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3 years ago

How do I solve this equation quick with an easy method?

Mathematics

1 answer:

Pani-rosa [81]3 years ago

3 0

Answer:

4/(3(x-2))

Step-by-step explanation:

3x^2-21x+30=3(x^2-7x+10)=3(x-5)(x-2)

3x-15=3(x-5)

----------------------------

So the common denominator must be 3(x-5)(x-2)

2(x-2)=2x-4

Add the numerators,

(2x-16)+(2x-4)=4x-16-4=4x-20

-----------------

(4x-20)/[3(x-5)(x-2)]

simplify 4x-20 into 4(x-5)

cancel out the (x-5)'s for both the denominator and the numerator

4/[3(x-2)]

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Step-by-step explanation:

Recall that for a parametrized differentiable curve C = (x(t), y(t)) with the parameter t varying on some interval [a, b]

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Let us break down C into 4 paths $\large C_1,C_2,C_3,C_4$ which represents the sides of the rectangle.

$\large C_1$ is the line segment from (0,0) to (5,0)

$\large C_2$ is the line segment from (5,0) to (5,1)

$\large C_3$ is the line segment from (5,1) to (0,1)

$\large C_4$ is the line segment from (0,1) to (0,0)

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$\large \displaystyle\int_{C}=\displaystyle\int_{C_1}+\displaystyle\int_{C_2}+\displaystyle\int_{C_3}+\displaystyle\int_{C_4}$

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r(t) = t(5,1)+(1-t)(5,0) = (5 , t) for 0≤ t≤ 1 and

r'(t) = (0,1) so

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r'(t) = (-5,0) so

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