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Fantom [35]
2 years ago
5

20. Sketch the level curve of the function f(x, y) that contains the point (5,0).

Mathematics
1 answer:
PolarNik [594]2 years ago
5 0

At the given point,

f(5,0) = \dfrac1{\sqrt{5^2 + 0^2 - 9}} = \dfrac1{\sqrt{16}} = \dfrac14

Then the level curve is

\dfrac1{\sqrt{x^2 + y^2 - 9}} = \dfrac14 \\\\ \implies \sqrt{x^2 + y^2 - 9} = 4 \\\\ \implies x^2 + y^2 - 9 = 4^2 \\\\ \implies x^2 + y^2 = 25 = 5^2

which is a circle centered at the origin with radius 5 - quite easy to sketch.

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3 years ago
A flag staff is fixed at one corner of a rectangular room of side 20×10m.The angle of elevation on the top of the flag from oppo
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Answer:

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Step-by-step explanation:

First we have to find the distance from the corner of the flag to the opposite corner, for this we will use Pythagoras

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h² = s1² + s2²

h² = 10² + 20²

h² = 100 + 400

h² = 500

h = √500

h = 22.36

Now that we know this measurement we can calculate the height of the flagpole

well to start we have to know the relationship between angles, legs and the hypotenuse

α = 30

a: adjacent  = 22.36

o: opposite  = ?

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

is the tangent

tan α = o/a

tan 30 = o/22.36

tan30 * 22.36 = o

12.9 = o

The height is 12.9m

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Answer:

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