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lianna [129]
3 years ago
15

Matthew has already baked 7 cakes, and he can bake 1 cake with each additional stick of

Mathematics
1 answer:
kenny6666 [7]3 years ago
5 0

Answer:

24

Step-by-step explanation:

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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.

(3<em>x</em>³ - 5<em>x</em>² - 3<em>x</em> - 40) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = 3 + (4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3))

Now decompose the remainder term into partial fractions:

(4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = (<em>ax</em> + <em>b</em>) / (<em>x</em>² + 4) + <em>c</em> / (<em>x</em> - 3)

Multiply both sides by the denominator on the left:

4<em>x</em>² - 15<em>x</em> - 4 = (<em>ax</em> + <em>b</em>) (<em>x</em> - 3) + <em>c</em> (<em>x</em>² + 4)

Expand the right side:

4<em>x</em>² - 15<em>x</em> - 4 = <em>ax</em>² + (<em>b</em> - 3<em>a</em>) <em>x</em> - 3<em>b</em> + <em>cx</em>² + 4<em>c</em>

4<em>x</em>² - 15<em>x</em> - 4 = (<em>a</em> + <em>c</em>) <em>x</em>² + (<em>b</em> - 3<em>a</em>) <em>x</em> - 3<em>b</em> + 4<em>c</em>

Then

<em>a</em> + <em>c</em> = 4

<em>b</em> - 3<em>a</em> = -15

-3<em>b</em> + 4<em>c</em> = -4

Solve this system to get

<em>a</em> = 5, <em>b</em> = 0, <em>c</em> = -1

We end up with

(4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = 5<em>x</em> / (<em>x</em>² + 4) - 1 / (<em>x</em> - 3)

and so

(3<em>x</em>³ - 5<em>x</em>² - 3<em>x</em> - 40) / ((<em>x</em>² + 4) (<em>x</em> - 3))

= 3 + 5<em>x</em> / (<em>x</em>² + 4) - 1 / (<em>x</em> - 3)

8 0
2 years ago
Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same info
kow [346]

Graph is your answer look below for proof

have a good day!

                                                                     

3 0
3 years ago
Pls help solve this...No hacker links
Cerrena [4.2K]

Answer:

x=13

Step-by-step explanation:

18-5=13. You have to subtract 5 from 5 itself and then 18.

8 0
2 years ago
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Nine less than the quotient of two and a number x
Sati [7]
Your answer is 2/x-9
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3 years ago
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Please huryy!!
ArbitrLikvidat [17]

Answer:

1.5

Step-by-step explanation:

8 0
3 years ago
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