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Mathematics

1 answer:

solmaris [256]3 years ago

6 0

Answer:

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Step-by-step explanation:

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Use partial fraction expansion to evaluate: LaTeX: \int\frac{x-1}{x^2+3x+2}dx ∫ x − 1 x 2 + 3 x + 2 d x a. LaTeX: -2\ln\left|x+1

ohaa [14]

$\frac{x-1}{x^2+3x+2}\\\frac{x-1}{(x+1)(x+2)}\\\frac{x-1}{(x+1)(x+2)}=\frac{A}{x+2}+\frac{B}{x+1}\\x-1=A(x+1)+B(x+2)\\\\\text{ Let } x=-1 \text{ then } -2=A(0)+B(-1+2) \text{ which means } B=-2\\\\\text{ Instead of choose } x \text{ to be -1, let's now set it equal to -2 to find } A\\\\-3=A(-1)+B(-2+2)\\-3=-A\\A=3\\\\ \text{ So your integral becomes } \\\int \frac{3}{x+2} dx+\int \frac{-2}{x+1} dx\\3 \ln|x+2|-2\ln|x+1|+C\\\\or\\-2\ln|x+1|+3\ln|x+2|+C$

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3 years ago

A 5 poundbag of peanuts costs $9.30. It's going to be divided into 3/4 pound bags. How much will one bag cost?

dsp73

9.3/5 means that each pound is $1.86.

3/4 ($1.86) =$1.395 or $1.40 for 3/4 pound of peanuts. Hope that helps. :)

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3 years ago

Sofia's taco truck lets customers choose 3 ingredients from the list below to add to their tacos. How many groups of 3 different

DIA [1.3K]

Using the combination formula, and considering that the list has 6 ingredients, it is found that 20 groups of 3 different ingredients can go on a taco.

The order in which the ingredients are chosen is not important, hence, the <em>combination formula</em> is used to solve this question.

<h3>Combination formula: </h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by: