A rock is dropped off the edge of a cliff and its distance s (in feet) from the top of the cliff after t seconds is s(t) = 16t2. Assume the distance from the top of the cliff to the water below is 96 ft.
A) When will the rock strike the water?
B) Make a table of average velocities and approximate the velocity at which the rock strikes the water.

Answers

Answer 1

Answer:

A) 2.45 seconds

B)[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]

Step-by-step explanation:

Distance [tex]s[/tex] (in feet) from the top of cliff after [tex]t[/tex] seconds when a rock is dropped off the edge of a cliff is given as:

[tex]s(t)=16t^2[/tex]

Distance from the top of cliff to water = 96 ft

To find:

A) When will the rock strike the water

i.e. The time taken by the rock to travel the distance of 96 ft.

B) Table of Average Velocity and approximate velocity at which the rock strikes the water ?

Solution:

A) Given that distance traveled = 96 ft

To find the value of [tex]t[/tex]

Putting the value of [tex]s[/tex] in formula: [tex]s(t)=16t^2[/tex] to find [tex]t[/tex]:

[tex]96 = 16t^2\\\Rightarrow t^2=6\\\Rightarrow \bold{t = 2.45\ sec}[/tex]

B) The velocity at which the rock hits the water:

We need to differentiate [tex]s(t)[/tex] w.r.to [tex]t[/tex] in order to find the velocity at any instant.

[tex]s'(t) =\dfrac{d}{dt}s(t) = \dfrac{d}{dt}(16t^2)\\\Rightarrow v = 2\times 16t^{(2-1)}\\\Rightarrow v = 32t[/tex]

The time taken to reach the water is 2.45 seconds.

Putting [tex]t[/tex] = 2.45 seconds to find the velocity:

[tex]v = 32\times 2.45 = 78.4\ ft/sec[/tex]

Average velocity is given as total distance traveled and total time taken.

[tex]\text{Average Velocity = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}[/tex]

[tex]\text{Average Velocity = }\dfrac{96}{2.45}\\\text{Average Velocity = 39.18\ ft/s}[/tex]

[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]


Related Questions

Point B lies on AC between A and C. If AB = 8 and AC = 10, find BC.
A. 2
B. 8
C. 10
D. 18

Answers

Answer:

BC = 2

Step-by-step explanation:

If B lies on AC it makes the line segments AB and BC.

AC=10

AB+BC=AC

AB+BC=10

8+BC=10

BC=2

The value of BC is 2 which is the correct answer that would be an option (A).

What is a Line Segment?

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment AC , where the length of line segment AC refers to the distance between its endpoints, A and C.

Point B lies on AC between A and C.

A______________B______________C

Given that B lies on AC it makes the line segments AB and BC.

AB = 8 and AC = 10

⇒ AB + BC = AC

⇒ AB + BC = 10

⇒ 8 + BC = 10

⇒ BC = 2

Therefore, the value of BC is 2 which is the correct answer that would be an option (A).

Learn more about the line segment here:

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Find the distance between (-4,5) and (4,0) round to the nearest hundredth

Answers

Answer:

Solution: 9.43

Step-by-step explanation:

Remember that we can determine the distance between any two points using the distance formula, d = √(x₂ - x₁)² + (y₂ - y₁)². Let's substitute known values to determine the distance:

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2},}\\ \\\\\mathrm{d}= \sqrt{(4 - (-4))^2 + (0 - 5)^2} = \sqrt{(4 + 4)^2 + (- 5)^2} \\= \sqrt{(8)^2 + 25} = \sqrt{64 + 25} = \sqrt{89}[/tex]

Hence the distance between the points (-4,5) and (4,0) is exactly √89. The question asks us to round off to the nearest hundredth, so your solution will be approximated off to two digits → 9.43.

simply 12 to the power of 16 over 12 to the power of 4

Answers

Answer:

12^12

Step-by-step explanation:

If the exponent bases are the same you can subtract the exponents. Numerator minus denominator. (16-4=12)

A rock has a density of 4.56 g/mL. If it weighs 235 g, what is its volume?

Answers

Answer:

51.54mL

Step-by-step explanation:

Density can be defined as the mass per unit volume of a particular object , substance or compound.

Density tell us how heavy or dense that object, substance or compound is.

Mathematically, the formula for Density = Mass(grams)/Volume(ml or cm³)

In the above question, a rock has the following criteria:

Density = 4.56 g/mL.

Mass = 235 g

Volume is unknown.

Imputing this values into the formula for Density, we have:

4.56g/mL = 235g/ Volume

Cross Multiply

4.56g/mL × Volume = 235g

Volume = 235g/4.56g/mL

Volume = 51.535087719mL

Approximately, the volume of the rock to 2 decimal places = 51.54mL

M=2*2*3*5*5 and N=2*2*2*3*3*7 find the largest number that divides exactly M and N​ please

Answers

Answer:

6

Step-by-step explanation:

Given the prime factors of both numbers

Then the greatest common factor GCF is the product of the common factors

Both 2 and 3 are common factors, thus

2 × 3 = 6 is the GCF

Please Help! Thank u!

