All categories

3 years ago

Find the square. (4x – 6y3)2

Mathematics

1 answer:

Artyom0805 [142]3 years ago

6 0

Answer:

16x^2 -48xy^3 +36y^6

Step-by-step explanation:

Use FOIL or the distributive property or the form of the square of a binomial to expand the square.

(4x -6y^3)(4x -6y^3) = 4x(4x -6y^3) -6y^3(4x -6y^3)

= (4x)^2 -(4x)(6y^3) -(6y^3)(4x) +(6y^3)^2

= 16x^2 -48xy^3 +36y^6

_____

The form referred to above is ...

(a +b)^2 = a^2 +2ab +b^2

You might be interested in

Omar went to the football game. He paid $13.50 for admission. He bought a program for $4.75, a bag of popcorn for $3.50, and a l

aalyn [17]

$25.10 is the answer

7 0

2 years ago

Read 2 more answers

Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = sin x, c = 3π/4

anyanavicka [17]

Answer:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Step-by-step explanation:

Given

$f(x) = \sin x\\$

$c = \frac{3\pi}{4}$

Required

Find the Taylor series

The Taylor series of a function is defines as:

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

We have:

$c = \frac{3\pi}{4}$

$f(x) = \sin x\\$

$f(c) = \sin(c)$

$f(c) = \sin(\frac{3\pi}{4})$

This gives:

$f(c) = \frac{1}{\sqrt 2}$

We have:

$f(c) = \sin(\frac{3\pi}{4})$

Differentiate

$f'(c) = \cos(\frac{3\pi}{4})$

This gives:

$f'(c) = -\frac{1}{\sqrt 2}$

We have:

$f'(c) = \cos(\frac{3\pi}{4})$

Differentiate

$f"(c) = -\sin(\frac{3\pi}{4})$

This gives:

$f"(c) = -\frac{1}{\sqrt 2}$

We have:

$f"(c) = -\sin(\frac{3\pi}{4})$

Differentiate

$f"'(c) = -\cos(\frac{3\pi}{4})$

This gives:

$f"'(c) = - * -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

So, we have:

$f(c) = \frac{1}{\sqrt 2}$

$f'(c) = -\frac{1}{\sqrt 2}$

$f"(c) = -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

becomes

$f(x) = \frac{1}{\sqrt 2} - \frac{1}{\sqrt 2}(x - \frac{3\pi}{4}) -\frac{1/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{1/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Rewrite as:

$f(x) = \frac{1}{\sqrt 2} + \frac{(-1)}{\sqrt 2}(x - \frac{3\pi}{4}) +\frac{(-1)/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{(-1)^2/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Generally, the expression becomes

$f(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Hence:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

3 0

3 years ago

Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon De

GuDViN [60]

This year is yer number 2 , so t = 2
which means that the next year will be t = 3

So, Epsilon-delta should order :
42000 (1.3 ^ (3/2))
= 62,254 Tags

Hope this helps

7 0

3 years ago

1 Point

Paha777 [63]

Answer:

Step-by-step explanation:

$f(x)=5^{3x}$

Horizontal asymptote: y = 0

Exponential growth.

5 0

3 years ago

Discounts: there are 125,000 American soldiers in Iraq . 25% are infantry. From the rest 40% are reservist. How many reservist a

Bond [772]

there are 87350 reservist

7 0

3 years ago