The 3rd term of (a-b)4 is

Mathematics

1 answer:

fgiga [73]1 year ago

4 0

The third term of the expansion is 6a^2b^2

<h3>How to determine the third term of the expansion?</h3>

The binomial term is given as

(a - b)^4

The r-th term of the expansion is calculated using

r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)

So, we have

3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)

Evaluate the sum and the difference

3rd term = C(4, 2) * (a)^2 * (-b)^2

Evaluate the exponents

3rd term = C(4, 2) * a^2b^2

Evaluate the combination expression

3rd term = 6 * a^2b^2

Evaluate the product

3rd term = 6a^2b^2

Hence, the third term of the expansion is 6a^2b^2

Read more about binomial expansion at

brainly.com/question/13602562

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You toss a rock of mass m vertically upward. Air resistance can be neglected. The rock reaches a maximum height h above your han

laiz [17]

Answer:

$v=\sqrt{\frac{3gh}{2}}$

Step-by-step explanation:

If air resistance is neglected, the energy is constant. That means that in every point in the trajectory the energy is the same.

At the point of height h, all the energy is potential and velocity is zero (no kinetic energy)

$E=mgh$

At point of height h/4, some of the potential energy has transformed in kinetic energy and the velocity is no longer zero. But we know the total amount of energy is the same as the maximum height point.

With that information, we can calculate the velocity v:

$E=mg(\frac{h}{4})+m\frac{v^2}{2}=mgh\\\\m\frac{v^2}{2}=mg(h-\frac{h}{4})\\\\\frac{v^2}{2}=\frac{3gh}{4}\\\\v^2=\frac{3gh}{2}\\\\v=\sqrt{\frac{3gh}{2}}$