Answers

16=4

49=7

289=17

Step-by-step explanation:

Karims wage was increased from £210 to £225 per week.What was the percentage increase,to one decimal place? please help iam stuck​

Answers

Answer: 7.1

Step-by-step explanation: 210/255 • x/100. This equals to 7.142857142857142.

The manager of a factory collected data in order to analyze the relationship
between the number of hours of training a worker receives and
the worker's error rate. The line of best fit for the collected data is y = 0.1 -0.005x, where x is the number of hours of training a worker
receives and y is the error rate.
What approximate error rate should the manager expect for a worker who receives 6 hours of training?
O A. 0.01
OB. 0.07
OC. 0.13
OD. 0.17

Answers

Answer:

B. 0.07

Step-by-step explanation:

You can use the "Desmos Graphing Calculator". It helps a lot.

Answer:

B

Step-by-step explanation:

10 less than a number is equal to 12

Answers

Answer:

The number is 22

Step-by-step explanation:

Let x be the number

Plug x in: x - 10 = 12Add 10 to each side, so it now looks like this: x = 22

Answer:

22

Step-by-step explanation:

Let the number be x:

x - 10 = 12

x = 12 + 10

x = 22

The answer is 22

How much is 571,863 rounded to the nearest thousand?

Answers

Answer:

572000

Step-by-step explanation:

571863 is rounded of to 572000

Because 8 in 571863 is greater than 5

And thus 1 in 571863 changes to 2 with the rest on the right being zero.

572,000
1,863 is the thousands
you look at the 8 to know you round the 1,000 up to make it 2,000

Michael drove 0.5 miles. How many inches did he travel?

Answers

Answer:

31680 inches

Step-by-step explanation:

To find miles to inches, multiply by 63360 to get the answer.

0.5 x 63360 = 31680

So, he traveled 31680 inches.

It would be 31,680 inches

Solve the equation.
-4+x= 12

Answers

Answer:

x = 16

Step-by-step explanation:

Get x alone on one side.

-4 + x = 12

(-4 + x) + 4 = 12 + 4

x = 16

PLEASE HELP! WILL GIVE BRAINLIEST!

Answers

Answer:

(18+21+17+x)÷4=20

x=24 students

Step-by-step explanation:

(18+21+17+x)÷4=20

(56+x)÷4=20

56+x=20*4

56+x=80

x=80-56

x=24

Point Fis on line segment EG . Given FG = 4 and EF = 9 determine the length EG

Answers

Answer:

EG is 13.

Step-by-step explanation:

So we have a line segment EG.

Point F is somewhere on EG.

And we are given that FG is 4 and EF is 9.

Therefore, the length of EG will be the combined lengths of FG and EF. In other words:

[tex]EG=EF+FG[/tex]

Substitute 9 for EF and 4 for FG. Thus: "

[tex]EG=9+4[/tex]

Add:

[tex]EG=13[/tex]

So, the length is EG is 13.

And we're done!

3 over 3 - square root 5

Answers

Answer:

-1.236.

Step-by-step explanation:

3/3 = 1.

√5 = 2.236.

1.000 - 2.236 = -1.236.

the answer is negative because the smaller number is subtracting the larger number..........u just subtract the normal way,( the larger number take away the smaller number), but u should insert a negative sign to the answer.

The picture shows the Alamillo bridge in Seville, Spain. In the picture m<1=58 and m<2=24. Find the measure of the supplement of <1= and of <2. Someone please help!

Answers

Answer:

Supplement of <1 = 122°

Supplement of <2 = 156°

Step-by-step explanation:

Two pairs of angles are said to be supplementary, if their measures in degrees add up to give us 180°. A supplement of am angle is simply 180° - the measure of that angle.

Given that meadure of angle 1 = 58°, the supplement of angle 1 = 180° - 58° = 122°

Also, if the measure of angle 2 = 24°, the supplement of angle 2 = 180° - 24° = 156°.

Thus:

Supplement of <1 = 122°

Supplement of <2 = 156°

Using inductive reasoning, what number is the most reasonable conjecture for the next number in the pattern 27,23,19,15,

Answers

Answer:

11

Step-by-step explanation:

Each number in the sequence decreases by 4, so the next reasonable number would be 11 (15-4=11)

f(x) = -3x + 4; Find f(2), f(0), and f(-4). (Select all that apply.) f(2)= 10 f(2) = -2 f(0) =4 f(0) = 0 f(-4) = 16 f(-4) = -8​

Answers

Answer:

(f)2=-2, (f)0=4 and (f)-4=6

Step-by-step explanation:

f(2)= -3(2)+4

-6+4=

-2

f(0)=-3(0)+4

=4

f(-4)=-3(-4)+4

-6+4

=

-2

I hope this helps.

p=s1t-s2t. Which equation sauce for tea........................

