The partial fraction expansion will look like
(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²
Get everything in terms of a common denominator, and compare the numerators on both sides:
x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)
Expand the right side:
x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)
x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d
Match up the coefficients and solve the resulting system of equations:
a + c = 0
-2a + b - c + d = 0
a - 2b + c = 1
b - c + d = -2
==> a = -1, b = -1/2, c = 1, d = -1/2
So the expansion into partial fractions is
(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)
… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)
What is the equation of the line that passes through the point (2,-2) and has a slope of -1/2?
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line
Answer:
y=-1/2x-1
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/2(x-2)
y+2=-1/2(x-2)
y=-1/2x+2/2-2
y=-1/2x+1-2
y=-1/2x-1
Answer my question 4 u could get 10 points
Answer:
30
Step-by-step explanation:
Split the trapezoid into parts, a rectangle and a triangle. The dimensions of the rectangle will be 3 and 8, so 3*8=24. 24 is part of the answer. The dimensions of the triangle are 4 and 3, and 4*3/2 is 6, so 6 is the other part of the answer. 24 + 6 = 30.
Find the magnitude of the following vector: v=15i + 8j
[tex]\text{Given that,}\\\\\vec{v} = 15 \hat{i} +8 \hat j\\\\ \\\text{Magnitude of the vector,}\\\\|\vec v| = \sqrt{15^2 +8^2}= \sqrt{289} = 17[/tex]
Need help asap!! :) 2. Solve for x.
5x/2 - 3x/4 = 10 1/2
how to solve this?
[tex] \frac{5x}{2} - \frac{3x}{4} = 10 \frac{1}{2} \\ [/tex]
[tex] \frac{5x}{2} - \frac{3x}{4} = \frac{21}{2} \\ [/tex]
Multiply both sides by 4
[tex]4 \times ( \frac{5x}{2} - \frac{3x}{4} ) = 4 \times \frac{21}{2} \\ [/tex]
[tex]10x - 3x = 42[/tex]
[tex]7x = 42[/tex]
Divide both sides by 7
[tex] \frac{7x}{7} = \frac{42}{7} \\ [/tex]
[tex]x = 6[/tex]
At a salad bar, the cost per ounce is
$
0.85
, and the container costs
$
0.25
. Which function represents the total cost of a salad weighing
w
ounces, and what is the total cost,
C
, of a salad weighing
8
ounces?
Answer:
0.85 × 9.412=8.0002 nearest so 0.25 × 9.421= 2.35525
Step-by-step explanation:
Y'all i need some help with this.
Answer:
Divide everything by 100.
Step-by-step explanation:
If you divide every number you want by 100, you get a decimal out of 100.
You are a civil engineer working on the design of a new
green space in your city. The space will include gardens,
playgrounds, and picnic areas. One section of the park will
be in the shape of a right triangle. A diagram of the
requirements for the triangular space is shown below.
2x+2 yards
2x yards
2x+4 yards
1. Explain what you know about the space you will be designing. List at least three pieces
of information. (2 points)
1) WET SURPRISE A water balloon is launched off of a patio. The path of the water
balloon can be modeled by h(t) = -6t2 + 13t + 5, where h(t) is the balloon's height in feet and t is the time in seconds after the balloon is launched.
a. How long will it take for the balloon to splat on the ground?
The function of the water balloon is an illustration of a quadratic function.
The balloon will splat on the ground after 2.5 seconds
The function is given as:
[tex]h(t) = -6t^2 + 13t + 5[/tex]
When the balloon splats on the ground, the value of h(t) is 0.
So, we have:
[tex]-6t^2 + 13t + 5 = 0[/tex]
Expand the expression
[tex]-6t^2 + 15t- 2t + 5 = 0[/tex]
Factorize the above expression
[tex]-3t(2t - 5)- 1(2t - 5 )= 0[/tex]
Factor out 2t - 5 in the 2t - 5
[tex](-3t - 1)(2t - 5 )= 0[/tex]
Split the equation into 2
[tex]-3t - 1 = 0\ or\ 2t - 5= 0[/tex]
Rewrite as:
[tex]-3t = 1\ or\ 2t = 5[/tex]
Solve for t
[tex]t = -\frac 13\ or\ t = \frac 52[/tex]
The value of t cannot be less than 0 i.e. negative.
So, we have
[tex]t = \frac 52[/tex]
Divide 5 by 2
[tex]t = 2.5[/tex]
Hence, the balloon will splat on the ground after 2.5 seconds
Read more about quadratic functions at:
https://brainly.com/question/11631534
Taylor Swift estimates the cost of a new Tesla model S to be $85,000. The actual cost is $100,690.
What is the percent error in Taylor's estimate? Round your answer to the nearest whole percent.
Answer:
should be 15%
Step-by-step explanation:
formula is |85,000 - 100,690| ÷ 100,690 × 100
What is the result of 3 divided by three-fifths?
[tex]\dfrac{3}{\tfrac 35} = 3 \times \dfrac 53 = 5[/tex]
Answer:
5
Step-by-step explanation:
3 -> [tex]\frac{3}{1}[/tex]
Method is "Keep, Change, Flip"
[tex]\frac{3}{1} / \frac{3}{5} =\frac{3}{1} * \frac{5}{3} = \frac{15}{3} = 5[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Type the correct answer in each box. Use numerals instead of words.
Step-by-step explanation:
A
let's bring everything on the right hand side back under the square root :
8² = 64
(x³)² = x⁶
so, we get
sqrt(448x^c) = sqrt(64×7×x⁶×x) = sqrt(448×x⁷)
therefore, c = 7
B
similar to A let's bring everything on the right side under the cubic root :
4³ = 64
(x)³ = x³
cubic root(576x^d) = cubic root(64×9×x³×x²) =
= cubic root(576×x⁵)
therefore, d = 5
–A – 22 = –2A – 30
pls
Answer:
A= -8
Step-by-step explanation:
-A - 22=-2A-30
+2A +22
A = -8
A sports tournament has 6 teams. Each team has the same number of players. There are 60 players total. How many players does each team have?
Answer:
10
Step-by-step explanation:
because
60:6=10
every team has the same number of players
(it was an easy proble to solve thats why im typing , so i the app can confirm it as an answer)
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Answer:
10
Step-by-step explanation:
no. of teams=6
no. of players=60
no. of players in each team=60/6=10
If the nominal interest rate is 4. 00% and the rate of inflation is 2. 25%, what is the real interest rate? 1. 75% 4. 50% 6. 25% 9. 0%.
Based on the information given the real interest rate is 1.75%.
Using this formula
Real interest rate =Nominal interest rate − Inflation rate
Where:
Nominal interest rate=4.00%
Inflation rate=2.25%
Let plug in the formula
Real interest rate=4.00%-2.25%
Real interest rate=1.75%
Inconclusion the real interest rate is 1.75%.
Learn more about real interest rate here:https://brainly.com/question/6106690
more fr33 points for u amazing people, stream scientist by twice while ur at it!!!! :))
Answer:
ye
Step-by-step explanation:
there is a proportional relationship between x and y. complete the table with the missing values
Answer:
I think you forgot to attach the table
The function f(x) goes through the point (4, 7). What point will this translate to in the function f(x) = (x - 6) + 3?
a. (10,10)
b. (-2,4)
c. (10,4)
d. (-2,10)
Answer:
a. (10,10)
Step-by-step explanation:
This was by accident the first answer is right
4(3q + 10) = 6( 2q - 9 )
Multiply the fractions and reduce to lowest terms: 3/4 x 1/3
Answer:
3/12 or 1/4
Step-by-step explanation:
Answer:
1/4 is the answer.
Step-by-step explanation:
3/4 x 1/3
=> 3/12
=> 1/4
Therefore, 1/4 is the answer.
Hoped this helped.
When you subtract a number, you get the same results as when you add the opposite number. Why?
Answer:
Step-by-step explanation:
Well, the opposite of a number is the same number with the opposite sign. For example, the opposite of -1 is 1.
So, say we have an equation where we're subtracting a number, for example, 2-1, which obviously equals 1. Now, if we add the opposite of 1 to 2, we get the equation 2+(-1) which still equals 1.
I hope this helps!
0.326
In word form and stranded form please help!!?! I am taking things that are from 4th grade ahh I can't even remember anything from then. please help me word form and stranded form.
Answer:
three hundred twenty six thousandths
if z=3+i/3-i find the value of 1/z and z+1/z
express the radical using the imaginary unit i
Answer:
27
Step-by-step explanation:
find three consecutive number whose sum shall equal 45
Answer:
14, 15, 16
Step-by-step explanation:
n + n+1 + n + 2 = 45
3n + 3 = 45
3n = 42
n = 14
14, 15, 16
A football team has a net yardage of −30 1 3 yards on a series of plays. The team needs a net yardage of 10 yards to get a first down. How many yards do they have to get on their next play to get a first down?
Answer:
36 yards
Step-by-step explanation:
10 yards needed minus 30 then add 1 and 3 and you have your answer
Please help asapppppp!!!!!
Answer:
x is 8.2 I think hold on
yeah I think
Find the exact value of the indicated trigonometric function of θ.
sin θ = [tex]\frac{1}{6}[/tex], sec θ < 0 Find cos θ and tan θ. ____________________
Answer:
cosθ = -√(35/36)
tanθ = -1/√35
Step-by-step explanation:
We know that
sin²θ + cos²θ = 1
(1/6)² + cos²θ = 1
1 - (1/6)² = cos²θ
35/36 = cos²θ
sec θ = 1/ cosθ
1/ secθ = cos θ
Because secθ < 0, 1/ secθ would also be < 0, so cos θ < 0
cosθ = -√(35/36)
tanθ = sinθ/cosθ = (1/6)/-√(35/36)
= (1/6) / -(√35/6)
= -1/√35
3,080 feet = ____ miles. Answer as a proper fraction or as a whole or mixed number
What is the domain and range?
Answer:
Domain: {-6, -2, -1, 1, 3, 6}
Range: {-6, -2, -1, 0, 3}
Step-by-step explanation:
to find the domain of a function, you look at all the possible x-values. this means you look at all the points, and see what their x-values are.
for example, the first point on the left is at (-6, -1). this means that -6 is in the domain. continue doing this for all the points, and you get {-6, -2, -1, 1, 3, 6}
to find the range of a function, it's just like domain but with y-values.
for example, for the leftmost point, it's at (-6, -1) so -1 is part of the range. continuing this with all the points, you get {-6, -2, -1, 0, 3}
