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Snezhnost [94]
3 years ago
8

Help me answer this please

Mathematics
1 answer:
Anna007 [38]3 years ago
5 0

Answer:

im pretty sure its B

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
BY using eight eights  and addition only can you make 1000?????/
creativ13 [48]
If u add 125 times 8 it will equal 1000
becouse
8*125=1000
then
\frac{1000}{8} =125
you also can combine it (if this is what are you looking for..)
888+88+8+8+8=1000
or any other combination like:
88+888+8+8+8=1000
or:
8+8+888+8+88=1000
8 0
3 years ago
Wilbur spends 2/3 of his income, share 1/12, and saves the rest. What part of his income does he save? Give the answer in simple
scoundrel [369]

Answer:

<em><u>1/4 of his income.</u></em>

Step-by-step explanation:

If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get <u>1/4</u>.

*Mark me brainliest!*

7 0
3 years ago
What is sin B ?
Neporo4naja [7]

Answer:

The answer to your question is sin B = \frac{8}{17}

Step-by-step explanation:

Sine is the trigonometric function that relates the opposite side and the hypotenuse.

In the picture, we have the hypotenuse and the adjacent side, so we must calculate the opposite side using the Pythagorean theorem.

                b² = c² - a²

                b² = 17² - 15²

                b² = 289 - 225

                b² = 64

               b = 8

Now, we can calculate the sine

               sin B = \frac{opposite side}{hypotenuse}

               sin B = \frac{8}{17}

3 0
2 years ago
Give an example of an infinite set.
Montano1993 [528]
Infinite sets may be countable or uncountable. Some examples are: the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably infinite set; and. the set of all real numbers is an uncountably infinite set.
5 0
3 years ago
Read 2 more answers
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