The partial fraction expansion for the rational function
S/ (s - 7) (s^2 - 49) = -25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16)
can be found by decomposing it into the sum of simpler fractions.
One way to do this is to use the method of long division and then match the coefficients of the resulting polynomials. The process is as follows:
Divide S by (s - 7) to get a quotient of S1 and a remainder of R1.
Divide R1 by (s^2 - 49) to get a quotient of S2 and a remainder of R2.
Write the expansion as S1 + S2 + R2/(s - 7)(s^2 - 49)
Alternatively, we can use the method of partial fraction decomposition by inspection.
To do this, you will write the rational function as the sum of simpler fractions with the same denominator.
S/ (s - 7) (s^2 - 49) = A/(s-7) + B/ (s^2 - 49) + (C*s + D)/(s^2 - 49)
where A, B, C, and D are unknowns that you will find by matching coefficients.
S = (A(s^2-49) + B(s-7) + C*s + D) / (s-7) (s^2-49)
You can use this equation to solve for A, B, C, and D by matching coefficients.
-25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16) = A/(s-7) + B/(s^2 - 49) + (C*s + D)/ (s^2 - 49)
To learn more about Partial function:
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(4x+7) (4x-7)=
give the solution pleasee
Answer:
16x - 49
Step-by-step explanation:
Answer:
Im not sure 4x+8 and then 4×-7??? do it on your calendar frl amd you can see amd type exactly what the guesting..
A store wants employees to start wearing uniforms to work. The plans to purchase the uniforms and hand out 5 uniforms to every employee one for each day or the week. Uniforms come in packs of 8, and the store plans to purchase 56 packs of uniforms. How many employees can the store give uniforms to?
Answer:
89 employees
Step-by-step explanation:
Uniforms come in packs of 8, and the store plans to purchase 56 packs of uniforms.
This means
1 pack = 8 uniforms
56 packs = x uniforms
Cross Multiply
x = 56 × 8 uniforms
x = 448 uniforms
The plan is to hand out 5 uniforms to every employee one for each day or the week.
Hence, the number of employees that the store can give can uniforms to is calculated as:
5 uniforms = 1 employee
448 uniforms = x employees
Cross Multiply
5x = 448 × 1 employee
x = 448/5
x = 89.6 employees.
Since a person cannot be represented by decimal, the store can give uniforms to 89 employees
Which pair of numbers has a sum of 100?
( A) 39,61
(B) 49,61
(C) 59, 51
(D) 39,51
Answer:
a
Step-by-step explanation:
39+61 is the only pair that make 100.
PLEASE HELP ONLY IF YOUR FOR SURE!! <3 What is the value of x in the figure?
Enter your answer in the box.
x =
Answer:
68. We just subtract 22 from 90
In UVW, u = 190 cm, v = 380 cm and w=560 cm. Find the measure of ZW to the
nearest 10th of a degree
Answer:
157.2
Step-by-step explanation:
Delta math
Answer: 157.2 degrees
Step-by-step explanation: Use law of cosines
Help me with 7 and 8 pleaseeeee
Answer:
7 is 8,and 8 is 23p+9
Answer:
7= 8
8=
Step-by-step explanation:
Which is equivalent to 72 inches?
O A 0.72 yards
O B. 2 yards
O c. 6 yards
O D. 7.2 yards
O E. 36 yards
the answer is B because there is 36 inches in 1 yard
Answer:
Its 2 yards
Step-by-step explanation:
divide 72 by 36
juanyra,hannah,and bella went out for pizza.juanyra ate 1/3 of the pizza,hannah ate 2/6 of the pizza,and bella ate 1/4 of the pizza.how much did they eat toghether.
Answer:
1 - (1/4 + 2/3)
1 - (3/12 + 8/12)
1 - 11/12
1/12 left
a b c d e f g h i j k l m n o p q r s t u v w x y z
Answer:
???
Step-by-step explanation:
Answer:
now i know my abc's
Step-by-step explanation:
Please help with ALEKS >-< ..................................
