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eduard
3 years ago
7

Will give brainliest to correct answer​

Mathematics
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
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