We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.

Answers

Answer 1

Answer:

An alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

Step-by-step explanation:

We know that :

[tex]a_x=\frac{dv_x}{dt}[/tex]

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex]

So, We will use chain rule over here :

[tex]a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}[/tex]

Hence an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

Answer 2

The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is [tex]a_x = v_x \frac{dv_x}{dx}[/tex]

Chain rule:

Here we used the chain rule:

It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).

So,

[tex]a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}[/tex]

Learn more about time here: https://brainly.com/question/11325462


Related Questions

HELPPS PLEASE FOR BRIANILIST

Answers

0.80¢ answer i’m pretty sure

Stephen says that the numbers 38 and 40 are relatively prime. Explain why he is incorrect in making this statement. (make a good explanation plz)

Answers

Answer:

He is incorrect in this statement because 38 and 40 both have factors, other than 1 x itself. Prime numbers are numbers the only have 1 factor pair, and that is 1 x itself. Factors are the numbers you multiply to get the end result, and an example is 10x4=40. The factors of 40 are 8x5, 4x10, 2x20, and of course, 1x40. The factors of 38 are 2x19, and 1x38.

Answer:

The definition of relatively prime is two numbers with a GCF of 1.The numbers 38 and 40 are not relatively prime.

Step-by-step explanation:

What is 8x - 6x + 4 +5 = 19

Answers

combine like terms!! 2x+9=19, subtract 9 from both sides to get 2x=10, divide by 2 to get x=5. can i get brainliest? hehe :D

Answer: x = 5

The step-by-step explanation is below.

Combine like terms

8x-6x = 2x

4+5=9

2x+9=19

Subtract 9

2x=10

Divide by 2

x = 5

Hope this helps!

what is the value of x in the equation 2/3(6x-9)=2(x+12)

Answers

Answer:

x=15

Step-by-step explanation:

hope this helps

(6. 10)
Ka, 8)
(4.b)
(2.2)
a. What is the slope of the line? Type the answer in the box below.
The slope of the ines

Answers

Hold
up here’s the answer ima do the work then ik giveu it

hello please help will give brainliest

Answers

Answer:

c

Step-by-step explanation:

288/6 = 48

Hope this helps

Answer:

c.

Step-by-step explanation:

For ratio, u should divide

So, 288/6 = 48:1 or 48/1

6 times 48=288

Pls mark me brainliest

11. Use an inequality symbol (<,>, 2, =) to compare -26
54
A.
B. =
O C.<
O D.>

Answers

Answer:

c. less than symbol < because -26 is less than 54 because its far to the left from 54

Help with this please

Answers

Answer:

158

Step-by-step explanation:


Are points B, J, and C collinear or noncollinear?

Answers

I’m pretty sure they’re collinear. I’m so sorry if I’m wrong.

A circular crop field has an irrigation system in which a pipe, with one end attached to a tower at the center of the field, turns continuously to deliver water. The horizontal distance, in meters, from the tip of the pipe to the farmhouse is represented by y = Equals 400 sine (StartFraction pi Over 8 EndFraction x + pi) + 500, where x represents time in hours.

What does the amplitude of this function represent?

A.the length of the pipe
B.the distance between the tower and the farmhouse
C.the time it takes for the pipe to complete one full circle
D.the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse

Answers

Answer:

It A: the length of the pipe

Step-by-step explanation:

Yomaro is buying soil for his garden. He needs to fill one pot with 12 cups of soil and another pot with 2 gallons of soil.
If the price of soil is $1.50 per quart, how much will he pay in all?

Answers

Answer the answer to your question is $7.50

Find the value of A, B and C, given that 2z^2 + z + C = A (z+1)^2 + B (z+1) + 4 for all values of z. Please show the step by step process. :)

Answers

2z² + z + C = A (z + 1)² + B (z + 1) + 4

Expand the right side completely and collect terms with the same power of z :

2z² + z + C = A (z² + 2z + 1) + B (z + 1) + 4

2z² + z + C = Az² + 2Az + A + Bz + B + 4

2z² + z + C = Az² + (2A + B)z + A + B + 4

Now match up terms on either side that have the same power of z. This gives

2 = A ................. (2nd power)

1 = 2A + B ......... (1st power)

C = A + B + 4 .... (0th power)

Solve for A, B, and C. The first equation gives A = 2 right away, so in the second equation we get

1 = 2*2 + B

B = -3

and in the third equation we get

C = 2 + (-3) + 4

C = 3

Write an equation for the line parallel to g(x) = 4x + 5 and passing through the point (10,7). Write the answer in slope-intercept
form.

