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4 years ago

2/5 1/8 find common denominator

Mathematics

1 answer:

emmasim [6.3K]4 years ago

8 0

Answer: LCD = 40

Equivalent Fractions with the LCD

2/5 = 16/40

1/8 = 5/40

Step-by-step explanation: If necessary, rewrite input as fractions: 2 / 5, 1 / 8 The least common multiple (LCM) is 40. The lowest common denominator (LCD) is therefore 40. Rewriting the original inputs as fractions equivalent to the LCD: 16 / 40, 5 / 40

Hope I helped!!!! :):):)

https://www.calculatorsoup.com/calculators/math/lcd.php

You can use that next time. :)

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Find the general solution to the homogeneous differential equation. d2ydx2−1dydx−30y=0 d2ydx2−1dydx−30y=0 Use c1c1 and c2c2 in y

lukranit [14]

Answer:

The general solution of second order homogeneous differential equation is $y(x)=c_1e^{6x}+c_2e^{-5x}$

Step-by-step explanation:

To find the general solution of this second order homogeneous differential equation $\frac{d^2y}{dx^2}-\frac{dy}{dx}-30y=0$ we are going to use this Theorem:

Given the differential equation $a \ddot{y}+b\dot{y}+cy =0, a\neq 0$ , consider the quadratic polynomial $ax^2+bx+c$ , called the characteristic polynomial. Using the quadratic formula, this polynomial always has one or two roots, call them $r$ and $s$ . The general solution of the differential equation is:

(a) $\ds y=Ae^{rt}+Be^{st}$ if the roots $r$ and $s$ are real numbers and $r\not=s$ .

(b) $\ds y=Ae^{rt}+Bte^{rt}$ , if $r=s$ is real.

(c) $\ds y=A\cos(\beta t)e^{\alpha t}+B\sin(\beta t)e^{\alpha t}$ , if the roots $r$ and $s$ are complex numbers $\alpha+\beta i$ and $\alpha-\beta i$

Applying the above Theorem we have:

$\mathrm{Substitute\quad }\frac{d^2y}{dx^2},\:\frac{dy}{dx}\mathrm{\:with\:}\ddot{y},\dot{y}$

$\ddot{y}-\dot{y}-30y=0$

The characteristic polynomial is $x^2-x-30$ and we find the roots as follows:

$\mathrm{Break\:the\:expression\:into\:groups}$

$\left(x^2+5x\right)+\left(-6x-30\right)$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+5x\mathrm{:\quad }x\left(x+5\right)$

$\mathrm{Factor\:out\:}-6\mathrm{\:from\:}-6x-30\mathrm{:\quad }-6\left(x+5\right)$

$\mathrm{Factor\:out\:common\:term\:}x+5$

$\left(x+5\right)\left(x-6\right)$

The roots of characteristic polynomial are $r=-5$ and $s=6$

Therefore the general solution of second order homogeneous differential equation is $y(x)=c_1e^{6x}+c_2e^{-5x}$

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4 years ago

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Answer:

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Step-by-step explanation:

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MatroZZZ [7]

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** at the end of 40th day or maybe even beginning of the 41st you will prob need to fill up the gas tank.

The problem wants you to replace these quantities with variables.
y = miles to/from work (13 mi)
x = miles until fill up (525 mi)
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Then just replace the quantities with the assigned variables...
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