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NARA [144]
3 years ago
11

The equation f = 0 + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate,

Mathematics
1 answer:
balandron [24]3 years ago
4 0

Answer: option 1 is the correct answer

Step-by-step explanation:

This equation is one of the Newton's equations of motion.

The equation is f = v + at which represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.

To determine an equivalent equation solved for a, we will make a the subject of the formula.

f = v+at

subtracting v from both sides of the equation, it becomes

f-v = 0 + at

Dividing both sides of the equation by t, it becomes

f -v = at

a = (f-v)/t

Option 1 is correct answer

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\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx

You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form

\dfrac{4x^2-6}{(x+5)(x-2)(3x-1)}=\dfrac a{x+5}+\dfrac b{x-2}+\dfrac c{3x-1}

\implies4x^2-6=a(x-2)(3x-1)+b(x+5)(3x-1)+c(x+5)(x-2)

You can use the "cover-up" method here to easily solve for a,b,c. It involves fixing a value of x to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.

  • If x=-5, then 94=112a\implies a=\dfrac{47}{56}
  • If x=2, then 10=35b\implies b=\dfrac27
  • If x=\dfrac13, then -\dfrac{50}9=-\dfrac{80}9c\implies c=\dfrac58

So the integral we want to compute is the same as

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and each integral here is trivial. We end up with

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\ln\left|(x+5)^{47/56}(x-2)^{2/7}(3x-1)^{5/24}\right|+C

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