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3 years ago

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Mathematics

1 answer:

Contact [7]3 years ago

6 0

Answer is C
Each additional year of

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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

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

6 0

3 years ago

Omar has a new credit card. He earns 300300300 reward points for every 100100100 dollars he spends. If omar earned 180018001800

jeka94

Omar spent 600 dollars for earning 1800 reward points.

Explanation

Omar earns 300 reward points for every 100 dollars he spends.

Suppose, he spent $x$ dollar for 1800 reward points.

Now according to the ratio of "amount of money spent" and "reward points" , the equation will be......

$\frac{x}{1800}=\frac{100}{300}\\ \\ 300x=180000\\ \\ x=\frac{180000}{300}=600$

Thus, Omar spent 600 dollars for earning 1800 reward points.

5 0

3 years ago

Read 2 more answers

What is the answer to the following?

enyata [817]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please add explanation

Igoryamba

The answer is C

The equation has x = 8/10

To get X by itself you need to divide both sides by 8, so the equation should become X = 10/8

5 0

3 years ago

Pairs that satisfy function y=2x+1

evablogger [386]

Test a pair from each table by substituting their values into the given equation and solving.

A) y = 2x + 1 .......... 2 = 2(0) + 1 .......... 2 ≠ 1

B) y = 2x + 1 .......... 1 = 2(0) + 1 .......... 1 = 1

C) y = 2x + 1 .......... -1 = 2(0) + 1 .......... -1 ≠ 1

D) y = 2x + 1 .......... -2 = 2(0) + 1 .......... -2 ≠ 1

The only pair that satisfied the equation was from answer choice B. Therefore, B is the correct answer.

8 0

3 years ago