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2 years ago

How many solutions does the system of equations in the graph have?

Mathematics

1 answer:

DaniilM [7]2 years ago

4 0

Answer:go find you a solution of getting some b1tc1es

Step-by-step explanation:

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The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

Kevin and his children went into a restaurant and he bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each

Musya8 [376]

Answer:

6 hot dogs, 2 drinks

Step-by-step explanation:

let y = number of hot dogs

let x = number of drinks

system:

y = 3x

4.5y + 2.25x = 31.50 (standard form: y = -1/2x + 7)

if you graph the system, lines intersect at (2, 6)

6 0

3 years ago

Simplify the expression. 9y^2−25/9y^2−30y+25

mezya [45]

Answer:

Step-by-step explanation:

56y^2/9-30y+25

4 0

3 years ago

What is a scalar <img src="https://tex.z-dn.net/?f=14%20%5Cdiv%2032" id="TexFormula1" title="14 \div 32" alt="14 \div 32" ali

djyliett [7]

A scalar is an element of a field which is used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector.

6 0

3 years ago

Adele is 5 years older than Timothy. In three years, Timothy will be 2/3 of Adele’s age. What is Adele’s current age?

Ostrovityanka [42]

A = 5 + t
t + 3 = 2/3a

t + 3 = 2/3(5 + t)
t + 3 = 10 + 2t / 3
3t + 9 = 10 + 2t
t = 1

a = 5 + 1
a = 6

4 0

3 years ago

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