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pentagon [3]
3 years ago
11

I'll give brainiest all quadrilaterals have four sides true or false pls explain why

Mathematics
1 answer:
babunello [35]3 years ago
4 0

Answer:

<em><u>True</u></em>

Every quadrilateral has 4 sides, 4 vertices, and 4 angles. 4. The total measure of all the four interior angles of a quadrilateral is always equal to 360 degrees.

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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +
Veronika [31]

Answer:

Verified

y(x) = \frac{3Ln(x) + 3}{x}

y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

                           x^2y' +xy = 3

- A general solution to the above ODE is also given as:

                          y = \frac{3Ln(x) + C  }{x}

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

                          y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x)  }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

                          -\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3

- Therefore, the complete solution to the given ODE can be expressed as:

                        y ( x ) = \frac{3Ln(x) + 3 }{x}

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)

- Therefore, the complete solution to the given ODE can be expressed as:

                        y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}

                           

Download docx
6 0
3 years ago
NEED DONE ASAP!!
almond37 [142]

Answer:

A. 3x^2 + 4 = 52

     3x^2 = 52 - 4

     3x^2 = 48

       x^2 = 48/3

       x^2 = 16

        x    = \sqrt{16}

        x = 4

B. x^2 - 121 = 0

     x^2  = 121

       x = \sqrt{121}

       x = 11

C. (b + 4 )2 = 49

    2b + 8 = 49

    2b  = 49 - 8

     2b = 41

        b = 41/2

3 0
3 years ago
V=pir^2h solve this equation for h
Nady [450]
Since we are solving for h, the equation:

V = πr²h

...divides πr² to the other side. Thus, it becomes....

\frac{V}{ \pi r^2} = h

Which can be rewritten as....

h = \frac{V}{ \pi r^2}
3 0
3 years ago
Read 2 more answers
A doctor administers a drug to a 36-kg patient, using a dosage formula of 51 mg/kg/day. Assume the drug is available in a 300 mg
Alex
500 is the square root of 36-kg because of 300 tablets
8 0
3 years ago
Applying Math
Feliz [49]
The answer is because 3 squared =9
7 0
3 years ago
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