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3 years ago

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Which one of the following U.S. customary units of volume is closest to 4 liters in volume? 64cups , 16quarts, 512 fluid ounces,

4.12 quarts

1 answer:

prohojiy [21]3 years ago

8 0

Answer:

4.12 quarts

Step-by-step explanation:

You might be interested in

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:

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

6 0

3 years ago

A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the build

Svetlanka [38]

We can see on this graph that the triangle has legs of x and 6 with a hypotenuse of 10 and we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem: a^2+b^2=c^2, where a and b are the legs of the triangle and c, is the hypotenuse

x^2+6^2=10^2 Plugin a=x, b=6, and c=10. Now let us solve for x

x^2+36=100 Square each individual term

x^2+=100+36 Subtract 36 from both sides

x^2=64 Combine like terms

sqrt(2)=sqrt(64) Take the square root of both sides

x = 8 Simplify the square root

So our answer is x = 8
The ladder touches the 8 feet mark on the wall.

5 0

3 years ago

Plz help I am bad at this

Vikentia [17]

Your answer is either A or D

8 0

2 years ago

PLEASE HELP WILL GIVE POINTS

Alexxx [7]

The rate of change is meaning the slope. The slope of A is 8, therefore, the answer would be 7.

hope this helps :)

3 0

3 years ago

Y=-25x+325 What is the slope of this equation?

Bezzdna [24]

Answer:

-25

Step-by-step explanation:

This equation is in the form y = mx + b where m is the slope and b is the y-intercept. Knowing this, we see that -25 is in place of m, so that's our answer.

7 0

3 years ago