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3 years ago

sound intensity is inversely proportional to the square of the distance from the source - the farther from the source you are, t

he less intense the sound. suppose the sound intensity is 30 watts per square meter (W/m^2) at 8 meters. what is the sound intensity at 4 meters?

Mathematics

1 answer:

Goryan [66]3 years ago

4 0

$\bf 
\qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
variation
\end{array}\\\\
-------------------------------\\\\$

$\bf \begin{array}{llll}
\textit{Sound intensity is inversely proportional}\\
\textit{to the square of the distance from the source}
\end{array}\implies s=\cfrac{k}{d^2}
\\\\\\
\textit{we also know that }
\begin{cases}
s=30\\
d=8
\end{cases}\implies 30=\cfrac{k}{8^2}\implies 8^2\cdot 30=k
\\\\\\
\boxed{1920=k}\qquad thus\qquad s=\cfrac{1920}{d^2}
\\\\\\
\textit{what's "s" when d = 4?}\qquad s=\cfrac{1920}{4^2}$

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3 years ago

Read 2 more answers

If a circle has a Diameter of 4m and a Radius of 4 units. Then what is Circumference and Area of the circle?

Fiesta28 [93]

Answer & Step-by-step explanation:

$Circumference=d\pi \\Area=r^2\pi$

The diameter of the circle is 8 m and the radius of the circle is 4 units. So, now we have to plug in the numbers so we can find the circumference and the area of the circle.

$Circumference=(8)\pi$

$Circumference=25.12$

So, the circumference of the circle is 25.12 m.

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$Area=16\pi$

$Area=50.24$

So, the area of the circle is 50.24 units².

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4 years ago

The formula for the volume of this rectangular prism is:

juin [17]

Answer:

Step-by-step explanation: Explanation:

and

represent the length, height and width of the prism, then the volume of the rectangular prism is :

............. (1)

Given :

−

;

............... (2)

(

−

)

;

(

)

Let

(

)

be the expression for the length, then the RHS of equation (1) becomes

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

−

..... (3)

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;

−

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3 years ago

to start to solve the system of equations below, which number would you multiply in the equation -2x-5y=-1? The two equations ar

Leviafan [203]

Answer:

The first equation can be multiplied by 2.

Step-by-step explanation:

The x-coefficients are -2 and 4. If the first one of these is multiplied by 2, it will be the opposite of the second of these. That is 2·(-2) = -4. When -4 and 4 are added, the result is 0, so the x-variable will be eliminated.

To solve these equations by "elimination", you look for simple relationships between the coefficients that will let you combine them to get zero.

_____

Here's the rest of the solution.

2(-2x-5y) +(4x+2y) = 2(-1) +(8) . . . . after multiplying the first equation by 2 and adding the second equation

-4x -10y +4x +2y = -2 +8 . . . . . the result of eliminating parentheses

-8y = 6 . . . . . the result of collecting terms

y = -6/8 = -3/4 . . . . divide by the y-coefficient

Since all of the coefficients in the second equation are even, a factor of 2 can be removed, and the equation written as ...

2x +y = 4

This can be solved for x, so you have ...

x = (4 -y)/2 = 2 -(y/2)

Filling in the above value of y, we find x to be ...

x = 2 -(-3/4)/2

x = 2 3/8

_____

Comment on eliminating y instead of x

If you divide the second equation by 2 so that y has a coefficient of 1, then you can multiply this equation by 5 to give y a coefficient that is the opposite of the coefficient -5 in the first equation. Then the elimination looks like

(-2x -5y) +5(2x +y) = (-1) +5(4)

-2x -5y +10x +5y = -1 +20 . . . . eliminate parentheses

8x = 19 . . . . simplify

x = 19/8 = 2 3/8 . . . . divide by the coefficient of x

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3 years ago