Answer:
4.5
Step-by-step explanation:
From the file, we see that;
Horizontal distance from bottom of ladder to side of house = 2
Length of ladder leaning against side of the house = 4 m.
Now we want to find the distance from the top of the ladder to the ground which we can call d.
Thus we can find it from pythagoras theorem.
d = √(2² + 4²)
d = √(4 + 16)
d = √20
d = 4.47
To the nearest tenth gives;
d = 4.5
Students in a class were asked to name their favorite type of soup. The results are shown in the circle graph. How many times more students prefer tomato soup than prefer French onion soup? French onion=0.06% Tomato=33%
Answer:
5.5 times
Step-by-step explanation:
0.33/0.06=5.5
Find the remainder when 2x^3 + 15x^2 + 31x + 12 is divided by (x-1)
Answer:
1/
2 3 15 2 31 12
2 1 14 -12 43
__________________
2 1 14 -12 43 -31
so the answer is r=-31
Answer:
remainder = 60
Step-by-step explanation:
Given f(x) divided by (x - h) then the remainder is f(h)
f(x) = 2x³ + 15x² + 31x + 12 , then
f(1) = 2(1)³ + 15(1)² + 31(1) + 12
= 2 + 15 + 31 + 12 = 60 ← remainder
A specialty shop procures silver necklaces for 15$ a piece and offers them to customers for 33$ each. What is the mark-up percentage?
Answer:
54.5%
Step-by-step explanation:
Given data
Cost price= $15
Selling price= $33
Mark up percent =????
%markup= selling-cost/selling*100
substitute
%markup= 33-15/33*100
%markup= 18/33*100
%markup=0.545*100
%markup= 54.5%
Hence the Percent markup is 54.5%
PLEASE HELP ANSWERS ONLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. 13n+15
2. 12n+18
3. 18n+12
Jon and Keith save money at the end of each month and begin saving money at the same time . Jon's savings after m months are modeled with the formula f(m) = 40m + 20 Keith's savings after m months are modeled with the formula g(m) = 35m + 45 At the end of how many months will they have saved the same amount of money ?
Answer:
g5654
Step-by-step explanation:
what’s the slope of the line? i’m marking a brainliest!
Answer:
m = -2
Step-by-step explanation:
To get the slope of the line, we are going to use the 2-points slope equation form
That will be;
m = (y2-y1)/(x2-x1)
(x1,y1) = (-5,11)
(x2,y2) = (8,-15)
m = (-15-11)/(8-(-5)) = -26/13 = -2
The possible mistake she might have made is placing the x-values difference over the y and her formula will look like;
m = (x2-x1)/(y2-y1)
It is an error of switching the numerator for the denominator
I need help asap!! This is an i-ready lesson.
Answer:
.........jdjdjdndjxbxbbxx
Answer: A because it keep going none stopping
Step-by-step explanation:
4х2 - 3x + 2,
How many terms are there
Answer:
3
Step-by-step explanation:
We are given an expression and are asked how many terms are there.
When it comes to terms, we need to see how many numbers have different endings, this can be variables, symbols, and exponents.
Looking into it, we see 4x^2 - 3x + 2
These are all different terms, therefore there are 3 different terms.
Find the area of a regular pentagon with an apothem of 8.95 cm and a side length of 13 cm. (round to the nearest whole number)
Answer:
C) 291 cm^2
Step-by-step explanation:
Sorry it took me so long to answer, but I am taking a test with this question and I want to make sure I got it right on the test before I gave you the answer.
The test I am taking is on USA TESTING and I got 100
solve for x in : 5^{2x-1} =12^{x}
Answer:
x=2.192785
Step-by-step explanation:
52x−1=12x
log(52x−1)=log(12x)
(2x−1)*(log(5))=x*(log(12))
2x−1=(
log(12)
log(5)
)*(x)
2x−1=1.543959*x
2x−1=1.543959x
2x−1−1.543959x=1.543959x−1.543959x 1.543959x
0.456041x−1=0
0.456041x−1+1=0+1
0.456041x=1
0.456041x
0.456041
=
1
0.456041
0.456041)
x=2.192785
Answer:
x = 2.19
Step-by-step explanation:
Given that,
An equation, [tex]5^{2x-1} =12^{x}[/tex]
To find,
The value of x.
