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?

Answers

Answer 1

Answer:

228.64 ft

Step-by-step explanation:

Given that the total time, t it takes for you to hear the stone hit the water below equals the time it spent falling, t1 plus the time it takes the sound to reach your ear t2.

Given that t = 4s and t = t1 + t2.

So t1 + t2 = 4  (1)

Also s = 16(t1)² and t2 = s/1100

Thus t2 = 16(t1)²/1000

From (1), t2 = 4 - t1

So 4 - t1 = 0.016(t1)²

0.016(t1)² + t1 - 4 = 0

(t1)² + 62.5t1 - 250 = 0

Using the quadratic formula to find t1,

[tex]t1 = \frac{-1 +/- \sqrt{1^{2} - 4 X -4 X 0.016} }{2 X 0.016}\\t1 = \frac{-1 +/- \sqrt{1 + 0.256} }{0.032} \\t1 = \frac{-1 +/- \sqrt{1.256} }{0.032} \\t1 = \frac{-1 +/- {1.121} }{0.032} \\t1 = \frac{-1 + 1.121 }{0.032} or t1 = \frac{-1 - 1.121 }{0.032}\\t1 = 0.121/0.032 or -2.121/0.032\\t1 = 3.78 s or -66.28 s[/tex]

Since t1 cannot be negative, t1 = 3.78 s

So, s = 16(t1)²

= 16(3.78)²

= 16(14.29)

= 228.64 ft


Related Questions

Liz and Rick are squeezing lemons for a lemonade stand. Liz squeezed 18 lemons in 6 minutes. Rick squeezed 24 lemons in 12 minutes. Who squeezed lemons at a faster pace?

A)liz
B)Rick

this is Compare rates: word problems please show and explain the work show WORK

Answers

Liz squeezed lemons faster. Liz squeezed 18 lemons in 6 minutes. To find out how many she squeezed in a minute, you would do 18 / 6, which gives you three. Rick squeezed 24 lemons in 12 minutes. To find out how many lemons he squeezed in a minute, you would do 24/12, which gives you 2. So, Liz squeezed 3 lemons per minute while Rick squeezed 2 lemons per minute.

PLEASE HELP!!!
The perimeter of a rectangular coffee table is given by the trinomial 2t2+4t+2. The table's length is 2t-3. What is the table's width?

Answers

Answer:

t^2+4

Step-by-step explanation:

The perimeter of the table can be given by the equation 2l+2w, and we know the length is 2t-3, meaning 2(2t-3)+2w=2t^2+4t+2, as we know 2t^2+4t+2 is the perimeter. Simplifying we get:

4t-6+2w=2t^2+4t+2

4t+2w=2t^2+4t+8

2w=2t^2+8

w=t^2+4

This means that the table's width is t^2+4

Pleaseeee help answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The answer to the question is 540°

Step-by-step explanation:

The reason to the answer is:-

There is a formula which is (n - 2) × 180

n is the number of sides the shape has, and there is 5 sides so we subtract 5 - 2 = 3

Therefore, 3 × 180 = 540°

I hope this answer helps!

Answer:

540°

General Formulas and Concepts:

Math

Counting

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Sum of Angles: 180(n - 2)°

Step-by-step explanation:

Step 1: Define

We have a polygon with 5 sides (a pentagon)

n = 5

Step 2: Find Sum

Substitute in n [Sum of Angles]:                                                                    180(5 - 2)°(Parenthesis) Subtract:                                                                                   180(3)°Multiply:                                                                                                           540°

Evaluate the expression 9.3^1

Answers

Answer:

9.3

Step-by-step explanation:

Graph the line with slope -5 and y-intercept 7.

Answers

Answer:

start your grap at (0,7) and go up 5 to the right 1 and down 5 to the left 1

mark invested 125 he earned a simple interest of 3% per year on the initial investment if no money was added or removed from the investment what was the amount of interest mark received at the end of two years

Answers

Answer:

$7.50

Step-by-step explanation:

formula for simple interest:

I = prt

I = ($125)(0.03)(2)

I = $7.50

Answer:

You time 125 by 1.03 twice subtract 125 from that awnser to get the amount of money from interest 7.6125 is the awnser

Step-by-step explanation:

Describe the meaning of y >_ 7.9 in words.

