Perform the indicated operations on the following polynomials.

Mathematics

1 answer:

Vesna [10]3 years ago

8 0

The answer would be 4x^3-3x^2+x-8

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What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

Binomial Series

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$

$\implies \left(\dfrac{120}{6}\right)a^{3}b^3$

$\implies 20a^3b^3$

7 0

2 years ago

What is the area of the shaded segment?

Whitepunk [10]

Answer:

$6\pi-9\sqrt{3$

Step-by-step explanation:

The area of a pie-slice shape can be found with the equation $A=\pi nr^2/360$ where n is the angle of the shape and r is the radius of the circle. In this case, n=60 and r=6. Therefore, the total area of the pie-slice is $\pi (60)(6^2)/360=6 \pi$

Next, the triangle that makes up the unshaded part of the segment is an equilateral triangle because the angle is 60. The area of an equilateral triangle is $\sqrt{3}r^2/4$ where r is the length of one of its side (in this case, r=6). Plugging that in, we get an area of $9 \sqrt{3}$