = [D / ( D + C) ]×100 = [152 /( 152 + 25)]×100 =[152/177] 100
negative predictive value = 85.9 %
Accuracy of the test = [A + D / ( A+B+C+D)] = [42 + 152 / ( 42+51+25+152)]
= [ 194 / 270 ]
Accuracy of the test = 71.9 %
335.71 divided by 1000
Faucet A can fill up a water cooler in 8 minutes. Faucet B can fill the same water cooler in 12 minutes. How long will it take both faucets together to fill the water cooler?
!!!!!Explanation Needed!!!!!
Answer:
in average a it take both faucets together to fill the water cooler=(8+12)/2=10minutes
Help help help help help pls
you deposit 3,800 in an account with an annual interest of 5.2% for 20 years
What is the value of x in the equation 3×=1
Answer:
x=1/3
Step-by-step explanation:
what is the value of 58 - 2 x 3 + 1
Answer:
53
Step-by-step explanation: