As the problem states, to solve this, we are going to use the equation

where

is the loudness in dB

is the intensity of a sound

<span>is the minimum intensity detectable by the human ear
</span>
We know for our problem that

; we also now that the minimum intensity detectable by the human ear is

, so

. Lets replace those values in our equation to find

:


Qe can conclude that since the explosion is under 100dB, it does not violates the regulation of the town. We used tow physical values to calculate the answer: the intensity of the sound of the explosion,

, and the minimum intensity detectable by the human ear

.
To answer this kind of question, you need to insert the first equation into second equation or vice versa. The equation from the question should be:
1. 3 paperback books + 5 hardcover book = $80.10
2. 7 paperback books + 4 hardcover book= $100.65
It would be easier to convert the 1st equation into
5 hardcover book = $80.10- 3 paperback books
hardcover book= $16.02- 0.6 paperback books
Then insert it to 2nd equation:
7 paperback books + 4 ($16.02- 0.6 paperback books)= $100.65
7 paperback books + $64.08- 2.4 paperback books= $100.65
4.6 paperback books = $100.65- $64.08= $36.57
paperback book= $7.95
Insert paperback book price to the first equation to find the hardcover book price
3 paperback books + 5 hardcover book = $80.10
3 ($7.95)+ 5 hardcover book = $80.10
5 hardcover book = $80.10 - $23.85= $56.25
hardcover book = $11.25
Then one paperback and one hardcoverbook= $7.95 + $11.25= $19.20
468=40x+18(x-3)
468=40x+18x-54
468=58x-54
522=58x
9=x
I'm not sure if you need to know x at all, if not, the top equation is all you need.
Answer:
The diameter of the wheel is 32 centimeters
Step-by-step explanation:
we know that
The <u><em>intersecting chords theorem</em></u> states that the products of the lengths of the line segments on each chord are equal.
so
In this problem

substitute the given values

solve for x

Remember that
LK goes through the center of the wheel
That means----> LK is a diameter

therefore
The diameter of the wheel is 32 centimeters
Answer:

Step-by-step explanation:
Given
Represent radius with r and height with h


when 
Express radius in terms of height



First, we need to determine the volume of the cone in terms of height.

Substitute 




Differentiate both sides w.r.t time (t)


Solve for 

At this point,
and 
So, we have:




Hence:
The rate is 