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Alinara [238K]
3 years ago
9

What is tan 25° to the nearest hundredth​

Mathematics
1 answer:
Nataliya [291]3 years ago
5 0

I believe that it is 30° if you round it to the nearest 10 but if it is to the nearest hundredth I think its 100?

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A population of 40 rats living near a restaurant dumpster is growing at a monthly rate of 50%
goldenfox [79]

[(40 ÷ .5) Y] + 40

Parentheses are rat growth

Brackets are rat growth by how many years or just exclude that and the brackets if you don't need to know how many years are there are

The 40 is the amount of rats already there

Growth of rats plus the amount already there.

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A parallelogram cant be a cross section of a triangular prism? never true,sometimes true,or always true
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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)

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Hatshy [7]
Divide them and then multiply
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