A ball is dropped from a height of 600 feet. The function describing the height of the ball at t seconds after it dropped is [tex]f(t)=-16t^2+600[/tex].

a) Find the average velocity of the object during the first 3 seconds.

b) Verify that at some time during the first 3 seconds the instantaneous velocity equals the average velocity. Find that time.

The average velocity: _ ft/sec
The instantaneous velocity equals to the average velocity at t = _ sec

Answers

Answer 1

The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

What is instantaneous and average velocities?

Instantaneous velocity  is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16[tex]t^{2}[/tex] + 600

a) Height at t = 0 = 600 feet

    Height at t = 3 seconds = f(3) = -16[tex](3)^{2}[/tex] + 600 = 456 feet

Distance travelled  = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken  = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = [tex]\frac{df(t)}{dt}[/tex] = [tex]\frac{d(-16t^{2} + 600) }{dt}[/tex] = -32t

  when instantaneous velocity equal average velocity

     -32t = -48

      t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

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Related Questions

Which expression shows the distance on the number line between −14 and −5?

∣∣−5−14∣∣

∣∣−14−(−5)∣∣

∣∣−14−5∣∣

∣∣−14+(−5)∣∣

Answers

Answer:

||−14+(−5)||

Step-by-step explanation:

Each cube in this figure measures 1 centimeter on each side.

What is the volume of this figure?


112 cm³

84 cm³

33 cm³

31 cm³

Answers

The answer is 84 by multiplying all the sides

Which value of x solves the equation below?
10(x - 1) = 8x - 2
x = 5
X= 6
th
x=2
X= 4

Answers

Answer:

x = 4

Step-by-step explanation:

10(x - 1) = 8x - 2

10x - 10 = 8x - 2

10x = 8x + 8

2x = 8

x = 4

Solve the following equations for x.

A. 7(x)^3=243

B. 5(x)^4+7=42

Answers

The values of x given the following expression are ∛243/7 and 7^1/4

Indices expression

Given the following expression

7x³ =243
x³ = 243/7

x = ∛243/7

For the expression

5x⁴ + 7 = 42
5x⁴  = 42 - 7

5x⁴ = 35

x⁴ = 7

x = 7^1/4

Hence the values of x given the following expression are ∛243/7 and 7^1/4

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Spencer took $21 with him to the mall. At the music store he spent 2/3 of his money on a DVD. He spent ¼ of what he had left on a drink. How much money did Spencer have left after he bought the drink?

Answers

Answer:

$10.50

Step-by-step explanation:

2/3 of $21 = $14

1/4 of $14 = $3.50

$14 - $3.5 = $10.50

Football boot sizes of a football team continuous or discrete

Answers

Answer:

discrete?

according to probability of basic things we know that there are more people different than same so there is more than enough probability of those sizes being discrete.

Which could be the missing data item for the given set of data if the median of the complete data set is 50?


21 23 60 60 50 54 54 59 26 15 43 15


A. 18

B. 24

C. 45

D. 57

Answers

Answer:

D. 57

PLEASE GIVE BRAINLIEST THANK YOU!!!

The area of one face of a cube is 144 square inches.what is the volume of the cube?

Answers

Check the picture below.

[tex](s)(s)=144\implies s^2=144\implies s=\sqrt{144}\implies s=12 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the cube}}{(s)(s)(s)\implies s^3}\implies 12^3\implies 1728~in^3[/tex]

Answer:

1728 in³

Step-by-step explanation:

Given that,

→ Area = 144 sq in

Then the length will be,

→ a² = 144

→ a = √144

→ [ a = 12 ]

Formula we use,

→ V = a³

Now required volume will be,

→ a³ = 12³

→ 12 × 12 × 12

→ 1728 in³

Hence, the volume is 1728 in³.

Three times a number decreased by 2 equals forty

Answers

Answer:

14

Step-by-step explanation:

40 plus 2 is 42

42 divided by 3 is 14

Pete is 14 and his grandfather is 54. How many years
ago was his grandfather 6 times as old as Pete?

Answers

Answer:

6 years ago

Step-by-step explanation:

[tex]6(14-x)=54-x\\84-6x=54-x\\30-6x=-x\\30=5x\\6=x[/tex]

So, Pete's grandfather was 6 times as old as Pete 6 years ago. This means that when Pete was 8 years old, his grandfather was 48 years old.

Help me with this question please /:

Answers

Answer:

B) D) E)

Step-by-step explanation:

Basically, the more days missed, the lower their grades are, so it is a negative linear relationship that has no clusters or outliers.

You plan to move to San Antonio. You earn a salary of $42,000 here in McAllen. How much more must you earn in San Antonio if the cost of living is 15% higher?

Answers

You must earn $6,300 more

What is the area of a rectangle with a length of 9
centimeters and a width of 4 centimeters?
Sketch: ?
Area: ?

Answers

Answer:

We are given a length of 9 cm and a width of 4 cm and we are also told that it our shape is a rectangle.  This means that we are able to use the rectangle formula which is [tex]A=l*w[/tex].

Therefore, we can just multiply 9 cm by 4 cm and we get [tex]A = 36\ cm^2[/tex]

Hope this helps!  Let me know if you have any questions

7 UNIT 2(CALCULATOR 7 OF S
Part A
The first type of cup the manager ordered is in the shape of a right circular cone with the dimensions, in centimeters (cm), as shown in the
figure.
-7 cm
9 cm
What is the volume, in cubic centimeters, of each cup?
O A 110.25m
OB. 47.25T
OC. 36.75m
OD. 10.5m
Part B

Answers

Answer:

Volume of Cone=1/3πd²/4×h

= 1/3π×7²/4×9

= 36.75cm³

6 worker can construct 10 m long wall in 4 days . in how many days 2 worker can contruct 15 m long wall ?

Answers

Answer:

it should take the workers 18 days to finish

Step-by-step explanation:

item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week? item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week?

Answers

Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,

The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams

Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

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awnser okease quicxkly

Answers

Answer:

P': (-9,10)

Q': (-2,10)

R':(-2,0)

S':(-9,0)

Answer:

the answer for all of this question should be.

P=(-9,-10)

Q=(-2,-10)

R=(-2,0)

S=(-9, 0)

so hopefully those are the correct answers and sorry if i get them wrong because i tried my best i could as possible to get them right so have a great day.

Step-by-step explanation:

PLEASE HELP ASAP!!!!
A scatter plot is shown below: if you need an image of it look at the bottom

A graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. The ordered pairs 0, 14 and 1, 11 and 2, 9 and 3, 10 and 4, 7 and 5, 7 and 6, 5 and 7, 5 and 8, 3 and 9, 1 and 10, 0 are shown on the graph.

Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot?

(4, 15) and (10, 7)
(1, 6) and (6, 0)
(0, 13) and (10, 11)
(0, 13) and (10, 0)

Answers

Answer: Choice D.  (0, 13) and (10, 0)

Reason:

If you were to draw a line through the points mentioned in choice A, the line wouldn't be close to the points since (4,15) isn't close to the points. The same goes for (10,7). So we can rule out choice A. Choices B and C are similar stories.

Choice D on the other hand has its line fairly close to all of the points.

Last option

(0,13)

The point will lie at top

(10,0)

The point will lie at bottom

So

both will contain most no of plots so Option D is correct

A cylinder has a base area of 50π cm². Express the volume V of the cylinder as a function of its height h. (V = πr²h)

Answers

Step-by-step explanation:

the last option is your answer

How do I solve augmented matrices??

Answers

Write the coefficients of the x-terms as the numbers down the first column.

Write the coefficients of the y-terms as the numbers down the second column.

If there are z-terms, write the coefficients as the numbers down the third column.

Draw a vertical line and write the constants to the right of the line.    

Express 5x²-15x+1 in the form p(x+q)²+r, where p,q,r ate constants

Answers

Answer:

[tex] 5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}[/tex]

Step-by-step explanation:

[tex] 5x^2-15x +1[/tex]

[tex]= 5\bigg(x^2-3x +\frac{1}{5}\bigg)[/tex]

[tex] =5\bigg[x^2-2.\frac{3}{2}x +\bigg(\frac{3}{2}\bigg)^2-\bigg(\frac{3}{2}\bigg)^2+\frac{1}{5}\bigg][/tex]

[tex] =5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{1}{5}-\frac{9}{4}\bigg][/tex]

[tex] =5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{4-45}{20}\bigg][/tex]

[tex] =5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}[/tex]

[tex] =5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}[/tex]

[tex] =5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}[/tex]

What is the measure of ZEKY in this figure?
O 104°
O 115°
O 129°
O I don't know.

Please answer fast!

Answers

Answer: 104 degrees

Step-by-step explanation:

Find f(-3) for f(x) = 4(2)^x.
ОА. 1/8
O B. -32
O C. -24
OD. 1/2

Answers

Answer:

D

Step-by-step explanation:

using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

substitute x = - 3 into f(x)

f(- 3) = 4([tex](2)^{-3}[/tex] = 4 × [tex]\frac{1}{2^{3} }[/tex] = 4 × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{2}[/tex]

Write 9.30 in scientific notation

Please help :)
I’ll give brainliest to whoever comments first and gets it right!

Answers

Answer:

9.30 × 10⁰ bro that was so easy

This is the Answer I got: The number 0.0000000930 in scientific notation is written as 9.30 × 10-8

Select all the expressions equal to sin (30°). *
sin 2/3
cos 5m/3
tan π/6
sin 5/6
cos 60°
cos 11π/6
Solve: log (15x+10) = 2*

Answers

The trigonometric expression sin 30° will be equal to cos 60°. Then the correct option is E.

How to convert the sine of an angle to some angle of cosine?

We can use the fact that:

sin(θ) = cos(90 - θ)

To convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).

The trigonometric expression sin 30° will be equal to

The sin 30° can be written as

sin 30° = cos(90° - 30)

sin 30° = cos 60°

Then the correct option is E.

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Can the sides of a triangle have lengths 3, 4, and 19?

Answers

no, because 4+3 is 7. It is not greater than 19

The diameter of a volleyball is 8.4 in. what is the approximate volume of the volleyball? a. 222 in.3 b. 233 in.3 c. 296 in.3 d. 310 in.3

Answers

Answer:

C.

Step-by-step explanation:

According to the volume equation of a sphere (V=4/3πr³)

8.4/2 equals a radius of 4.2, which when cubed equals 74.088 (base area). You then multiply your base area by the numerator of 4/3, giving you 296 when rounded or 296.352 when not rounded. Giving you the answer of C.

A hyperbola has its foci at (1, 7) and (1, –13). a directrix of the hyperbola is y = . what is the equation of the hyperbola?

Answers

The equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

How to determine the hyperbola equation?

The foci are given as:

(1, 7) and (1, -13)

The foci of a hyperbola are represented using: (m, n+p) and (m, n-p)

Where the center of the hyperbola is (n,p)

By comparison, we have:

m = 1

n + p = 7

n - p =13

Where n = ae

The solution to the above system of equations is

m = 1, n = 10 and p = -3

The directrix is given as:

y = 64/10

The directrix is represented as:

y = a/e

So, we have:

a/e = 64/10

Substitute n = ae in n = 10

ae = 10

Solving ae = 10 and a/e = 64/10, we have:

a = 8 and e = 10/8

To calculate b, we make use of:

[tex]b = a\sqrt{(e^2 - 1)[/tex]

So, we have:

[tex]b = 8\sqrt{(\frac{10}{8}^2 - 1)[/tex]

Evaluate

b = 8 * 0.75

b = 6

The equation of the hyperbola is then calculated using:

[tex]\frac{(y - p)^2}{a^2} -\frac{(x - m)^2}{b^2} = 1[/tex]

This gives

[tex]\frac{(y + 3)^2}{8^2} -\frac{(x - 1)^2}{6^2} = 1[/tex]

Evaluate

[tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

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What is the volume of a
triangular pyramid that is
12 ft tall and has a base
area of 5 squar & ft?

Answers

Answer:

60 ft³

Step-by-step explanation:

Concepts

The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.

Application

In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.

Solution

12 × 560 feet³

What is the y-intercept of the line 15 - 3y = x?​

Answers

the y-intercept is 15 because the slope is 3y

The y-intercept of the line 15 - 3y = x is ( 0 , 5 )

Sure hope this helps you

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