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3 years ago

Find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)

Mathematics

1 answer:

elena55 [62]3 years ago

3 0

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

$dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\$

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= root 2 cm.

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Given CD is an altitude such that AD=BC , AB=3 cm and CD= √2 cm.

Let AD=x, Since given AB=3

AD+DB=3

x+DB = 3

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Since ΔBCD is rght angle triangle, let's apply Pythagoras theorem

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$BC^{2} = (3-x)^{2} +(\sqrt{2} )^{2}$

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Since given AD=BC,let us plugin BC=x in above step.

$x^{2} =(3-x)^{2} +2$

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Now we know AD=x= $\frac{11}{6}$ and given CD=√2.

Let us apply Pythagoras theorem for ΔACD

$AC^{2} =AD^{2} +DC^{2}$

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Answer:

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Step-by-step explanation:

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MrMuchimi

Answer:

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Find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)​

Find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)