Mathematics College

Am I starting this off right? What does it mean to find instantaneous velocity?

Answers

Answer 1

Answer:

yesv(t) gives the instantaneous velocity at time t

(a) correct

(b) -48 ft/s

(d) 9.257 s

(e) -296.216 ft/s

Step-by-step explanation:

You are given an equation of motion and asked to find velocity and time at different points in the motion. This requires you differentiate the position function to find velocity, and that you solve the position function to find the time at a particular position.

(a)

The coin is "dropped", so is presumed to have no initial velocity. The initial height is given as 1371 feet. Putting these values into the given equation, you have ...

s(t) = -16t² +1371

The velocity is the derivative of this function:

v(t) = -32t

(b)

The average velocity on an interval is the change in position divided by the change in time:

(s(2) -s(1))/(2 -1) = ((-16·2² +1371) -(-16·1² +1371))/1 = -16(4 -1) = -48 . . . ft/s

(Note: the average velocity for a quadratic position function is the velocity at the midpoint of the interval: v(1.5) = -32(1.5) = -48 . . . ft/s.)

(c)

Use the velocity function you found in part (a) to determine the instantaneous velocity at the given times:

v(1) = -32(1) = -32 . . . ft/s

v(2) = -32(2) = -64 . . . ft/s

(d)

The coin will reach the ground when s(t) = 0. Solving for t, we find ...

s(t) = 0

-16t² +1371 = 0

1371 = 16t²

t = √(1371/16) = (√1371)/4 ≈ 9.257 . . . . seconds

(e)

The velocity at impact will be ...

v(√1371/4) = -32(√1371/4) = -8√1371 ≈ -296.216 . . . ft/s

Related Questions

HELP PLEASE : )
Simplify the expression:

6/3(13−18)+2^4÷6

Answers

Answer:

-7.33

Step-by-step explanation:

Answer:

-7.333

Step-by-step explanation:

To solve this you have to use B O D M A S theorem and we have to solve the given expression according to the theorem.

That is,

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Let us solve it now.

[tex]\frac{6}{3} (13-18)+2^{4}[/tex] ÷ [tex]6[/tex]

2 ( -5) + 16÷ 6

-10 + 2.667

-7.333

What is the solution to the equation -3(h + 5) + 2 = 4(h + 6) - 9

Answers

Answer:

The solution would be h=-4

Step-by-step explanation:

By distributing, we are able to find this answer.

A square garden plot has an area of 24 ft2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot.

Answers

Answer:

4.9 ft

Step-by-step explanation:

Area of square = side squared

S² = A

Sub in 24 for A, then take square root of each side to find S.

S² = 24

S = sqrt (24)

= sqrt (4×6) - factorize

= 2(sqrt (6)) ft

≈ 4.9 ft

Question 3 of 10
Which expression is the simplest form of 5(22–3)-3(x+4)?
9
O A. 7x - 3
-
O B. 134-27
9
O c.
72-3
9

Answers

Answer:

(D)

Step-by-step explanation:

[tex]\frac{5(2x-3) -3(x+4)}{9}[/tex] = [tex]\frac{10x-15-3x-12}{9}[/tex] = [tex]\frac{7x-27}{9}[/tex]

1. You live in New York and travel by express subway to work 4 times a week for a cost of $15.00 each day. You can get an unlimited week pass for $34. How much can you save by buying the pass?

Answers

Answer:

$26

Step-by-step explanation:

4 times a week, $15 a day

It means that he have to pay $60 a week for travelling

$60-$34 = $26

By buying the pass I can save $26 a week

Answer:26 DOLLARS saved

Step-by-step explanation:

Applications of Differential Equations : Mass-spring system

The motion of a certain mass in a spring is described by:

[tex]\sf x''+2x'+2x=5sin(t)[/tex]

a) What is the amplitude of the resulting constant periodic oscillations?

b) Suppose the mass is initially at rest, that is, x(0)=0 and x′(0)=0, find the position function x(t).

Answers

Answer:

Step-by-step explanation:

The motion of a certain mass in a spring is described by:

can someone help me please?? :))

Answers

Answer: 52.8 minutes

====================================================

How I got that answer:

The interval 0 < t < 30 has the midpoint of 15 since (0+30)/2 = 15

The interval 30 < t < 60 has the midpoint 45 because (30+60)/2 = 45

We add up the endpoints and then divide by 2 to get the midpoint.

Repeat this for each of the intervals mentioned.

From top to bottom, the midpoints are:

154575105

Notice we add 30 to each midpoint to get the next one. This is directly due to the fact that each interval is 30 units wide (eg: 90-60 = 30).

Multiply each midpoint by the corresponding frequency for a given row.

15*7 = 10545*27 = 121575*12 = 900105*4 = 420

Then add up those products.

105+1215+900+420 = 2640

Lastly, we divide this over the sum of the frequencies 7+27+12+4 = 50 to get 2640/50 = 52.8

The average time spent on homework is estimated to be about 52.8 minutes

Note that the majority of the the students (27) are in the 30 < t < 60 interval, so the mean of 52.8 fits this interval perfectly. It's closer to the right endpoint of the interval due to the fact the other 12+4 = 16 students are above this, and they make up the second most majority compared to the 27.

The reason why 52.8 is an estimate rather than the actual mean is because we are estimating each interval by picking out the midpoint each time. The midpoint is at the direct center, so it's the best guess we can do.

How would I graph this?

Answers

Answer:g(x) = f(x) + 1.5

Step-by-step explanation: The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

2
3
4
5
6
the step function f(x) is graphed.
5
4+
3+
2+
1+
-5-4-3-2-1

#
-2+
-3+
1
92
2 3
8
9
4 5 X
10
What is the value of f(1)?
0
1
2
4

Answers

Answer:

Step-by-step explanation:

Help! Urgent! its due in 2 hours

Answers

Answer:

diameter-- last picture on right side

radius-second last picture on right side

πd=2πr

2r=d/2

Step-by-step explanation:

diameter is a line segment that goes through the center of a circle

this will match to the last image on the right side

radius is half of the diameter or from a point on the outer edge of the circle to the center

this will match to the second one on the right side

πd-- d=2*radius

2πr

2r=d/2

because radius is half of the diameter

The diameter of a circle is 11 cm. Find its circumference in terms of .

Answers

Answer:

C= 34.56 cm

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving for C

C= πd = π·11 ≈ 34.55752cm

Describe a set of transformations that would map Red Triangle to the Blue Triangle.

Answers

1) translation of 2 down
2) translation of 5 right

4. A rational number is any number that can be expressed as the quotientor fraction of two integers, p and q
a. True
b. False

Answers

True because 2 and 4 are integers hope this helps.

The graph shows the distance, y in miles, of a moving train from a station for a certain period of time, x, in hours: A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 50, 100, 150, 200, 250, 300, 350, 400. The graph shows a straight line joining the ordered pairs 0, 100, and 1, 150, and 2, 200, and 3, 250, and 4, 300. What is the speed (in miles per hour) of the train?

Answers

Answer:

Step-by-step explanation:

I just did it with my friend.

8) Find the % of change.
Original price: $185
New price: $160
(Explanation too)

Answers

Answer:

15.6% gives you 24.96 which is almost the equivelenth of 160-185

Step-by-step explanation:

take the number and try to find a percent that works.

How many minutes are there from 14h10 pm to 15h50 pm, the same day?

Answers

Answer:

100 minutes

Step-by-step explanation:

subtract 14h10 from 15h00

this will equal 50

then add the remaining 50minutes from 15h00

01. Se tienen los angulos consecutivos AOB, BOC y COD. se cumple m& AOC=125° m

Answers

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°.

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.

Cómo analizar tres ángulos consecutivos

Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.

