Suppose you were to drop a stone down a well. A falling object obeys the equation s=16(t1)2 , where s is the distance fallen in feet and t is the time in seconds. Sound waves travel at a speed of about 1100 ft/sec, and the time it takes to travel a distance s is t2=s1100 . The total time it takes for you to hear the stone hit the water below equals the time it spent falling plus the time it takes the sound to reach your ear. What is the distance to the water's surface in the well if you hear the stone hit the water 4 seconds after dropping the stone?

Answer:

[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}[/tex]

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt  = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]

Therefore:

[tex]\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]

Next, the surface area of a sphere S is given by:

[tex]\displaystyle S=4\pi r^2[/tex]

Therefore:

[tex]\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}[/tex]

We can divide both sides by 2:

[tex]\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}[/tex]

We can substitute this into dV/dt. Rewriting:

[tex]\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)[/tex]

So:

[tex]\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}[/tex]

Since dV/dt = 0.03 or 3/100:

[tex]\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)[/tex]

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

Answer:

7

Step-by-step explanation:

i have checked, i have spoken

Answer:

C

Step-by-step explanation:

So your total is 15. There are 3 vans, and we want to know how many are on each van.

3 (number of people on each van)=15

Number of people are unknown

3x=15

Divide both sides by 3 to solve for x

x=5

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]D = s.t[/tex]

Required

Which represents 400km

This question requires options. Since none were given, I will answer on a general term.

Situation 1:

s = 20km/h and t = 20h

[tex]D = s.t[/tex]

[tex]D = 20km/h * 20h[/tex]

[tex]D = 400km[/tex]

Situation 2:

s = 10km/h and t = 40h

[tex]D = s.t[/tex]

[tex]D = 10km/h * 40h[/tex]

[tex]D = 400km[/tex]

Situation 3:

s = 40km/h and t = 10h

[tex]D = s.t[/tex]

[tex]D = 40km/h * 10h[/tex]

[tex]D = 400km[/tex]

So, all you literally have to do is multiply the values of s and t. If the product gives 400, then; that situation is D = 400

Answer:

-10 ||10||

Step-by-step explanation:

Answer:

$21.40

Step-by-step explanation:

7% is equal to .07

multiply .07 times 20

=1.40

add the $1.40 sales tax to the meal price to get 21.40

Answer:

-21 - (-14) = -21 + 14 = -7

Step-by-step explanation:

A - and a - make a +. So -21 - (-14) makes -21 + 14. Solve to get -7.

Hope it helps!

Answer:

around 126

Step-by-step explanation:

Answer:

0.0022x

Step-by-step explanation:

Given that,

The credit card company raised her APR from 14% to 15.2%.

Her average daily balance this month is x dollars.

We need to find the algebraically the increase in this month's finance charge due to the higher APR. It can be calculated as follows :

[tex]y=x\times \dfrac{12\%}{14}-x\times \dfrac{15.2\%}{14}\\\\=x\times \dfrac{12}{1400}-x\times \dfrac{15.2}{1400}\\\\=-0.0022x[/tex]

So, the required increase in the month's finance is 0.0022x.

Answer:

0.001x

Step-by-step explanation:

Answer:

where is the paragraph?

Step-by-step explanation:

Answer

6 months / the $30 ($5 per month) will be cheaper

Answer:

1) Six months

2) The second plan ($30 sign up fee, $5 per month)

Step-by-step explanation:

1) Six months

We can write an equation such as 30 + 5m = x, where m = months and x = total cost after a certain amount of months. If we know that the first plan costs $12 a month, we can find the LCM of 12 and 30 + 5m, which is 60. If we plug in 60 as m in the equation I showed, we'll get this:

30 + 5m = 60

Solve for x = 6.

2) The second plan

Write the first plan as an equation 12m = x, where m is months and x is the total cost after a certain amount of months. If we plug in 12 for m (since there's 12 months in a year), we'll get 12(12) = x, where x is equal to $144 after a year.

Write the second plan as an equation 30 + 5m = x, where m is months and x is the total cost after m months. Plug in 12 again so our equation looks like

30 + 5(12) = x. Solve for x and get $90 after a year.

Answer:

This function is exponential

Answer:

48.8 years

Step-by-step explanation:

A=p(1+r/n)^nt

A= total amount

p= initial investment (800_

r/n= annual interest rate over number of years( 2.25)

t= number of years compounded ( annually , biannually, quarterly etc.)

48.8 years

Answer:

$21,807.10

Step-by-step explanation:

Amount ( percent decrease)^time

32,000(0.88)^3 = $21,807.10

Percent decrease = 100 - 12 = 88%

Answer:

thirty two multiplied by one fourth equals eight

Step-by-step explanation:

Answer:

Only the third sequence is arithmetic

Step-by-step explanation:

If the sequence has a common difference, then it is arithmetic.  To find the common difference, substract a term from the next term.

First sequence:  

10 - 20 = -10     5 - 10 = -5    The differences are not the same,   so the sequence is NOT arithmetic

Second sequence:

-6 - (-3) = -3     -18 - (-6) = -12   The differences are not the same,   so the sequence is NOT arithmetic

Third sequence:

 10 -  5 =  5     15 - 10 = 5   20 - 15 = 5  The differences are the same,   so the sequence is arithmetic

Fourth sequence:

10 - 5 = 5    20 - 10 = 10   The differences are not the same,   so the sequence is NOT arithmetic

Answer:

y = 3, y = - 1

Step-by-step explanation:

P is the centroid of the triangle.

Centroid of a triangle divides the median in the ratio 2 : 1

Therefore,

BP : PV = 2 : 1

[tex] \frac{BP}{ PV} = \frac{2}{1} \\ \\ \frac{ {y}^{2} + 1 }{y + 2} = \frac{2}{1} \\ \\ {y}^{2} + 1 = 2y + 4 \\ \\ {y}^{2} + 1 - 2y - 4 = 0 \\ \\ {y}^{2} - 2y - 3 = 0 \\ \\ {y}^{2} - 3y + y - 3 = 0 \\ \\ y(y - 3) + 1(y - 3) = 0 \\ \\ (y - 3)(y + 1) = 0 \\ \\ y - 3 = 0 \: \: or \: \: y + 1 = 0 \\ \\ y = 3, \: \: y = - 1 [/tex]

Answer:

150

Step-by-step explanation:

So first you divide 120 by 4 so you know how much times 4 was increased, 4 was increased by 30 times

Next you multiply 5 by 30 because 4 was multiplied by that much

The answer is 150 girls

Answer:

don't cry because it is over smile because it happened

Step-by-step explanation:

Answer:

D. 6x(63-3y)

Step-by-step explanation:

You would be multiplying

Step-by-step explanation:

You want to be very carful with the parentheses for this question.

You want to find the equation that is 6 times the value of 63 - 3y, so you want to put the equation 63 - 3y in one big parentheses.

6 x (63 - 3y)

Answer: up

Step-by-step explanation: good

Answer:

7

Step-by-step explanation:

(-1^2)x 3 = 3

-1 x 4 = -4

3--4 = 7

Answer: 2x+10 is equivalent but id.k if it was a choice bc u didnt put any

Step-by-step explanation: thx for the points

Answer:

1.) 18

2.) 55

3.)43

Step-by-step explanation:

Answer:

B). ∠BAC and ∠CAD

C). ∠BAE and ∠EAD

D). ∠EAD and ∠DAC

Step-by-step explanation:

As we know, a linear pair consisting of angles at a single point of the line has a sum of 180° in total. In other words, two supplementary angles together comprise a linear pair. In the given figure, the pair of supplementary angles ∠BAC and ∠CAD, ∠BAE and ∠EAD, and ∠EAD and ∠DAC are the linear pairs as their sum is 180°. Thus, options B, C, and D are the correct answers.

Step-by-step explanation:

EAD ∠BAC and ∠CAD ∠BAE

Answer:

0     7

1     7.20

2    7.40

3    7.60

Step-by-step explanation: