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2 years ago

I don’t understand this. The number line question the first one.

Mathematics

1 answer:

Mama L [17]2 years ago

8 0

Answer:

-2 + 5 = 3

Step-by-step explanation:

The arrow represents an addition, you start with -2 and add 5, so you end up at +3.

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What is the value of the negative zero of the function, f, defined by<br> f(x) = x^2 - 16

Lelu [443]

Answer:

x = -4

Step-by-step explanation:

f(x) = x² - 16

This is the difference of squares

which factors as

f(x) = (x - 4)(x + 4)

Therefor the negative zero is

x = -4

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2 years ago

Susan deposited $275 in a savings account that earns simple interest at a rate of 4.5%. She made no additional deposits and no w

Tresset [83]

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Step-by-step explanation:

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scoray [572]

Answer:

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2 years ago

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:

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

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2 years ago

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inna [77]

Answer:

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Step-by-step explanation:

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2 years ago