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Find the complete time-domain solution y(t) for the rational algebraic output transform Y(s):_________

Answers

Answer 1

Answer:

Answer:

y(t)= 11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)

Step-by-step explanation:

$Y(s)=(s+3)/((s^2+3s+2)(s+4)) + (s+3)/(s^2+3s+2) +(1)/(s^2+3s+2)$

We know that $s^2+3s+2=(s+1)(s+2)$ , so we have

$Y(s)=(s+3+(s+3)(s+4)+s+4)/((s+1)(s+2)(s+4))$

By using the method of partial fraction we have:

$Y(s)=(11)/(3(s+1)) - (5)/(2(s+2)) -(1)/(6(s+4))$

Now we have:

$y(t)=L^(-1)[Y(s)](t)$

Using linearity of inverse transform we get:

$y(t)=L^(-1)[(11)/(3(s+1))](t) -L^(-1)[(5)/(2(s+2))](t) -L^(-1)[(1)/(6(s+4))](t)$

Using the inverse transforms

$L^(-1)[c(1)/(s-a)]=ce^(at)$

we have:

$y(t)=11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)$

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Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.x-intercept 7; y-intercept -5

Answers

Answer:

The line with the x- and y-intercepts below has the following equation:

$f(x) = (5x)/(7) - 5$

Step-by-step explanation:

The equation of the line has the following format:

$f(x) = ax + b$

We are given two points, we are going to substitute them into the above equation, and find the equation of the line given the conditions.

Solution

Starting from the y-intercept makes the solution easier, since the term a is multiplied by 0

y-intercept -5

This means that when $x = 0, y = f(x) = -5$ , so:

$f(x) = ax + b$

$-5 = a(0) + b$

$b = -5$

For now, the line has the following equation:

$f(x) = ax - 5$

x-intercept 7

This means that when $y = f(x) = 0,x = 7$ , so:

$f(x) = ax - 5$

$0 = 7(a) - 5$

$7a = 5$

$a = (5)/(7)$

So, the line with the x- and y-intercepts below has the following equation:

$f(x) = (5x)/(7) - 5$

What is 23 squared ?

Answers

The value of the 23² number will be 529.

What is an expression?

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that there is a number 23 and is squared. The value of the 23² will be calculated as:-

E = 23²

E = 23 x 23

E = 529

Therefore, the value of the 23² number will be equal to 529.

To know more about an expression follow

brainly.com/question/51920

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what is 23 squared ? :

23^2 is 529.

Does sine inverse have an exponent? If not, why is there a negative one there? If so, why can't you just divide?

Answers

Answer:

see below

Step-by-step explanation:

the actual way of writing sin inverse is arcsine, not sin⁻¹

since the output of sin is from -1 to 1, the domain of arsince is from -1 to 1. This is different than 1/sin(x), whose domain is all real numbers. we now write sin⁻¹ to fit it on the tiny buttons on our calculators

What is the value of P+Q+R+S?

Answers

The question is not clear at all

A manufacturer knows that their items have a normally distributed length, with a mean of 13.1 inches, and standard deviation of 4.1 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.1 inches

Answers

Answer:

0.73% probability that their mean length is less than 11.1 inches

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = (\sigma)/(√(n))$