Answers

this means that y can be equal to 7.9 or any other number above

-11r + 88 = 77
Solve for r

Answers

Answer:

r=1

Step-by-step explanation:

77 - 88 = -11

-11/-11 = 1

A blank is a fraction with a denominator of one

Answers

Answer:

Whole Number

Step-by-step explanation:

Answer:

A whole is a fraction with the denominator of one.

Step-by-step explanation:

Triangle XYZ is rotated 90° counterclockwise about the origin.
What are the coordinates of point Y’?
(4, –2)
(1, 4)
(–4, 1)
(–1, –4)

Answers

Answer:

i think 42

Step-by-step explanation:

Answer:

B -(1,4)

Step-by-step explanation:

find the volume of the earth if the diameter is 7917.5​

Answers

Answer:

Step-by-step explanation:

diameter=7917.5

r=3958.75

the earth is sphere

V=4/3x3.14xr^3

V=2.6*10^11

Solve this system of linear equations. Separate the x- and y- values with a comma.
17x = 43 - 15y
8x = -68 + 15y

Answers

Answer:

(-1,4)

Step-by-step explanation:

Using elimination, add the two equations to get rid of the y variable.

17x = 43 - 15y

+8x = -68 + 15y

=25x = -25

x = -1

Now plug in -1 for x in any of the equations.

17(-1) = 43 - 15y

-17 = 43 - 15y

-60 = -15y

y = 4

Is(3, 2) a solution to the system on inequalities ?Explain.

Answers

Answer:

No

Step-by-step explanation:

The solution of the system of inequalities is the intersection region of all the solutions in the system. Example 1: Solve the system of inequalities by graphing: y≤x−2y>−3x+5. First, graph the inequality y≤x−2 .

What is an equation of the line that passes through the points (-6, 2) and
(-4, -1)? Put your answer in fully reduced form.

Answers

Answer (assuming the equation can be written in point-slope form):

[tex]y-2 = -\frac{3}{2}(x+6)[/tex]

Step-by-step explanation:  

When knowing a point the line crosses through and its slope, you can write an equation in point-slope form, or [tex]y-y_1= m (x-x_1)[/tex].

1) First, find the slope of the line. Use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and the x and y values of the two points given, then solve like so:

[tex]\frac{(-1)-(2)}{(-4)-(-6)}\\= \frac{-1-2}{-4+6}\\= \frac{-3}{2}[/tex]

Thus, the slope is [tex]-\frac{3}{2}[/tex].

2) Now, use point-slope form, [tex]y-y_1= m (x-x_1)[/tex]. Substitute the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.

The [tex]m[/tex] represents the slope, so substitute [tex]-\frac{3}{2}[/tex] in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line crosses through. Any of the two points will work, and I chose (-6,2) for this answer. So, substitute -6 for

[tex]y-(2)= -\frac{3}{2}(x-(-6)\\y-2 = -\frac{3}{2}(x+6)[/tex]

Betsy bought 10 pencils for $0.15 each, 8 notebooks for $1.50 each, and a book for $45.00.

Answers

$58.50 is the answer

There is a cube that is 1 unit long, 1 unit wide,
and 1 unit deep. What is the volume of this
cube?
a. 4 cubic units
b. 3 cubic units
c. 2 cubic units
d. 1 cubic unit

Answers

D because of lx w x h and you would get one cubic unit

Please help with what you can!

Thank you!

Answers

Answer:

The answer to number 9 is: 148.16

50 students were randomly sampled and asked if they preferred Coke or Pepsi. 12 preferred Pepsi. If there are 620 students in the school how many students would you expect in the entire school to prefer Coke?

