Resol x^2+y^2+z^2=98 | Microsoft Math Solver

Resoleu x (complex solution)

x=-\sqrt{98-z^{2}-y^{2}}

x=\sqrt{98-z^{2}-y^{2}}

Resoleu y (complex solution)

y=-\sqrt{98-z^{2}-x^{2}}

y=\sqrt{98-z^{2}-x^{2}}

Resoleu x

x=\sqrt{98-z^{2}-y^{2}}

x=-\sqrt{98-z^{2}-y^{2}}\text{, }|y|\leq \sqrt{98-z^{2}}\text{ and }|z|\leq 7\sqrt{2}

Resoleu y

y=\sqrt{98-z^{2}-x^{2}}

y=-\sqrt{98-z^{2}-x^{2}}\text{, }|x|\leq \sqrt{98-z^{2}}\text{ and }|z|\leq 7\sqrt{2}

Prova

Algebra

5 problemes similars a:

{ x }^{ 2 } + { y }^{ 2 } + { z }^{ 2 } =98

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Which point of the sphere x^2+y^2+z^2=19 maximize 2x+3y+5z?

https://math.stackexchange.com/questions/2246736/which-point-of-the-sphere-x2y2z2-19-maximize-2x3y5z

By the Cauchy-Schwarz inequality 2x+3y+5z \leq \sqrt{x^2+y^2+z^2} \sqrt{2^2+3^2+5^2} = 19 \sqrt{38} and equality is achieved if (x,y,z)=\lambda(2,3,5), i.e. for \lambda=\frac{1}{\sqrt{2}}.

Convert x^2+y^2+z^2=49 to spherical coordinates

https://math.stackexchange.com/q/1149939

This is equation of a sphere, so you can write immediately that R^2=49, since x^2+y^2+z^2=R^2. But you could get to this the way you started, simply by repeatedly using \cos^2x+\sin^2x=1 to ...

Volume of the solid bounded by the sphere x^2 + y^2 + z^2 = 9 and paraboloid 8z = x^2 + y^2

https://math.stackexchange.com/q/1050273

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Show that x^2+y^2+z^2=999 has no integer solutions

https://math.stackexchange.com/q/2114429

My immediate solution was the same as Jorge Fernández Hidalgo, using \bmod 8 limits, but carrying on from your sticking point (and trusting your work to that point): k_1^2+k_2^2+k_3^2+k_1+k_2+k_3 = 249 \\ (k_1^2+k_1) + (k_2^2+k_2)+(k_3^2+k_3) = 249 \\ k_1(k_1+1) + k_2(k_2+1)+k_3(k_3+1) = 249 \\ ...

Use the chain rule to compute ∂z/∂x and ∂z/∂y for 2x^2+y^2+z^2=9. Where exactly do I use it and how?

https://math.stackexchange.com/questions/2215399/use-the-chain-rule-to-compute-%e2%88%82z-%e2%88%82x-and-%e2%88%82z-%e2%88%82y-for-2x2y2z2-9-where-exactly

You need to use implicit differentiation. The idea is that, suppose you can write z = g(x,y). Then you can rewrite the equation about as F(x,y, g(x,y)=z) = 0 where F = 2x^2+y^2+z^2-9. To compute ...

Evaluate the directional derivative of f for the points and directions specified

https://math.stackexchange.com/q/1312172

(a) The outward normal of the sphere given is \left(\frac{x}{3},\frac{y}{3}, \frac{1}{3}\sqrt{9-x^2-y^2}\right). The same at the given point is \overline n=\left(\frac{2}{3},\frac{2}{3}, \frac{1}{3}\right). ...

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