2 years ago

Please..help

Mathematics

1 answer:

Dominik [7]2 years ago

6 0

Answer

7% . . ...................

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Dy/dx= y^4 and y(2)= -1. Y(-1)=

cupoosta [38]

It looks like you're asked to find the value of y(-1) given its implicit derivative,

$\dfrac{dy}{dx} = y^4$

and with initial condition y(2) = -1.

The differential equation is separable:

$\dfrac{dy}{y^4} = dx$

Integrate both sides:

$\displaystyle \int \frac{dy}{y^4} = \int dx$

$-\dfrac1{3y^3} = x + C$

Solve for y :

$\dfrac1{3y^3} = -x + C$

$3y^3 = \dfrac1{-x+C} = -\dfrac1{x + C}$

$y^3 = -\dfrac1{3x+C}$

$y = -\dfrac1{\sqrt[3]{3x+C}}$

Use the initial condition to solve for C :

$y(2) = -1 \implies -1 = -\dfrac1{\sqrt[3]{3\times2+C}} \implies C = -5$

Then the particular solution to the differential equation is

$y(x) = -\dfrac1{\sqrt[3]{3x-5}}$

and so

$y(-1) = -\dfrac1{\sqrt[3]{3\times(-1)-5}} = \boxed{\dfrac12}$

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2 years ago

A bottle holds 64 fluid ounces of lemonade. How much is this in pints?

myrzilka [38]

Answer:

there are 4 pints

Step-by-step explanation:

64 / 16 = 4

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Perrys Bikes rents bikes for $17 plus $6 per hour. john paid $59 to rent a bike. For how many hours did he rent the bike?

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7 hours

Let x represent hours rented
59=17+6x
42=6x
x=7

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Stefanie is painting her bedroom. She can paint 12 1/3 square feet in 1/5 of an hour. How many square feet can she paint in one

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Step-by-step explanation:

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ratelena [41]

Hi, what exactly is the question ?

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