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4 years ago

Solve this system: 2x+5y+z=3 x-3y+2z=2 -x+2y-3z=-7

Mathematics

1 answer:

12345 [234]4 years ago

4 0

Answer:

x= -3

y= 1

z= 4

Step-by-step explanation:

Please see the attached pictures for the full solution.

*I evaluated the determinants using Sarrus' rule (see last picture):

∆= aei +bfg +cdh -gec -hfa -idb

*The symbol '∆' (delta) is usually used to denote a determinant.

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What is the approximate area of a regular heptagon with a side length of 4 inches and a distance from the center to a vertex of

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3 years ago

X^2-14x+49 as a graph

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Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

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Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

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respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

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3 years ago

Write the equation in spherical coordinates. (a) x2 y2 z2 = 64

vekshin1

The equation in spherical coordinates will be a constant, as we are describing a spherical shell.

r(φ, θ) = 8 units.

<h3>How to rewrite the equation in spherical coordinates?</h3>

The equation:

x^2 + y^2 + z^2 = R^2

Defines a sphere of radius R.

Then the equation:

x^2 + y^2 + z^2 = 64

Defines a sphere of radius √64 = 8.

Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:

r(φ, θ) = 8 units.

If you want to learn more about spheres, you can read:

brainly.com/question/10171109

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