Answers

Answer:

around 470 students would prefer coke

Step-by-step explanation:

50 - 12 = 38

38 / 50 = 76%

620 (0.76) = 471.2

Elizabeth swims 50 feet in ten seconds. Jesse swims 110 feet in 20 seconds.
Reagan swims 160 feet in half a minute. Who swims fastest?

Answers

Answer: Jesse

Step-by-step explanation:

Elizabeth - 50f/10s

Jesse - 55f/10s

Reagan - 53.3333333/10s

Jesse is the fastest

Answer:

I think that Jessie swam the fastest

Step-by-step explanation:

Jessie swam the fastest bc Reagan only swims 160 feet in half a minute and 110 is less than 160 and 20 + 20 =40 so if Jessies swimming speed and time was multiplied by 2, she would still swim faster!

(sorry Im not the best at math but I hope you can understand my logic lol)

If 500 calories adds 1 pound to your weight how many 1000 calorie banana splits would you need to eat to gain 10 pounds

Answers

500cal=1lb
1000cal=2lbs
2x5=10
1000x5=5000
Answer: 10 banana splits

Answer: 5

Step-by-step explanation:

each banana split is equal to 2 lbs. therefore, to gain 10 lbs. you need to eat 5 banana splits.

500cal = 1 lb.

1000cal = 1 banana split

1 banana split = 2lbs.

to gain 10lbs, divide 10lbs by 2lbs = 5 banana splits

Solve for the variable
X-11 = 8

Answers

This is pretty easy to do.

First, you have to get x alone by getting rid of the terms next to it. In this case, it’s -11.

To get rid of a term, do the opposite.


So x - 11 + 11 = 8 + 11
Remember to do it on both sides.

x = 19
Answer: 19
Why?
You have to get x alone so you have to add 11 to both sides
X-11+11= 8+11
The 11 cancel out on the left and 8+11 equals 19 so x=19

HAIRCUT Josiah went to the local
barber to get his hair cut. It cost
$18 for the haircut. Josiah tipped
the barber 15%. What was the total
cost of the haircut including the
tip?

Answers

The correct amount would be $20.70

fill in the missing number 21-(-17)=21+...

Answers

Answer:

the answer of 21-(-17)=21+17=38

can you guys help me?

Answers

Pretty sure you have to use the Pythagorean Theorem.
a^2+b^2=c^2

So you would plug in your numbers that you already have (6 and 10) But notice that 10 is the hypotenuse (longest side) so
6^2+x=10^2

Then you would solve it and you should end up with 11.6619

3. Solve for x. Round to the nearest tenth *
25
16
22

Answers

Answer:

51.3 degrees

Step-by-step explanation:

In the figure below, AB is a diameter of circle P.
What is the arc measure of major arc ABC in degrees?

Answers

Answer: 249

Step-by-step explanation: Khan Academy

Answer:

111

Step-by-step explanation:

GOT IT RIGHT!

good at math? PLEASE HELPPPP!!

Answers

Answer:

b

Step-by-step explanation:

what is the initial value of the function:
f(x)=3/2(2)^x

Answers

Answer:

the initial value -- f(0) -- results in a value of 1.5

Step-by-step explanation:

f(0) = [tex]\frac{3}{2}[/tex] · [tex]2^{x}[/tex]     (any value raised to the power of zero equals one)

f(0) = [tex]\frac{3}{2}[/tex] · 1

f(0) = 3/2 or 1.5

It’s NONE. You can use symbolab

For every $10,000 a company earns, it gives $500 to charity. How much does the company give to charity for every $1 earned?

Answers

Answer:

$0.05 i think

Step-by-step explanation:

SOMEBODY PLEASE TELL ME HHOW TO MAKE FRACTIONS INTO PERCENTS WORTH 20 POINTS

Answers

Step-by-step explanation:

Easy steps!

Turn the fraction into a decimal first (or in other words, divide) (For Example: 1/2 = 0.5)Move the decimal point to the right TWO times, and voila (For example: 0.5 = 50%)
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