2.4 square miles = square yards

Which expression can be used to find the volume of the sphere? A sphere with radius 9 inches. V = four-thirds pi r squared = fou

Varvara68 [4.7K]

Answer:

b

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

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:

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

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6 0

3 years ago

1) In a yoga class, 75% of the students are women. There are 24 women in the class. How many students are in the class?

mel-nik [20]

Answer:

c

Step-by-step explanation:

5 0

2 years ago

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Jenny and Hanan are collecting clothes for a clothing drive. Hanan collected 1/2 as many bags of clothes as Jenny did. If Jenny

Montano1993 [528]

Answer:

Hanan collect $\frac{3}{8}$ of a bag of clothes

Step-by-step explanation:

Let

x ------> amount of clothing bag that Jenny collected

y ------> amount of clothing bag that Hanan collected

we know that

$y=\frac{1}{2}x$ -----> equation A

$x=\frac{3}{4}$ -----> equation B

Substitute equation B in equation A

$y=\frac{1}{2}(\frac{3}{4})$

$y=\frac{3}{8}$

therefore

Hanan collect $\frac{3}{8}$ of a bag of clothes

5 0

3 years ago

Can y’all please explain this to me, I know the answer but I don’t know how to get it thanks

EleoNora [17]

Answer:

250 jars

6 hours

Step-by-step explanation:

We know they make 50 jars in an hour, so 50 times 5 is 250 jars in 5 hours. Since 300 is 50 more than 250, and we know 50 times 6 is 300, we can say that we would need 6 hours to make 300 jars.

8 0

2 years ago