Given f(x) = 4x - 6, evaluate f(3). A. 2 B. 1 C.12 D. 6

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

Type the missing numbers in this sequence: 93, __, __, 87, 85, 83

Phantasy [73]

Answer:

if you noticed, it is reduces by 2

so the sequence would be

93, 91, 89, 87, 85, 83

-------------------------------------------------

Hope this helps!

5 0

2 years ago

Read 2 more answers

Find the sum of all numbers from 150 to 200 which are divisible by7

podryga [215]

Step-by-step explanation:

The sum is 1225

Solution :

The numbers from 150 to 200 divisible by 7 are 154,161 ,168,…., 196

Here, a=154,d=7a=154,d=7 and tn=196tn=196

tn=a+(n−1)dtn=a+(n-1)d …(Formula )

∴196=154+(n−1)×7∴196=154+(n-1)×7 …(Substituting the values )

∴196−154=(n−1)×7∴196-154=(n-1)×7

∴427=n−1∴427=n-1 ∴n−1=6∴n-1=6 ∴n=7∴n=7

Now, we find the sum of 7 numbers.

Sn=n2[t1+tn]Sn=n2[t1+tn] ...(Formula )

=72[154+196)=72[154+196)

=72×350=72×350

=7×175=7×175

=1225

8 0

3 years ago

EXPLAIN HOW TO FIND THE AREA OF THE SHADED Region.

marin [14]

Answer:

Find the area of the circle then divide by two

Step-by-step explanation:

7 0

3 years ago

Explain why (–4x)0 = 1, but –4x0 = –4.

hodyreva [135]

Any number raised to power of 0 is 1.
In (-4x)^0, because of the parenthesis, the whole number is being raided to 0, which gives 1.
But in -4x^0, only x is being raised to 0, thus -4x^0 = -4(1) = -4.

5 0

3 years ago