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klio [65]
3 years ago
15

during a long race a professional cyclist was able to sustain a speed of 20 miles per hour. How far could this cyclist travel at

that speed for 2 hours, 3 hours, and 3.5 hours?
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
4 0
You would just be multiplying, 20m by 2hr, 3hr, and 3.5hr. So 40, 60, and 70. <span />
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Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=
jasenka [17]

Answer:

The function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

The function is continuous at point x=36 if:

  1. The function \\ f(x) exists at x=36.
  2. The limit on both sides of 36 exists.
  3. The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}

\\ f(36) = \frac{36*6}{900} = \frac{6}{25}

The limit of the \\ f(x) is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Since

\\ f(36) = \frac{6}{25}

And

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Then, the function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

8 0
3 years ago
HELP! ITS EASY BUT I CANT DO IT!! Find the volume of a rectangular prism with length = 8.4mm, width = 3.5mm and height = 5.6mm.
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Answer:

164.64

Step-by-step explanation:

you just have to multiply

8.4 x 3.5= 29.4 then you do 29.4 x 5.6 = 164.64

4 0
2 years ago
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kkurt [141]
1. 5:2
2. 5/2
3. 5 to 2
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Which number is equivalent to 0.3
Strike441 [17]
3/10 that's equivalent
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Find the equation of the line<br> In the form y=mx+b
Aleonysh [2.5K]

Answer:

y = -1/3x + 5

Step-by-step explanation:

-1/3 is the slope because the line goes down 1 unit and right 3 units.

The y-intercept is 5 because that is where the line crosses the y-axis.

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