How can you solve real-world and mathematical problems with numerical and algebraic equations and inequalities?

1 answer:

7 0

You can solve real-world and mathematical problems with numerical and algebraic equations and inequalities. Algebra can be applied to the temperature in different places that both change, height of a growing child over time, the speed of a car that changes over time (mph), and the age of people that increases over year. Algebra is used in parts of our everyday life, we just don’t realize it.

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How do you integrate arctan(x dx? i think that if you simplify the integral you get:?

Temka [501]

Integration by parts will help here. Letting $u=\arctan x$ and $\mathrm dv=\mathrm dx$ , you end up with $\mathrm du=\dfrac{\mathrm dx}{1+x^2}$ and $v=x$ . Now

$\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du$
$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx$

For the remaining integral, setting $y=1+x^2$ gives $\dfrac{\mathrm dy}2=x\,\mathrm dx$ , so

$\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C$

Putting everything together, you end up with

$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\frac12\ln(1+x^2)+C$

6 0

3 years ago

How do you work out 9/10 divided by 6/7??

Helga [31]

$\frac{9}{10} \div \frac{6}{7}$
You just flip 6/7 so it would be 7/6 and then you times it.
$\frac{9}{10} \div \frac{6}{7}$
$\frac{9}{10} \times \frac{7}{6} = \frac{63}{60} = \frac{21}{20}$

6 0

3 years ago

X + 2y + 5z = -17<br> 2x – 3y + 2z = -16<br> 3x + y - z = 3

Tatiana [17]

Answer:

first one : x=−2y−5z−17

2nd one: x= 3 /2 y−z−8

3rd one: x= −1 /3 y+ 1 /3 z+1

Step-by-step explanation:

8 0

3 years ago

Nifal earned 9$ for washing two cars .He recived $1 more for the second car.How much was he paid for washing each car?Which two