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WINSTONCH [101]
3 years ago
7

Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance

and time according to this function v(t,x) = x/t. Your measured distance and time have the following values and uncertainties x = 8.1 meters, Δx = 0.9 meters and t = 1.7 seconds and Δt = 1.7 seconds. What is the uncertainty in the average speed, Δv ?
Mathematics
1 answer:
zzz [600]3 years ago
4 0

Answer:

\frac{\Delta v}{v}=0.426

Step-by-step explanation:

you have that the average sped is given by the following formula:

v(x,t)=\frac{x}{t}

The uncertainty formula for a division is given by:

\frac{\Delta v}{v}=\sqrt{(\frac{\Delta x}{x})^2+(\frac{\Delta t}{t})^2}        (1)

Δv: uncertainty in speed

Δx: uncertainty in the distance = 0.9m

Δt: uncertainty in time = 0.7s

x: distance = 8.1m

t: time = 1.7s

You replace the values of all parameters in the equation (1):

\frac{\Delta v}{v}=\sqrt{(\frac{0.9}{8.1})^2+(\frac{0.7}{1.7})^2}\\\\\frac{\Delta v}{v}=0.426

Hence, the relation between the uncertainty in the average velocity is 0.426

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Match the following rational expressions to their rewritten forms.
Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}

And the rewritten forms:

(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}

So, correct option is 3.

(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}

So, correct option is 1.

(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}

So, correct option is 2.

(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}

So, correct option is 4.

The answer is also attached in the answer area.

7 0
2 years ago
Simplify (g^{2}h)^{4}
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Answer:

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8 0
2 years ago
What is a signed number?
MrRa [10]
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5 0
3 years ago
Write an equation in slope-intercept form of the line that passes through (6,-2) and (12,1)
yarga [219]

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

y =\frac{1}{2}x-5

Step-by-step explanation:

Given points are:

(x1,y1) = (6,-2)

(x2,y2) = (12,1)

The slope intercept form is:

y=mx+b

We have to find the slope first

m =\frac{y_2-y_1}{x_2-x_1}\\=\frac{1-(-2)}{12-6}\\= \frac{1+2}{6}\\=\frac{3}{6}\\=\frac{1}{2}

Putting the value of slope

y = \frac{1}{2}x+b

To find the value of b, putting (12,1) in the equation

1 = \frac{1}{2}(12)+b\\1 = 6+b\\b = 1-6\\b=-5

Putting the values of m and b

y =\frac{1}{2}x-5

Hence,

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

y =\frac{1}{2}x-5

Keywords: Equation of line, slope-intercept form

Learn more about equation of line at:

  • brainly.com/question/4361464
  • brainly.com/question/4390083

#LearnwithBrainly

8 0
3 years ago
Is 0.121122111222 a repeating or terminating decimal? If so, why?
oksian1 [2.3K]

Answer:

I'm just guessing that it is. That question is on my math homework and the definition in the back of my math book says: A decimal in which one or more digits repeat infinitely and I put yes. Because they repeat.

7 0
2 years ago
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