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3 years ago

7

Will give brainliest to correct answer

1 answer:

likoan [24]3 years ago

3 0

The answer is B

hope that helps

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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

3 years ago

A cube has side length a. The side lengths are decreased to 50% of their original size. Write an expression in simplest form for

vaieri [72.5K]

Answer:

V = a³/8

Step-by-step explanation:

The volume of the original cube is the cube of the side length:

V = a³

When the side length is reduced to half its former value, the new volume is ...

V = (a/2)³ = a³/2³

V = a³/8 . . . . volume of the new cube

6 0

3 years ago

Complex numbers<br> [ = square root symbol<br><br> -[-64<br> How would I find this?

cestrela7 [59]

$-\sqrt{-64}=-\sqrt{8^2\cdot (-1)}-8\sqrt{-1}=-8i$

8 0

3 years ago

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distributio

san4es73 [151]

Answer:

74.72

Step-by-step explanation:

Given

mean $\left ( \mu \right )=70$

Standard deviation $\left ( \sigma \right )=7$

For Top 25%

$P\left ( Z$

and Z value for 75 % is 0.6744

Thus score which separates the Top 25% of students is

$=\mu +\sigma \cdot Z$

$=70+7\cdot 0.6744=74.7208$

8 0

3 years ago

Please please use explanation with answer

KIM [24]

Answer:

$\large\boxed{\theta=-\dfrac{\pi}{4}+k\pi\ or\ \theta=k\pi}\ for\ k\in\mathbb{Z}$

Step-by-step explanation:

$\tan^2\theta+\tan\theta=0\\\\\tan\theta(\tan\theta+1)=0\iff\tan\theta=0\ \vee\ \tan\theta+1=0\\\\\tan\theta=0\Rightarrow \theta=k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\tan\theta+1=0\qquad\text{subtract 1 from both sides}\\\\\tan\theta=-1\Rightarrow\theta=-\dfrac{\pi}{4}+k\pi\ \text{for}\ k\in\mathbb{Z}$

5 0

3 years ago