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Charra [1.4K]
3 years ago
10

Max drove 460 miles in 8 hours at a constant speed. How long would it take him to drive 661.25 miles at that speed

Mathematics
2 answers:
alexira [117]3 years ago
4 0
Rate x time = distance

8r = 460  Divide both sides by 8

rate = 57.5 miles per hour

At that speed (57.5mph) and the distance of 661.25miles we should divide

661.25 miles ÷ 57.5 mph = 11.5 hours

Makovka662 [10]3 years ago
3 0

Answer:

It will take 11.5 hours.

Step-by-step explanation:

Max drove 460 miles in 8 hours, so he drove 460/8 = 57.5 miles in one hour. Now,

\frac{57.5 miles}{1 hour} = \frac{661.25 miles}{x hours}

we found x,

x = \frac{661.25*1}{57.5}

x = 11.5 hours.

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Write the equation of a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2(sqrt5)
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Answer:

\frac{x^2}{16}-\frac{b^2}{4}=1

Step-by-step explanation:

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The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4

The foci c is at +/-2√5, using c² = a² + b²:

c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2

Substituting the value of a and b to get the equation of the hyperbola:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1

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3 years ago
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