Determine the smallest integer value of x in the solution of the following inequality

The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.

[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]

(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.

Reasons:

(a) The distance from the cart to the pulley, r is given by Pythagoras's

theorem as follows;

r = √((3 - 0.6)² + x²) = √(2.4² + x²)

The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]

The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]

By chain rule, we have;

[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]

[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]

Therefore;

[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]

[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]

(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;

[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]

The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s

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Answer:

1162.0356

Step-by-step explanation:

Answer:

Austin: [tex]25[/tex]

Dante: [tex]64[/tex]

Yoko: [tex]16[/tex]

Step-by-step explanation:

Total: [tex]105[/tex]

Austin: [tex]y+9[/tex]

Dante: [tex]4y[/tex]

Yoko: [tex]y[/tex]

Equation:

[tex]y+9+4y+y=105\\6y+9=105\\6y=96\\y=16[/tex]

Invisible Steps:

Combine like terms: [tex]y+y+4y=6y[/tex]

Subtract 9 from each side: [tex]6y+9-9=6y[/tex]

                                            [tex]105-9=96[/tex]

Divide by 6 on each side: [tex]6y[/tex] ÷ [tex]6=y[/tex]

                                           [tex]96[/tex] ÷ [tex]6 = 16[/tex]

Answer:

I think 25.5678

it's the correct answer

Step-by-step explanation:

gamsahamnida

Answer:

24

Step-by-step explanation:

x-3=5, solve for x so that x=5+3

now put this in place of x in the expression 2(x+4)

2[(5+3)+4]

2(8+4)

2(12)

24

Answer:

(25, 30) = 150 ,300 450

(15, 24) = 120 225 300

Step-by-step explanation:

Prime Factorization of 15 is:

3 x 5 => 3^1 x 5^1

Prime Factorization of 24 is:

2 x 2 x 2 x 3 => 2^3 x 3^1

Prime Factorization of 25 is:

5 x 5 => 5^2

Prime Factorization of 30 is:

2 x 3 x 5 => 2^1 x 3^1 x 5^1

Answer:

1/2

Step-by-step explanation:

Answer: 2/3 of 30.5 is 20.3333333333

Answer: The prime factors of 2 × 2 × 2 × 3 × 11. The final answer is 264.

Answer:

$4,720

Step-by-step explanation:

$4,000 fridge

$120/1 year

[tex]\frac{120}{1} = \frac{x}{6}[/tex]

120 * 6 = 720

720 / 1 = 720

$720 for 6 years

720 + 4,000 = 4,720

$4,720

Answer:

$4,720

Step-by-step explanation:

Answer:

Step-by-step explanation:

45 minutes is 3/4 hr.

(3/4)(12 + b) = 9 + 3b/4 miles

Answer:

-5/6

Step-by-step explanation:

1. Change 3/4 to 6/8 by cancelling the common factors.

2. Divide how you normally would

Answer:

- [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

-3[tex]\frac{1}{8}[/tex] ÷ 3[tex]\frac{3}{4}[/tex]

[tex]\frac{-25}{8}[/tex] ÷ [tex]\frac{15}{4}[/tex]

[tex]\frac{-25}{8}[/tex] × [tex]\frac{4}{15}[/tex]

[tex]\frac{-100}{120}[/tex]

[tex]\frac{-50}{60}[/tex]

- [tex]\frac{5}{6}[/tex]

* Keep in mind that - [tex]\frac{5}{6}[/tex], [tex]\frac{-5}{6}[/tex], and [tex]\frac{5}{-6}[/tex] mean the same thing!

First, I converted -3 1/8 and 3 3/4 to improper fractions. I then switched the sign of division to multiplication and changed 15/4 to 4/15. I then multiplied -25 with 4 and 8 with 15, resulting in -100/120. I simplified this to -5/6.

