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AfilCa [17]
3 years ago
8

A drum used for percussion has sides modeled by a hyperbola. The total height of the drum is 35 inches. The diameter at the top

of the drum is 16 inches, and the minimum diameter is 8 inches, occurring at a height of 22 inches. Determine the equation of a hyperbola that models the sides of the drum assuming that the center of the hyperbola occurs at the height where the diameter is the least.
Mathematics
1 answer:
lakkis [162]3 years ago
8 0

look at the screen shot ya know

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Write the equation of the circle whose center is (-4,8) and has a diameter of 18
svetoff [14.1K]

Answer:

(x + 4)^2 + (y - 8)^2 = 81

or

(x + 4)^2 + (y - 8)^2 = 9^2 depending on how your teacher wants it written.

Step-by-step explanation:

The standard form for a circle is

(x + h)^2 + (y + k)^2 = r^2

r is the radius.

You are given the diameter

r = d/2

r = 18/2

r = 9

So you already have the right hand side of the equation

(x + h)^2 + (y + k)^2 = 9*2

(x + h)^2 + (y + k)^2 = 81

You basically have h and k as well. They come from the center point.

h = 4

k = - 8

So the equation of the circle (and the answer) is

(x + 4)^2 + (y - 8)^2 = 81

One question remains. Why do the x and y values change signs? If you know what the distance formula is, then what you are finding is the distance r of all points on the circle from the center of the circle.

It is the distance formula that is actually the formula for the circle.

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2 years ago
A canister contains 12 ounces of flour. When the canister is full, it holds 6 times as much flour.
RSB [31]

Answer:

72

Step-by-step explanation:

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Please use the following images in order to answer the question correctly:
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<u>Given</u>:

The line segments are AB, DB, AB, OB and BC

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Thus, the line segment AB is a secant.

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The diameter of the circle is line that passes through the center and touches the two ends of the circle.

Thus, from the figure, the line segment DB passes through the center and touches the two ends of the circle.

Hence, the line segment DB is the diameter.

<u>Line segment AB (</u>\overline{A B}<u>):</u>

The line joining any two points on the circle is called the chord of the circle.

Thus, from the figure, the line segment AB touches the two points on the circle.

Hence, the line segment \overline{A B} is the chord of the circle.

<u>Line segment OB (</u>\overline{O B}<u>):</u>

The radius of the circle is any line from the center of the circle to any point on the circle.

Thus, from the figure, the line segment OB is a line from center of the circle to the point B on the circle.

Hence, the line segment \overline{OB} is the radius of the circle.

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A tangent is a point that touches the exterior point of the circle exactly one time.

Thus, from the figure, the line segment BC is a touches the circle exactly once.

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Step-by-step explanation:

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