Solution,
We have,
[tex]5^{2x-1} =12^{x}[/tex]
Taking log both sides,
[tex]\text{log}(5^{2x-1})=\text{log}(12^x)[/tex]
We know that,
[tex]\text{log}\ a^n=n\ \text{log}a[/tex]
So,
[tex](2x-1)\text{log}5=x\ \text{log}12[/tex]
So,
[tex](2x-1)0.6989=1.0791x\\\\1.3978x-0.6989=1.0791x\\\\1.3978x-1.0791x=0.6989\\\\0.3187x=0.6989\\\\x=\dfrac{0.6989}{0.3187}\\\\x=2.19[/tex]
So, the value of x is equal to [tex]2.19[/tex].
Reference,
https://brainly.com/question/14968632
PLEASE HELP!!! I need an urgent answer and I'll give brainiest just please answer this easy question!
do like show in pic
hope it helps you
What is the solution to the inequality?
n - 15 > -5
pls help ♀️
Step-by-step explanation:
Given inequality
n - 15 > - 5
The inequality can also be written as :
n - 15 = - 5
n = - 5 + 15
n = 10
or
n > 10
Hope it will help :)
Answer:
n>10
Step-by-step explanation:
n-15>-5
n>-5+15
n>10
The freshman convention was held at the activity center with 12 567 seats. If 120 seats were not occupied. How many seats were occupied?
Nathan launches a water balloon vertically from a platform on his roof. The height of the balloon (in feet) is represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds) after he launches the water balloon. What is the maximum height of the balloon?
Answer:
45.27feet
Step-by-step explanation:
Given the height of the balloon (in feet) represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds)
Note that the velocity of the balloon at maximum height is zero, hence;
v = dh/dt =0
-32t+28.7 = 0
-32t = -28.7
t = 28.7/32
t = 0.897secs
Get the maximum height
Recall that h=−16t²+28.7t+32.4
h = -16(0.897)²+28.7(0.897)+32.4
h= -12.87+25.74+32.4
h = 45.27feet
Hence the maximum height reached is 45.27feet
The equations 3x - 4y = -2,4x-y-4, 3x+4y= 2, and 4x+y=-4 are shown on the graph below.
-5
0
5 X
Which is the approximate solution for the system of equations 3x+4y = 2 and 4x+y=-4?
Answer:b
Step-by-step explanation:
Please help urgent !!
A or D. not sure 'bout it. sorry.
Answer:
b. [tex] {x}^{4} \:varies \: directly \: as \: y[/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{4} }{y} = 7 \\ \\ \implies {x}^{4} = 7y \\ \\ \implies {x}^{4} \: \alpha \: y \\ {x}^{4} \:varies \: directly \: as \: y[/tex]
Brainliest to whoever gets it right: Apply the appropriate mathematical operation to solve this occupation related problem.
Labor rate: $8.75 per hour.
Hours worked: 16
Total price of services: $224
Overhead rate: %
Answer:
37.5%
Step-by-step explanation:
Labor rate = 8.75 dollars per hour.
Hours worked = 6
Direct cost of labor = 140 dollars
Total price of services = 224 dollars
Therefore, the overheads = 84 dollars which is
84 X 100 / 224 = 37.5%
Help me please!!!!!!!!!!!!
find x or solve for x .
What is the midpoint between points (4, 7) and (1, 1)?
Answer:
(2.5, 4)
Step-by-step explanation:
Refer to the formula above. We will sub our points into it.
(4, 7) (1, 1)
(x¹, y¹) (x², y²)
[tex]( \frac{4 +1}{2} \frac{7 + 1}{2} )[/tex]
(5/2, 8/2)
(2.5, 4)