The intensity of soundwave at a distance of 12 miles is 222.22 miles.
What is Directly proportional and inversely proportional?
The link between two variables whose ratio is equal to a constant number is known as a direct proportional, while the multiplication of two variables whose ratio is equal to a constant number is known as an inversely proportional.
It is given that the intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. therefore, the relation between the intensity of the radio wave(I) and distance(r) can be written as,
[tex]I\propto \dfrac{1}{r^2}\\\\\\I=k \dfrac{1}{r^2}[/tex]
Now, it is stated that the intensity of the radio wave at a distance of 2 miles is 8000 units, therefore, substituting the value in the above equation to get the value of the constant,
[tex]I=k\dfrac{1}{r^2}\\\\8000=k\dfrac{1}{2^2}\\\\8000=k\dfrac{1}{4}\\\\k = 8000 \times 4 = 32,000\rm\ units[/tex]
Thus, the value of the constant k is 32,000 units, and the equation of the intensity of the radio signal can be written as,
[tex]I=\dfrac{32,000 }{r^2}[/tex]
Further, the intensity of soundwave at a distance of 12 miles will be equal to,
[tex]I=\dfrac{32,000 }{r^2}\\\\I=\dfrac{32,000 }{12^2}\\\\I=\dfrac{32,000 }{144}\\\\I = 222.22\rm\ units[/tex]
Hence, the intensity of soundwave at a distance of 12 miles is 222.22 miles.
Learn more about Inversely proportional:
https://brainly.com/question/2548537
If 1 measures 135°, what is the measure of 6? (Lines b and c are parallel.)
65°
45°
135°
90°
Answer:
45 degrees
Step-by-step explanation:
135+135=270
360-270=90
90/2=45
your answer is 45 degrees
Answer:
Step-by-step explanation:
Two angles form linear pair if they are adjacent angles and their non common arms are opposite rays.
Corresponding angles: When two parallel lines are intersected by the transversal, the angles formed on the matching corners of the same side of the transversal are called corresponding angles.
∠1 + ∠2 = 180° {Linear pair}
135 + ∠2 = 180
∠2 = 180 - 135
∠2 = 45°
∠6 = ∠2 {Corresponding angles}
∠6 = 45°
What is the average rate of change from -1 to 3?
Answer:
-15
Step-by-step explanation:
(y2 - y1)/( x2 - x1) = (4-64)/(3+1) = -60/4 = -15
If suzannah's budget limit is 0.10 per month, how many text messages can she send per month
Answer:
How much is her phone bill? There is not enough information for me to solve this. Not even answer choices.
Mrs. Johnson wants to know which type of cake she should make for the middle school dance. She will conduct a survey asking certain students which kind of cake they prefer. Which method would provide the most accurate results
Answer:
Asking four boys and four girls from each first period class which type of cake they prefer.
Step-by-step explanation:
cant really explain it just knew it off the top of my head.
Identify the shape and solve for X
(will give Brainliest)
PLEASE HELP
Answer:
see explanation
Step-by-step explanation:
the figure has 4 congruent sides and 4 right angles and is therefore a square, then
8x - 15 = 3x + 11 ( subtract 3x from both sides )
5x - 15 = 11 ( add 15 to both sides )
5x = 26 ( divide both sides by 5 )
x = 5.2
Answer:
It's a square
x = 26/5
Step-by-step explanation:
Well, since all the sides are equal (shown by the 3 lines in the sides) and all the angles are 90 degrees (show by the little squares in the corners), I believe the shape is a square.
Because the sides are equal, you would set up the equation by making the two expressions equal to each other:
3x + 11 = 8x - 15
The next step is to get the variable (x) on only one of the sides. You can do this by subtracting 3x from both sides or by subtracting 8x from both sides. I will subtract 3x here just so the new number can be positive, but either will work.
3x + 11 = 8x - 15
-3x -3x
0 + 11 = 5x - 15
Now, you isolate the x by adding 15 to both sides. Remember, whatever you do to one side, you must also do it to the other side of the equal sign.
11 = 5x - 15
+15 +15
26 = 5x
Lastly, get rid of the number in front of the x so that x is alone on a side of the equal sign. You do this by dividing both sides by 5.
x = 26/5
Now, you can either make this into a mixed number or a decimal or keep it how it is. I hope this helps :]
Write the equaition in slope-intercept form of the line through (6,9) and (-12,-3)
By selling a jacket for Rs 729, Sunanda lost 10 %. What was the cost price of the
jacket?
Answer:
810
Step-by-step explanation:
SP = 729, LOSS = 10.1
[tex]loss \: = \frac{(cp - sp)}{cp} \times 100 \\ \\ 10 = ( \frac{cp - 729}{cp} ) \times 100[/tex]
10 CP = CP x 100 - 729 x 100
729 x 100 = 90 CP
[tex]cp = \frac{729 \times 100}{90} = 810 [/tex]
Cost Price,
$810
Write an algebraic expression that is the product of two factors. One of which should be a sum
Answer:
2x + 9
Step-by-step explanation:
because you need a variable in it to make it an algebraic
what percent of 250 is 182?
Answer:
182 is 72.8% of 250
i need an explanation please
===================================================
Explanation:
The [tex]n^2[/tex] terms cancel out because
[tex]n^2 + (-n^2) = n^2 - n^2 = 0n^2 = 0[/tex]
The n terms combine to
5n + (-3n) = 5n - 3n = 2n
Lastly, the constants combine to
-6 + 4 = -2
Overall we have 2n - 2 as the simplified result.
61280 divide by 72 I do not know how to get this answer please help
Answer:
851.1
Step-by-step explanation:
It would be 851.1
The Smiths bought an apartment for $65,000. Assuming the value will appreciate at most 3% a year, how much will the apartment be in 4 years?
Answer:
$73158.07
Step-by-step explanation:
The way to get this is realize that appreciate by 3% means that the value will go up 3% each year. in order to do this we must multiply 65000 by 1.03 4 times. 65000 times 1.03 times 1.03 times 1.03 times 1.03 = 73158.07.
please mark me as brainlyest
Answer: $73,157.50
Step-by-step explanation:
Given: bought price of apartment(p) = $75000, rate of appreciation(r) = 4.3% and time(t) = 7 years
We know the compound interest/appreciation formula is:
S=p(1+r/100)^t
[tex]\begin{aligned}S &=\$ 65000\left(1+\frac{3}{100}\right)^{4} \\&=\$ 65000\left(\frac{100+3}{100}\right)^{4} \\&=\$ 65000\left(\frac{103}{100}\right)^{4} \\&=\$ 65000\times 1.1255 \\&=\$ 73,157.50\end{aligned}[/tex]
Therefore, the apartment will be worth about $73,157.50 in 4 years
Factor completely
x²-9
Answer:
(x + 3)(x - 3)
Step-by-step explanation:
Use difference of squares property:
(x + 3)(x - 3)
3. Maria signed up for a lawn service. She was
charged an initial fee of $75 plus $18 for every
application. How many applications did she
get with $525?
Step-by-step explanation:
525 - 75 = 450
18 for ever one
equals to 450
18x = 450
450÷18 = x
450 ÷ 18 is
comment and i will check
please put brainest
what is the value of \sqrt{21} rounded to the nearest tenth
Answer:
4.5
explanation:
4.5 x 5(This number is not exactly important, but is used as an example)
Is extremely close to the true square root of 21.
That is 4.58257569495584 unrounded.
in rectangle QRST , QS = 5x-31 and RT= 2x+11. Find the lengths of the diagonals of QRST
Answer:
11.7
Step-by-step explanation:
I just solved and added them all-
GIVING BRAINLIEST 100 points
Answer:
A) 4n+30=95
B) 95-30=65 4n=65 65/4=16.25 or 17 weeks to save a little more than $95
C) the least number of weeks would be 17 since it says a whole week
Step-by-step explanation:
Hope this helped.
A brainliest is always appreciated.
Answer:
i dont know
Step-by-step explanation:
A cylinder has radius 2.5 meters. its volume is 50pi meters. Find its height.