Answers

Answer:

f444444444444444444444444Step-by-step explanation:

f

A cyclist rides his bike at a rate of 15 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 10 minutes?

Answers

Answer:

This is 0.25 miles per minute

The cyclist would travel 2.5 miles in 10 minutes

Step-by-step explanation:

The equation to convert miles per hour to miles per minute is to divide by 60, the number of minutes in an hour.

The list below shows the amount of money Hannah earned mowing lawns for the past five weeks.
$40, $15, $20, $40, $35
Which measure shows that the amount of money she earned varied?

Answers

Answer:

the answer is mean

Step-by-step explanation:

the answer is mean because

Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for 1/3 every cup of nuts.
To satisfy his grandmother’s request, Dave must mix
cups of fruit for a single cup of nuts.

Answers

Answer:

3/5 cup of fruit for every 1 cup of nuts

Find the interquartile range for the data. {50, 46, 56, 55, 54, 51, 45, 50, 47}

Answers

Answer:

51

Step-by-step explanation:

I think the answer is 51 because you have to find the number between the first three to the middle

Answer:8

Step-by-step explanation:

Leanne works at a restaurant. For dinner, there is a choice of 3 main dishes and 2 sides.
Main Dish: Burger(B), Chicken (C), Pasta (P)
Sides: Apple (A), Fries (6)
Leanne lists all possible ways a person could order their dinner. She lists these combinations:
BA, BF, CA, CF, PA, PF, AB, FB, AC, FC, AP, FP.
Is Leanne correct? Use the drop-down menus to explain your reasoning.
Click the arrows to choose an answer from each menu.
For each main dish, there are Choose... different sides a person can choose. So, there are
a total of Choose... possible ways a person could choose their dinner. Leanne is
Choose...

Answers

Answer:

I feel like its that but im rlly not sure.

Step-by-step explanation:

Leanne's list is incorrect and  there are 3 different sides a person can choose. So, there are a total of 6 possible ways a person could choose their dinner.

How to determine the number of combinations?

The given parameters are:

Main Dish: B, C and P

Sides: A and F

Using the above parameters, the combination of dishes are:

BA, BF, CA, CF, PA and PF

Hence, we can conclude that Leanne list is incorrect

Also, we have:

Dish = 3

Sides = 2

So, the number of dinner to choose is:

Dinner = 3 * 2 = 6

Hence, a person could choose their dinner in 6 ways

Read more about combination at:

https://brainly.com/question/11732255

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is the quotient of two rational numbers always a rational number explain ​

Answers

It is not always rational since zero is a rational number. If we have a rational number on the numerator and a 0 on the denominator then the quotient is not rational therefore the quotient of any two rational numbers is not always rational.

can someone help me please

Answers

[tex]\large{\bf Step-by-step~explanation:}[/tex]

To simplify this expression, we combine all the like terms. We cannot solve for x because there is no equal sign and/or no value for x.

Equation: (10x² - 10x - 6) + (x + 6)

[tex]\bf Step~1:[/tex]

-10x and x are like terms. Remember: there is an invisible 1 behind the variable x. We add these like normal numbers.

[tex]\bf -10x+1x=-9x[/tex]

[tex]\bf Step~2:[/tex]

-6 and 6 are also like terms. Again, we add them as written.

[tex]\bf -6+6=0[/tex]

Since our answer is 0, we do not have to write it in our simplified expression.

[tex]\bf Step~3:[/tex]

Now, let's add the terms together. Since 10x² doesn't have any like terms, we just let it be. We take our previous number, -9x, and we add it to 10x².

[tex]\bf 10x^2+-9x[/tex]

[tex]\large\boxed{\bf Our~final~answer:10x^2-9x}[/tex]

Plz help me answer this

Answers

Answer:

sure

Step-by-step explanation:

Tracy bought 5 trays of plants for $105.


Each tray contained 12 plants.

Each plant cost the same amount.

Plants can be purchased individually.


How much more money will Tracy need to spend for 15 additional plants?

Answers

Answer:

8.75

Step-by-step explanation:

Answer:

$1150

Step-by-step explanation:

If 5stray cost $105

X=$105 ×15 =$1575

Carla is making bracelets she wants to put 10 charms on each bracelet charms are sold in packets of 12 what is the least number of packages she can buy to make bracelets with no charms left over​

Answers

Answer:

Carla can buy 5 packets of charms.

Step-by-step explanation:

5 packets of charms would be able to make 6 bracelets.

*please give me brainliest, i only need three more*

For the diagrams, find the following measures.
X=
DCB=
ABC=

Answers

To set this up you will set the two angles equal to 180° since it is a straight line
This will make the equation x+6x+19=180
Combine like terms. 7x+19=180.
Subtract 19 from both sides. This will make it 7x=161
Divide both sides by 7. That will make it x=23
Next plug in the x to solve for abc. 7(23)+19. This equals 157

X= 23

Hope this helped :)
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