EASY 13 POINTS RIGHT HERE 10.31 as a mixed number

Mathematics

1 answer:

sergeinik [125]3 years ago

5 0

Answer:

Step-by-step explanation:

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Finf the exact value of sin A and cos A where a = 9 and b = 10 and <c is a right angle

Katyanochek1 [597]

To solve for the longest side, the hypotenuse, you have to use the pythagorean theorem. It will be 10^2 + 9^2 = c^2. 100 + 81 =c^2.
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)

8 0

3 years ago

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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:

<u>Binomial Series</u>

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

<u>Factorial</u> 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:

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

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

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

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