De acuerdo con el enunciado, tenemos las siguientes condiciones:

∠AOB + ∠BOC = 125° (1)

∠BOC + ∠COD = 100° (2)

Por (1) y (2) tenemos las siguiente identidad:

∠AOB - 25° = ∠COD

∠AOB - ∠COD = 25°

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°. [tex]\blacksquare[/tex]

En el segundo caso, tenemos el siguiente sistema:

∠AOB = ∠BOC + ∠COD (3)

∠AOB + ∠BOC - ∠COD = 40° (4)

Por (3) y (4) tenemos la siguiente identidad:

2 · ∠BOC = 40°

∠BOC = 20°

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°. [tex]\blacksquare[/tex]

Para aprender más sobre ángulos, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/21209282

Can yall pls help me its due im 1 hour

Answers

The third option is correct

Answer:

option 1 is correct

Which of the following graphs best represents the solution to the pair of equations below? y = −2x + 2 y = 2x + 2 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 2 and the x axis at 1. The other line passes through the y axis at negative 2 and the x axis at 1. The lines intersect at 1 comma 0. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 2 and the x axis at 1. The other line passes through the y axis at 2 and the x axis at negative 1. The lines are parallel and do not intersect. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 2 and the x axis at 1. The other line passes through the y axis at 2 and the x axis at negative 1. The lines intersect at 0 comma 2. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 2 and the x axis at negative 1. The other line passes through the y axis at negative 2 and the x axis at negative 1. The lines intersect at negative 1 comma 0.

Answers

The lines are

i) y=-x+6

ii) y=2x-3

The solution of the system of equations is found by equalizing the 2 equations:

-x+6=2x-3

-2x-x=-6-3

-3x=-9

x=-9/(-3)=3

substitute x=3 in either i) or ii):

i) y=-3+6=3

ii) y=2(3)-3=6-3=3

(the result is the same, so checking one is enough)

This means that the point (3, 3) is a point which is in both lines, so a solution to the system.

In graphs, this means that the lines intersect at (3, 3) ONLY

Answer: The graph where the lines intersect at (3, 3)

PLEASE ANSWER FAST I NEED HELP
Part D
? Question
Suppose Coach Bennet selects one senior and one junior as the first two players. The coach then randomly selects
the third player from either group.
Taylor and Jamie are both juniors on the team. If Taylor is selected as one of the first two players, what is the
probability that Jamie will be selected as the third player?
Type in the correct answer in the box. Use numerals instead of words. If necessary, round your answer to the
nearest tenth.
The probability that Jamie will be selected as the third player, given that Taylor is selected as one of the

Answers

The question is an illustration of conditional probability, and the value of the conditional probability P(A|B) is 0.38

How to determine the value of the probability expression?

The question is incomplete, as the required parameters are not given.

So, I will give a general explanation.

The question is an illustration of conditional probability

What is a conditional probability?

The conditional probability is used to determine the probability of an event, given that another independent event has already occurred.

The conditional probability is calculated using:

P(A|B) = n(A and B)/n(B)

Assume the following parameters

n(A and B) = 9

n(B) = 24

The equation to calculate the probability expression is represented as:

P(A|B) = n(A and B)/n(B)

Substitute the assumed values

P(A|B) = 9/24

Evaluate the expression

P(A|B) = 0.38

Hence, the value of the conditional probability P(A|B) is 0.38

Answers

Answer: A≈50.27m²

The area of a circle with a radius o 4 meters is A≈50.27m²

Step-by-step explanation:

Jasmine has a 2-gallon bucket. How
many 1-quart containers will it take
to fill Jasmine's bucket?

Answers

Hi!

Your answer is 8 1-quart containers.

There are 4 quarts in a gallon.

If there is a 2-gallon bucket, and she needs to fill it using 1-quart containers, we simply multiply the number of quarts in a gallon (4) by the number of gallons total (2).

2 x 4 = 8

Mathematics question :)

Answers

[tex]\bold{FULL EXPLANATION:}[/tex]

~
(1)

40 = 40 =
—>
(2)

~
—> 18 = 22 + 18 + —> 18 = 40 + 62 + —> 18 - 102 =
—> 78 =
Now,

(3)

~
—>
ANS:

=

what is the product of the mixed number 5 x 1 1/6?

Answers

5 5/6

5 x 1 1/6 = 5 5/6

Answer:

The answer is 5 5/6. Hope this helps!

How can you find a unit rate from a graph?

Answers

Answer:

To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate. So in this case, divide the numerator and denominator of 70/5 by 5, to get 14/1, or 14 students per class, which is the unit rate.

Also, what are unit rates? A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Step-by-step explanation:

Please help now, I will give Brainliest!!! :D

Peter is 19 years old. He lives at home with his parents and goes to college part time. He recently started working as a server, working 40 hours per week.

Where Peter lives, the minimum wage for tipped and non tipped employees is $7.25 per hour.

In the average week, he serves 90 tables whose typical bill is $21 with an average tip of 15%.

How much money does he make in a typical week??

Answers

Answer: $573.50

Step-by-step explanation:

40hrs x $7.25 per hour= $290 per week$21 x 0.15 = $3.15$3.15 x 90 tables per week = $283.50$283.50 + $290 = $573.50

4 cm
14 cm
5 cm
9cm

Answers

Hey there!

The area of the figure is 86 cm²

☆Explanation:

¤ We that area of a Rectangle = length × breadth

¤ Here, it is said to find the area of the given figure.

Now,

Area of first Rectangle = length × breadth

= 9 cm × 4 cm

= 36 cm²

Again,

Area of the second Rectangle = length × breadth

= 14 - 4 × 5

= 10 × 5

= 50 cm²

Finally,

Area of the figure = Area of first Rectangle + Area of second Rectangle.

= 36 cm² + 50 cm²

= 86 cm²

Hope it helps

PLEASE HELP
Which graph best represents this function?

Answers

Answer:

D is the correct answer

Step-by-step explanation:

A is not correct because it does not meet the fourth criteria, B is not correct because it doesnt meet the second criteria, C is not correct because it does not meet the third criteria, D IS CORRECT because it meets the fourth criteria.

What is an equation of the line perpendicular to 5x−4y=10 that passes through the point (−1,−6) ?

Answers

Answer:

y = -4/5x-34/5

Step-by-step explanation:

1. Put into slope-intercept form: 5x-4y = 10 ⇒ 4y = 5x-10 ⇒ y = 5/4x - 5/2

2. A perpendicular slope is the negative reciprocal of the original slope. ⇒ m = -4/5

3. Make a general solution using the new slope: y = -4/5x + b

4. Plug in the point (-1,-6) and solve for b: -6 = -4/5(-1) + b ⇒ -6-(4/5) = b ⇒

b = -34/5

5. Put b in the general solution to find the particular solution: y = -4/5x-34/5

PLS HELP FAST THIS IS DUE NOW
Dalia is painting her room. After painting 1/10 of her room, Dalia has used 1/2 of a can of paint. Select all of the true statements.
1. each can of paint will cover 1/20 of Dalia's room
2. painting 1/2 of Dalia's room requires 10 cans of paint
3. Dalia's entire room requires 20 cans of paint
4. 3 cans of paint will cover 60% of Dalia's room
5. Dalia's entire room requires 5 cans of paint

THANK YOU WILL ADD BRAINLIEST FOR RIGHT ANSWER

Answers

Answer:

4. 3 cans of paint will cover 60% of Dalia's room

5. Dalia's entire room requires 5 cans of paint

Step-by-step explanation:

If Dalia has painted 1/10 of her room with 1/2 can of paint, then she will paint 2/10 of her room with 1 can of paint (since there are 2 halves in a whole).

2/10 = 1/5 ⇒ 1 can of paint covers 1/5 of the room.

Therefore, to paint the entire room, she will need 5 cans of paint.

60% of 5 cans of paint = 0.6 × 5 = 3

Therefore, 3 cans of paint will cover 60% of the room.

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