Answers

Answer:

y=4x-33

Step-by-step explanation:

the slope for parallel lines is the same so it would be 4

(y-y₁)=m(x-x₁)

(y-7) =4(x-10)

(y-7) =4x-40

  +7       +7

 y=4x-33

A single reese cup cost $.25 each, you bought 5 and the sales tax is 5%. How much did you spend?

Answers

$1.31, If you bought 5 pieces for 25¢ its a 1.25 as your total and now you have to add sales tax so if you calculate 5% of 1.25 you get .0625 now if you round that to the nearest hundredths place you get .06 so now add .06 to the total $1.25, you get $1.31

What is the slope of a line parallel to the line whose equation is 2x + y = 3. Fully
reduce your answer.

Answers

Answer:

m= -2

Step-by-step explanation:

Isolate the y into slope- intercept form 2x + y = 3 -> y = -2x+3

Parallel lines have the same slope, so the slope is -2.

The slope of a line parallel to the line whose equation is 2x + y = 3 is -2.

Given that, the equation of a line is 2x + y = 3.

What is slope of a line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope of a line parallel to given line is m1=m2.

The given equation can be rewritten as y=3-2x

The standard form of an equation of a line is y=mx+c

Now, compare y=3-2x with y=mx+c, we get

Slope (m) = -2

So, slope of parallel to the line is m1=m2= -2

Therefore, the slope of a line parallel to the line whose equation is 2x + y = 3 is -2.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ6

que es suma y resta de fracciones homogeneas

Answers

Answer:

responder

Step-by-step explanation:

Para sumar y restar fracciones, sus denominadores deben ser iguales. Por tanto, sumar o restar fracciones homogéneas es más fácil, dado que ya tienen el mismo denominador.

Answer:

Recuerda que cuando se suman fracciones homogéneas se hace lo mismo que cuando se suman objetos del mismo tipo. Por ejemplo, la suma tres décimos más dos décimos da como resultado cinco décimos: , por la misma razón que sumar tres vacas más dos vacas da como resultado cinco vacas.

Step-by-step explanation:

1) Qual a área lateral do prisma triangular regular, cuja aresta da base mede 5 cm e a altura 10 cm ? *
1 ponto
Imagem sem legenda
a) 50 cm²
b) 100 cm²
c) 150 cm²
d) 200 cm²
2) Um prisma triangular regular tem a aresta da base igual à altura. Calcular a área total do sólido, sabendo-se que a área lateral de uma das faces é 10 m². *
1 ponto
a) 5 (√3 + 6) m²
b) 2√3 + 36 m²
c) 56 m²
d) 2 (√3 + 6) m²

Answers

Answer:

1) c) 150 cm²

2) a) 5 (√3 + 6) m²

Step-by-step explanation:

1) A fórmula para a área lateral do prisma triangular regular é

L.A = Perímetro × Altura

Perímetro = 3 × borda da base

L.A = 3 × 5 cm × 10 cm

L.A = 150cm²

Opção c. 150cm² é a opção correta²

2) Diz-se na pergunta que a área lateral de uma das faces = 10m²

A área lateral de todo o prisma = 3 × 10m²

= 30m²

Onde a borda da base = altura

A área da superfície lateral de uma das faces é: 10m² = Borda da base × Altura da base

Portanto, Altura = √10m

= Borda da base = √10m

A área de superfície total de um prisma triangular é:

2B + Ph

Ph = área de superfície lateral

B = Área de Base

2 (Área da Base) = 2( Borda da Base² × √3/4)

2 (Área da Base) = 2((√10)² × √3 / 4)

2 (Área de Base) = 2(10√3/4)