Answer :
8 meters .⠀
Explanation :
The volume of the cylinder is 50π cubic meters.The cylinder has radius 2.5 meters.⠀
To Find :
The height of the cylinder.⠀
Solution :
⠀
We know,
[tex]{ \longrightarrow\qquad \bf\pi {r}^{2}h = \bf{Volume_{(cylinder) } }}[/tex]
⠀
Where,
r is the radius of the cylinder.h is the height of the cylinder.⠀
Now, Substituting the values :
[tex]{ \longrightarrow\qquad \sf\pi \times {(2.5)}^{2} \times h = {50 \pi } }[/tex]
[tex]{ \longrightarrow\qquad \sf\pi \times 6.25 \times h = {50 \pi } }[/tex]
⠀
Cancelling π from both sides :
[tex]{ \longrightarrow\qquad \sf \cancel\pi \times 6.25 \times h = {50 \: \cancel \pi } }[/tex]
[tex]{ \longrightarrow\qquad \sf 6.25 \times h = {50 } }[/tex]
[tex]{ \longrightarrow\qquad \sf h = { \dfrac{50}{6.25} } }[/tex]
[tex]{ \longrightarrow\qquad {\pmb {\bf{h = {8 } }}}}[/tex]
⠀
Therefore,
The height of the cylinder is 8 meters .Solve this:
Profit and Loss
ʘ‿ʘ
Answer:
181.44
Step-by-step explanation:
In term of Rajan
CP= Rs 180
P= 20%
So,
P = 20*180/100
= Rs 36
SP=CP + P
=Rs 216
In term of Sajan
CP= Rs 216
loss=20%
l = 20*216/100
= Rs 43.2
SP= CP - l
= Rs 172.8
In term of Nirajan
CP= 172.8
P = 5%
P = 5*172.8/100
= Rs 8.64
so,
SP=CP + P
=172.8 + 8.64
= Rs 181.44
i do not know this answer
Answer:
try (-4,6)
Step-by-step explanation:
if you use tracing paper, put a mark where the point is
put the tip of the pencil on the point which it will rotate around
spin the paper by the degrees
see where the traced point ends up
NEED HELP ASAP EASY 10 to 20 POINTS
Given :
Find the gcf of the first two terms and the GCF of the last two terms for the polynomial.[tex] \qquad \longrightarrow \sf \: 5p {}^{3} + 10 {p}^{2} + 3p + 6[/tex]
Solution :
The first two terms of the polynomials are :
[tex]\qquad \longrightarrow \sf \: 5p {}^{3} + 10 {p}^{2} [/tex]
[tex]\qquad \longrightarrow \sf \: 5p {}^{2} (p + 2)[/tex]
Therefore,
Their Greatest common factor is 5p² .⠀
The last two terms of the polynomials are :
[tex]\qquad \longrightarrow \sf \: 3p + 6[/tex]
[tex]\qquad \longrightarrow \sf \: 3(p + 2)[/tex]
Therefore,
Their Greatest common factor is 3 .in simple terms, how do u factor a polynomial by distribution? for example " 36a^2 + 24a?
Answer:
6a (6a + 4)
Step-by-step explanation:
What is the highest number that goes both into 36 and 24? That is 6. What else do they have in common? The letter a
So 6a(6a + 4)
Need help on this question ASAP pleasee
Answer:
c
Step-by-step explanation:
vertical translation down two units
Which shows the products ordered from least to greatest?
57
x 564
57
101
X 564
102
29
x 564
27
101
x 564
102
57
x 564
57
29
x 564
27
101
x 564
102
29
x 564
27
57
x 564
57
29
x 564
27
57
x 564
57
101
x 564
102
Answer:
101 divide by 102 multiply by 564
or Jake is admiring a statue in Cedarburg Park from 8 meters away. If the distance between the top of the statue to Jake's head is 10 meters, how much taller is the statue than Jake?
Answer:
Step-by-step explanation:
Jake is 5 feet tall. The distance from the flagpole to Jake is 28 feet and the distance between the tip of the shadows and jake is 7 feet.
To raise money for a class trip, students sold bags of mixed nuts and bags of dried fruit. Evan sold 12 bags of mixed nuts and 10 bags of dried fruit and collected $54. Brett sold 8 bags of mixed nuts and 15 bags of dried fruit and collected $61. How much did they charge for each type of bag?
12 bags of mixed nuts for R2 each and 10 bags of dried fruit for R3 each
HELP Please
I really need the answer
Step-by-step explanation:
a full circle has 360°.
so, since each individual result is represented by an amount of degrees, the total sum of all results must be 360°.
labour = 360 - 136 - 34 - 54 - 14 = 122°
the fraction 122/360 represents the 183 votes for labour.
122/360 = 183
the fraction 1/1 = 1 then represents the total number of votes in the whole system.
61/180 = 183
1/180 = 3
1 = 3×180 = 540
540 pupils voted altogether.
When a photographer can't change a scene, she changes her angle and lens to capture the best of that scene. Similarly, when you can't change your situation in your life, change your perspective and mindset to get the best out of that situation.
Answer the question below:
What does the quotation above tell us?
Answer:
idrk the answer but now I know
HELP PLEASE ASAP!!!!!!!!!!!!!!!!!!
Answer:
(3, 5)
Step-by-step explanation:
Answer:
(3, 5)
explanation:
solve for x:
5x-10=-3x+14
5x + 3x = 14 + 10
8x = 24
x = 3
solve for y:
y = 5x -10
y = 5(3) - 10
y = 5
In (x, y) form → (3, 5)
Solve for x round to nearest tenth of a degree
To find the measure of angle NLM which is x, we must use trigonometry.
In this case we use the sine function:
[tex]sin(x) =[/tex] (side opposite angle NLM) / (hypotenuse)
[tex]sin(x) = \frac{4.9}{7.5} \\x = sin^{-1}(\frac{4.9}{7.5})\\x= 40.8 degrees[/tex]
Hope that helps!