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mel-nik [20]
3 years ago
13

What is the value of x?

Mathematics
1 answer:
alexandr402 [8]3 years ago
8 0
What is the equation?
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Xy′ = √(1 − y2 ), y(1) = 0
Ulleksa [173]

Answer:

The particular solution is y=\sin (\ln|x|) .

Step-by-step explanation:

The given differential equation is

xy'=\sqrt {1-y^2}

It can be written as

x\frac{dy}{dx}=\sqrt {1-y^2}

Use variable separable method to solve the above equation.

\frac{dy}{\sqrt {1-y^2}}=\frac{1}{x}dx

Integrate both sides.

\int \frac{dy}{\sqrt {1-y^2}}=\int \frac{1}{x}dx

\sin^{-1} y=\ln|x|+C            .... (1)

It is given that y(1)=0. It means y=0 at x=1.

\sin (0)=\ln|1|+C

0=0+C

0=C

The value of constant is 0.

Substitute C=0 in equation (1) to find The required equation.

\sin^{-1} y=\ln|x|+0

Taking sin both sides.

y=\sin (\ln|x|)

Therefore the particular solution is y=\sin (\ln|x|) .

7 0
3 years ago
A wall is in the shape of a trapezium. The first level of the wall is made up of 50 bricks where as the top level has 14 bricks.
alukav5142 [94]

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

Similarly, 3rd level will contain number of bricks = 46 - 4 = 42

Therefore, sequence formed for the number of bricks in each level of the wall will be,

50, 46, 42........14

This sequence is an arithmetic sequence having,

First term 'a' = 50

Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence T_{n}= 14

i). Expression representing last term will be,

  T_{n}=a+(n-1)d

  Here T_{n} = nth term

  a = first term

  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

  n = 10

ii). Number of bricks used in the wall = Sum of the sequence

   Expression for the sum of an arithmetic sequence is,

   S_n=\frac{n}{2}[2a+(n-1)d]

   S_n=\frac{10}{2}[2\times 50+(10-1)(-4)]

        = 5(100 - 36)

        = 320 bricks

4 0
3 years ago
What is the slope of f(x)=x^2+3 when x=-1 ?
irinina [24]
F(x)=(-1)^2+3
f(x)=1+3
f(x)=4

The slope is 0 because 4 is a constant.
8 0
3 years ago
2. At an amusement park, 60% of the people were adults, and the rest were
Aneli [31]

Answer:

Step-by-step explanation:

they had at least 989 people at the amusement park

7 0
3 years ago
I need help with this math problem
dimaraw [331]
Choice J both prices are per a unit
7 0
3 years ago
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