20. Rectangle ABCD is transformed to create rectangle EFGH. What sequence of

Express into partial fractions 3x³ - 5x² - 3x - 40/( x² + 4)(x - 3)

Fudgin [204]

First simplify the rational expression by dividing. The degree in the numerator has to be at least 1 less than the degree in the denominator before you can decompose into partial fractions.

(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3)) = 3 + (4x² - 15x - 4) / ((x² + 4) (x - 3))

Now decompose the remainder term into partial fractions:

(4x² - 15x - 4) / ((x² + 4) (x - 3)) = (ax + b) / (x² + 4) + c / (x - 3)

Multiply both sides by the denominator on the left:

4x² - 15x - 4 = (ax + b) (x - 3) + c (x² + 4)

Expand the right side:

4x² - 15x - 4 = ax² + (b - 3a) x - 3b + cx² + 4c

4x² - 15x - 4 = (a + c) x² + (b - 3a) x - 3b + 4c

Then

a + c = 4

b - 3a = -15

-3b + 4c = -4

Solve this system to get

a = 5, b = 0, c = -1

We end up with

(4x² - 15x - 4) / ((x² + 4) (x - 3)) = 5x / (x² + 4) - 1 / (x - 3)

and so

(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3))

= 3 + 5x / (x² + 4) - 1 / (x - 3)

8 0

2 years ago

100,85,70,_,40 What is the number pattern?

nirvana33 [79]

Answer:

55

Step-by-step explanation:

its subtracting 15 each time

3 0

2 years ago

Read 2 more answers

Aunty Joan packs a packet of sweets to Alice and Olivia. Alice and Olivia share sweets in the ratio 7:3. Alice gives 3 sweets to

aivan3 [116]

Initially, Alice had 28 sweets and Olivia 12 sweets.

Step-by-step explanation:

First assume that Aunty Joan has x number sweets.

Alice and Olivia shared the x sweets in a ration of 7:3, this means

Alice had 7/10 x sweets and Olivia had 3/10 sweets.

Alice gives 3 sweets to Olivia, Alice will remain with ;

$\frac{7}{10} x-3$

Then the new ratio changes to 5:3 which means Alice will have 5/8 x number of sweets.

Equate the number of sweets for Alice in the two cases, which is

$\frac{5}{8}x=\frac{7}{10} x-3\\ \\\frac{7}{10} x-\frac{5}{8} x=3\\$

$\frac{56x-50x}{80} =3\\\\\\\frac{6}{80} x=3\\\\\\6x=80*3\\\\\\x=240/6\\\\x=40$

So there were 40 sweets at first

Using the ratio of 7:3 then

Alice had 7/10 *40 = 28 sweets

Olivia had 3/10*40= 12 sweets

Alice gave Olivia 3 sweets, so she will remain with 28-3 =25 sweets. Olivia will now have 15 sweets.The new ratio will be 25:15 simplified as 5:3.

Learn More

Ratio : brainly.com/question/11095585

Keywords : Ratio

#LearnwithBrainly

5 0

3 years ago

90 points please help!!!!!!!!

just olya [345]

To model this situation, we are going to use the exponential function: $f(t)=P(1+ \frac{r}{n} )^{nt}$
where
$P$ is the initial number of cars
$r$ is the growing rate in decimal form
$n$ is number of tames the growing rate is increasing per year
$t$ is the time in years

To convert the growing rate to decimal form, we are going to divide the rate by 100%
$r= \frac{12}{100}$
$r=0.12$
Since the growing rate is increasing quarterly, $n=4$ . We also know that the initial number of cars is 920, so $P=920$ . Lets replace all those values in our function:
$f(t)=920(1+ \frac{0.12}{4} )^{4t}$
$f(t)=920(1+0.03)^{4t}$
$f(t)=900(1.03)^{4t}$

We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03

3 0

3 years ago

Read 2 more answers

Two opposite sides of the square are increased by 8 inches and the other two sides are decreased by 5 inches. the area of the ne

Iteru [2.4K]

Answer:

The length of a side of the square would be 8.

Step-by-step explanation:

7 0

2 years ago