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3 years ago

Three tenths of a number is 2.1. Determine the number .

Mathematics

1 answer:

REY [17]3 years ago

6 0

Ok so... Let x be 2.1

x = 2.1 / (3/10)

multiply both the numerator and denominator by 10 which gives

x = 21/3 SO the answer is......

x = 7 Yay!!! Have a god day

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Evaluate the integral, show all steps please!

zalisa [80]

Answer:

$\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x$

Take partial fractions of the given fraction by writing out the fraction as an identity:

$\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}$

Calculate the values of A and B using substitution:

$\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}$

$\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}$

Substitute the found values of A and B:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}$

$\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}$

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/28155016

4 0

2 years ago

Estimate the problem 3,844 ÷75

blondinia [14]

Answer:88

Step-by-step explanation:

3 0

4 years ago

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Please answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Ilya [14]

Answer:

The length of the hypotenuse is 26 inches

Step-by-step explanation:

The leg(brace) attached to the wall is 10 inches

Perpendicular = 10 inches

Your surfboard sits on a leg that is 24 inches.

Base = 24 inches

Formula : $Hypotenuse^2 = Perpendicular^2 +Base^2$

$Hypotenuse^2 = 10^2+24^2$

$Hypotenuse = \sqrt{10^2+24^2}$

Hypotenuse = 26

Hence the length of the hypotenuse is 26 inches

3 0

3 years ago

I need this know please i will give brainliest

Olegator [25]

Answer:

b,,,,,d

Step-by-step explanation:

number of bags times how much it carries so the result equals kg hold

so we must the number 10 always so substitute in each equation to get the number 10

6 0

3 years ago

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Find the value of the following expression:

Misha Larkins [42]

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3 0

4 years ago

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