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3 years ago

Solve the equation for x :

Mathematics

1 answer:

fiasKO [112]3 years ago

5 0

X=8 my photo has the work done

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First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

8 0

4 years ago

The Rotation maps all 60° about O the center of the regular hexagon. State the image of B for the following rotation. R^3

Digiron [165]

Answer:

the correct answer you are looking for is D

Step-by-step explanation:

6 0

3 years ago

Mike wants to join a gym. He has to pay an initiation fee of $16 and equal monthly payments for the year. The most he wants to p

baherus [9]

Answer:

16+x*12≤580

Step-by-step explanation:

x would be the money you pay per month

Can I have brainliest plz

Hope dis helps :P

4 0

3 years ago

Read 2 more answers

Whats the percent increase from 20 students to 30 students rounded to the nearest percent

yaroslaw [1]

Given Situation: What is the percent increase from the 20 students to the 30 students. Solution: => Let’s find how many percent did it increase. Let’s have 20 as the first total number of the students in the first counts. => Then it became 30 students, let’s find out how many students added. => 30 – 20 = 10, there are 10 students added 10 is 50% of 20, thus, 50% added to the number of students. And that makes it 30 as the total count.

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3 years ago

A Is a number that Is a multiple of two or more denominators.

34kurt

The answer to 1 is common multiple. And the answer to 2 is common denominator

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4 years ago