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photoshop1234 [79]
3 years ago
8

A wooden plaque is in the shape of an ellipse with height 26 centimeters and width 16 centimeters. Find an equation for the elli

pse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point. (Round your answer to the nearest hundredth if necessary.)
Mathematics
1 answer:
Hoochie [10]3 years ago
8 0

Answer:

14.19

Step-by-step explanation:

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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (6, 1280)(6,1280).
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Answer:

y=20(2)^x

Step-by-step explanation:

We want to write an exponential function that goes through the points (0, 20) and (6, 1280).

The standard exponential function is given by:

y=ab^x

The point (0, 20) tells us that <em>y</em> = 20 when <em>x</em> = 0. Hence:

20=a(b)^0

Simplify:

20=a(1)\Rightarrow a=20

So, our exponential function is now:

y=20(b)^x

Next, the point (6, 1280) tells us that <em>y</em> = 1280 when <em>x</em> = 6. Thus:

1280=20(b)^6

Solve for <em>b</em>. Divide both sides by 20:

64=b^6

Therefore:

b=\sqrt[6]{64}=2

Hence, our function is:

y=20(2)^x

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