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2 years ago

Why is the square root of 7 irrational

Mathematics

1 answer:

BigorU [14]2 years ago

3 0

Answer:

dude you should know this one it's obviously not see and if it's a perfect square root then it wouldn't be irrational the answer B

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Consider the function f given by f(x)=x*(e^(-x^2)) for all real numbers x.

NISA [10]

Answer:

$\frac{\sqrt{\pi}}{4}$

Step-by-step explanation:

You are going to integrate the following function:

$g(x)=x*f(x)=x*xe^{-x^2}=x^2e^{-x^2}$ (1)

furthermore, you know that:

$\int_0^{\infty}e^{-x^2}=\frac{\sqrt{\pi}}{2}$

lets call to this integral, the integral Io.

for a general form of I you have In:

$I_n=\int_0^{\infty}x^ne^{-ax^2}dx$

furthermore you use the fact that:

$I_n=-\frac{\partial I_{n-2}}{\partial a}$

by using this last expression in an iterative way you obtain the following:

$\int_0^{\infty}x^{2s}e^{-ax^2}dx=\frac{(2s-1)!!}{2^{s+1}a^s}\sqrt{\frac{\pi}{a}}$ (2)

with n=2s a even number

for s=1 you have n=2, that is, the function g(x). By using the equation (2) (with a = 1) you finally obtain:

$\int_0^{\infty}x^2e^{-x^2}dx=\frac{(2(1)-1)!}{2^{1+1}(1^1)}\sqrt{\pi}=\frac{\sqrt{\pi}}{4}$

5 0

2 years ago

Read 2 more answers

(F x G)(x)<br> F(G(x))<br> G[F(x)]<br> F[G(x)]<br> G(F(x))

pentagon [3]

The results of the composite functions are:

$(f \times g)(x) = 6x^2-9x$

$f(g(x)) = 6x - 3$

$g(f(x)) = 6x - 9$

<h3>What are composite functions?</h3>

Composite functions are functions that are obtained by combining two or more functions together

Assume that:

$f(x) = 2x - 3$

$g(x) = 3x$

Then the computation of the composite functions are as follows:

<h3>Function (f * g)(x)</h3>

$(f \times g)(x) = f(x) \times g(x)$

$(f \times g)(x) = (2x-3) \times (3x)$

$(f \times g)(x) = 6x^2-9x$

<h3>Function f(g(x))</h3>

We have: $f(x) = 2x - 3$

This gives

$f(g(x)) = 2g(x) - 3$

So, we have:

$f(g(x)) = 2(3x) - 3$

$f(g(x)) = 6x - 3$

<h3>Function g(f(x))</h3>

We have: $g(x) = 3x$

This gives

$g(f(x)) = 3f(x)$

So, we have:

$g(f(x)) = 3(2x - 3)$

$g(f(x)) = 6x - 9$

Read more about composite functions at:

brainly.com/question/10687170

4 0

2 years ago

How can a decimal be converted to a percentage?

Alexxandr [17]

B, because percent means per 100.

3 0

2 years ago

What is the first step?<br><br> 4x+y=9<br><br> −x+y=7 <br><br> Help Me Out Please!

KonstantinChe [14]

Answer:

Combine like terms.

Step-by-step explanation:

3x+2y=16

6 0

3 years ago

Read 2 more answers

Twice a number increased by 10 is 4. Find the number

Serjik [45]

Answer:

negative 3

Step-by-step explanation:

so if you know basic algebra you can make an equation 2x+10=4 simplify it to x+5=2 and if you subtract 5 from both sides you end up with x=negative three

3 0

2 years ago