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3 years ago

12

kinata goes for swimming lesson every 5 days while wagos goes every 6 days. if both kinaata and wayos had swimming lesson togeth

er at the pool today after how many days will both meet again at the pool for lesson

1 answer:

diamong [38]3 years ago

4 0

I think it’s either 4 or 20

5 x 4 =20

6 x 4 =20

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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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2 years ago

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3 years ago

The area of the base of the oblique pentagonal pyramid is 50 cm^2 and the distance from the apex to the center of the pentagon i

Verdich [7]

The complete question in the attached figure

Part a)
we know that
ABC is a right triangle
∠ACB=45°
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the answer part a) is
AB=6 cm

Part b)
we know that
volume of the pyramid=(1/3)*Area of the base*height
area of the base=50 cm²
height=6 cm
so
volume of the pyramid=(1/3)*50*6----> 100 cm³

the answer part b) is
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