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3 years ago

Change 4 5/9 from a mixed number to an improper fraction

Mathematics

2 answers:

zhannawk [14.2K]3 years ago

8 0

Answer:

the answer is D. you would multiply the whole number and numerator. keeping the denominator. :)

Darina [25.2K]3 years ago

4 0

Step-by-step explanation:

Hello, there!!

The answer would be 41/9.

The reason for above answer is to change any mixed fraction into improper fraction we should follow a simple step:

multiply the denominator with whole number.
Add the answer (after mutiplied ).

look here, 

= $\frac{4 \times 9 + 5}{9}$ 

we get 41/9.

Hope it helps...

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3 years ago

1. Use separation of variables to find the solution to the differential equation subject to the given initial condition.

andrew11 [14]

Answer:

Step-by-step explanation:

Given the differential equation dy/dx = 5y/x subject to the condition y = 4 and x = 1. Using the variable separable method of solving differential equation, we will have;

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Integrate both sides of the expression

$\frac{1}{5}\int\limits \frac{1}{y} \, dy = \int\limits \frac{dx}{x} \\ \\\frac{1}{5}lny = lnx + C\\\\lny = 5lnx+5C\\$

using the initial condition y = 4 while x = 1

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Substituting the value of C back into the expression;

$lny = 5 lnx+5(ln4/5)\\lny = 5lnx+ln4\\lny = lnx^5+ln4\\lny = ln(4x^5)\\y = 4x^5$

Hence the solution to the differential equation is y = 4x⁵

b) Given 4(du/dt) = u²

du/dt = u²/4

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u⁻²du = 1/4 dt

integrate both sides of the equation

$\int\limit {u^{-2}} \, du = \int\limits\frac{1}{4} \, dt\\\\\frac{u^{-1}}{-1} = \frac{t}{4} + C\\\\\frac{-1}{u} = \frac{t}{4} + C$

Imputing the initial condition u(0) = 7 i.e when t = 0, u = 7

$\frac{-1}{7} = \frac{0}{4} + C\\\\\frac{-1}{7} = C\\$

$\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}$

Hence the solution to the DE is $\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}$

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Ksenya-84 [330]

Answer:

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4 years ago

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