If f(x)=81, what is x?

How do you do 39 divided by 936 long division

viva [34]

936 <span>39 </span>= 24

24 = 240 to the nearest tenth

24 = 24 to the nearest hundredth

24 = 24 to the nearest thousandth

= 0 to the nearest tenth

= 0 to the nearest hundredth

= 0 to the nearest thousandth

8 0

3 years ago

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

-3.6,-5.4,-8.1,-12.15 arithmetic or geometric or neither.

Brums [2.3K]

Answer:

Geometric Sequence

Step-by-step explanation:

1. Check the difference.

The difference between the 1st and 2nd term

$( - 5.4) - ( - 3.6) = - 1.8$

The difference between the 2nd and 3rd term

$( - 8.1) - ( - 5.4) = - 2.7$

The difference is not the same. Therefore, it is not an arithmetic sequence.

2. Check the ratio

The ratio between the 1st and 2nd term

$( - 5.4) \div ( - 3.6) = 1.5$

The ratio between the 2nd and 3rd term

$( - 8.1) \div ( - 5.4) = 1.5$

The ratio is the same. Therefore, it is a geometric sequence.

8 0

3 years ago

I don’t really get this question so if anyone knows it please help

Mars2501 [29]

Answer:

$116.82\:\text{square inches}$

Step-by-step explanation:

The window consists of a large square and 4 smaller triangles on the outside. The side length of this square is marked as 10, and therefore the area of this square is $10^2=100\:\mathrm{in^2}$ .

The area of a triangle is given by $\frac{1}{2}\cdot b\cdot h$ . Since the problem states that the overlapping squares are congruent, both legs of the triangle will be $2.9$ and intersect at a $90^{\circ}$ angle.