If the area of the domain of the function fx-y - -16-x2-y2 - -x- - y is k- sq- units- then the value of k is

From the first radical sign, x^2 + y^2 ≤ 16 and nbsp;from nbsp;the second radical sign, y ≤ |x| ∴ Area =34 × area of circle =34×π×4^2=12π Hence, the value ...

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Standard XII

Mathematics

Graph of [x]

If the area o...

Question

If the area of the domain of the function $f (x, y) = \sqrt{16 - x^{2} - y^{2}} - \sqrt{| x | - y}$ is $k π$ sq. units, then the value of $k$ is

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Solution

From the first radical sign, $x^{2} + y^{2} \leq 16$
and from the second radical sign, $y \leq | x |$

$∴$ Area $= \frac{3}{4} \times$ area of circle
$= \frac{3}{4} \times π \times 4^{2} = 12 π$
Hence, the value of $k$ is $12.$

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If the area of the domain of the function f(x,y)=√16−x2−y2−√|x|−y is kπ sq. units, then the value of k is

From the first radical sign, x2+y2≤16 and from the second radical sign, y≤|x| ∴ Area =34 × area of circle =34×π×42=12π Hence, the value of k is 12.

If the area of the domain of the function $f (x, y) = \sqrt{16 - x^{2} - y^{2}} - \sqrt{| x | - y}$ is $k π$ sq. units, then the value of $k$ is

From the first radical sign, $x^{2} + y^{2} \leq 16$
and from the second radical sign, $y \leq | x |$

$∴$ Area $= \frac{3}{4} \times$ area of circle
$= \frac{3}{4} \times π \times 4^{2} = 12 π$
Hence, the value of $k$ is $12.$