= 20√3/4

2 (Área da Base) = 5√3 m²

A área de superfície total de um prisma triangular é:

2B + Ph

= 5√3 m² + 30 m²

= 5 (√3 + 6) m²

giving brainliest ! :))

Answers

Answer:

I did this before ok  gh and jk  is 5

Step-by-step explanation:

add the sum of 296 and 173 to their difference​

Answers

Uhh the sum would be 469....nice

38.5 divided by 0.5 simplified

Answers

Answer:

77

Step-by-step explanation:

38.5 ÷ 0.5 = 77

77 x 0.5 = 38.5

(think of 5 x 7)

0.5 x 70 = 35 (3.5 left)

0.5 x 7 = 3.5 (0 left)

70 + 7 = 77

Write 0.00000000007 in scientific notation


HHhhHHHHEEEEEElLllLlpPpPp!!!!!

Answers

Answer:

7x10^-11

Step-by-step explanation:

You probably don't need this answer anymore.

Miss Rockwell surveyed her class and found that 12 out of 30 students chose peaches as their favorite fruit write the number of students who chose peaches as a fraction in the simplest form then write the fraction as a decimal

Answers

Answer: 8282828

Step-by-step explanation: I’m not sure

If 5x + 6 = 10, what is the value of 10x + 3 ?

Answers

Answer:

11

Step-by-step explanation:

Janet can make 4/5 of a necklace in 20 minutes. At this rate, how many necklaces, to the nearest tenth of a necklace, can Janet make in 1 hour?

Answers

Answer: 4 necklaces

Step-by-step explanation: 4/5 x 5 = 4

hope this helps

Answer:

Janet makes 2.4 necklaces in 1 hour

Step-by-step explanation:

first you need to find how many minutes it takes to make one necklace.

to do this, divide 20 by 4 and multiply by 5.

20/4 = 5

5 * 5 = 25

janet makes one necklace every 25 minutes.

one hour is 60 minutes.

60/25 = 2.4

is math hard or easy. comment your answer

Answers

math is hard, but sometimes it can be easy

Answer:

a little bit of bth

Step-by-step explanation:

If f(x) = 2(x - 5), find f(8).
4
6
8
16

Answers

Answer:

6

Step-by-step explanation:

So, eq. 8 in f(x)

f(8)=2(8-5)

    =2(3)

Multiplying,

     =6

Pls Mark me brainliest!!!

Answer:

if (x-5) is an exponent: the answer is 8

Step-by-step explanation:

Substitute:

f(8)=2(8-5)

f(8)=2(3)

f(8)=8

Chris claims that any fraction located between 1/7
1/9 on a number line must have a
denominator of 8. Enter a fraction that shows Chris’ claim is incorrect.

Answers

Answer:

2/15

Step-by-step explanation:

if we multiple 1/7 and 1/9 by 2 we get 2/14 and 2/18. we can then get a fraction in between such as 2/15

I need the answer plzz help me

Answers

Answer: A) a translation 3 units down

Step-by-step explanation: Notice how your y-values are decreasing by 3.

y-values only increase or decrease, so if they’re decreasing, they are going down.

Hope this helps!

Learning Task 4. Solve the problem. Estimate the total amount. Mr. Cruz's monthly
income is P75,000.00. He divide his income to the following expenses:
Food: P 22, 450.89
Recreation: P5, 676.63
Clothes: P 15,670.25
Transportation: P 10,067.15​

Answers

Step-by-step explanation:

Answer: 21,135.08

Step-by-step explanation: because

22,450.89+5,676.63+15 ,670.25+10,067.15=53,864.92

so now 75,000 - 53,864.92 = 21,135.08 that's it

Round 57,824,279 to the nearest ten-million.
57,824,279 rounded to the nearest ten-million is

Answers

Answer:

60,000,000

Step-by-step explanation:

5 and up - round up

4 and down - round down

You can see 7, so we round up.

57,824,279 is rounded to 60,000,000

Let me know if I'm wrong!

Answer:

57,824,279 to the nearest ten million is 60,000,000

Look at the 5 and the 7. Since 7 is greater than 5, round up to 6. We will have 60,000,000.

Step-by-step explanation:

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