Hope this helps, and if you have any questions, let me know!

the correct answer whould be 65.62. but that is not a option for you so I dont know. try 72 it's the closest.

b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5  20/5 = 4    4×4 = 16   so 4/5 is equivalent to 16/20

2/4   20/4 = 5    5×2 = 10   so  2/4 is equivalent to 10/20  

Add:    16/20 + 10/20 = 26/20

brainliest me

The recursive formula for the geometric sequence is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

The recursive equation for a geometric sequence is:

[tex]f(n) = qf(n - 1)[/tex]

In this problem, the sequence is: {-320, -80, -20, -5, . . .}

Hence, the recursive equation is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

You can learn more about geometric sequence at https://brainly.com/question/11847927

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

n the following sequence  -320, -80, -20, -5,...

The The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]is given as:

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

Learn more on geometric functions here: https://brainly.com/question/222209

Answer:

I think it's -28/-12

Step-by-step explanation:

y-y/x-x

Answer:

wdym

Step-by-step explanation:

The probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that is defective is 72.97%.

Given that a biochemical research company produces 50% of its insulin in Kansas and the rest in Jefferson, and 0.5% of Kansas's insulin is defective, while 1.35% of Jefferson's also is defective, to determine what is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective, the following calculation must be performed:

Therefore, the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that is defective is 72.97%.

Learn more in https://brainly.com/question/15462248

Answer:

huh? this doesn't even make sense or I'm just tripib

Step-by-step explanation:

-xoxo

Answer:

36 feet

Step-by-step explanation:

shadow/height = shadow/height

11/6 = 66/h

h = 66 * 6 / 11

h = 36

Answer:

The answer is not reasonable.

The error that Clayton made was that he accidentally added all of the products that had a saved price tag on it, he did not find the difference between the old price and the new, sales price.

Step-by-step explanation:

Hope this helps :) Mark me brainliest if anyone else answers this question.

Answer:

sry I just wanted the points I'm in middle school so I don't know this stuff either but can you give free brainlyest I'm soo close to my next rank I'd really appreciate it if you would

The scale Trent used for his elementary school which has a school yard of 85

meters wide in real life and 102 millimetre wide in drawing  is 51 : 42500

Firstly, let's do the conversion of the units

1 meters = 1000 millimetres

85 meters = ?

cross multiply

length in millimetres = 85 × 1000 = 85000 millimetres

Since the schoolyard width is 85000 millimetres in real life but it's 102 millimetres wide in drawing , the scale will be as follows:

= 102 / 85000

= 51 / 42500

Therefore, the scale is as follows:

51 : 42500

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A scale is chosen to plot the large graphs on smaller paper representing each unit by a supposed unit.

1.2 mm is used to represent 1 meter.

In the scale given the 102 mm is drawn to represent 85 meters.

So dividing the graph line with the original length the scale Trent has used can be found.

102/85= 1.2

This shows that 1.2 mm is used to represent 1 meter.

Multiplying 85 with 1.2 gives 102 .

https://brainly.com/question/25798457

Answer:

b

gnzjfzjgzjxjgzfjsngdjgsjfzgjskzjtztjsgjd5uduajai

Answer:

  (d)  (x,y) ⇒ (x, y)

Step-by-step explanation:

Rotation 360° about any point brings the object back to its original location. The coordinates are unchanged.

  (x,y) ⇒ (x, y)

Using the z-distribution, it is found that the 90​% confidence interval for the percentage of successful challenges is (17.28, 29.34).

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

31 out of 133 challenges were successful, hence:

[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]

90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]

As percentages:

0.1728 x 100% = 17.28%

0.2934 x 100% = 29.34%

The 90​% confidence interval for the percentage of successful challenges is (17.28, 29.34).

A similar problem is given at https://brainly.com/question/16807970

Answer:

  19 cups

Step-by-step explanation:

Let c represent the number of cups of tea. The total cost will be ...

  10c +3(45) ≤ 332

  10c ≤ 197 . . . . . . . . . . . subtract 135

  c ≤ 19.7

Bidula can buy up to 19 cups of tea with ₹332.

Answer:

ang masasabi ko lang thans sa points

Step-by-step explanation: