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lakkis [162]
3 years ago
7

Some friends went to the local movie theater and bought four buckets of large popcorn and six boxes of candy. The total for the

snacks was $46.50. The last time you were at the theater, you bought a large popcorn and a box of candy and the total was $9.75. How much would 2 large buckets of popcorn and 3 boxes of candy cost?
Mathematics
1 answer:
OleMash [197]3 years ago
7 0
23.25 just cut the cost of the example in half
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LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6
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LORAN follows an hyperbolic path.

The equation of the hyperbola is: \mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}

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\mathbf{(x,y) = (-60,0)\ (60,0)}

The center of the hyperbola  is  

\mathbf{(h,k) = (0,0)}

The distance from the center to the focal points is given as:

\mathbf{c = 60}

Square both sides

\mathbf{c^2 = 3600}

The distance from the receiver to the transmitters  is given as:

\mathbf{2a = 100}

Divide both sides by 2

\mathbf{a = 50}

Square both sides

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We have:

\mathbf{b^2 = c^2 - a^2}

This gives

\mathbf{b^2 = 3600 - 2500}

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The equation of an hyperbola is:

\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}

So, we have:

\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}

\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}

Hence, the equation of the hyperbola is: \mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}

Read more about hyperbolas at:

brainly.com/question/15697124

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Step-by-step explanation:

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