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Lesechka [4]
3 years ago
11

Need answer ASAP !!!!

Mathematics
2 answers:
aniked [119]3 years ago
7 0

Answer:

Step-by-step explanation:

y = ax² + bx + c

( - 6)²a - 6b + c = 0 ⇒ 36a - 6b + c = 0

( - 4)²a - 4b + c = 3 ⇒ 16a - 4b + c = 3

2²a + 2b + c = 0 ⇒ 4a + 2b + c = 0

A = \left[\begin{array}{ccc}36&-6&1\\16&-4&1\\4&2&1\end{array}\right] = - 96

A_{a} = \left[\begin{array}{ccc}0&-6&1\\3&-4&1\\0&2&1\end{array}\right] = 24

A_{b} = \left[\begin{array}{ccc}36&0&1\\16&3&1\\4&0&1\end{array}\right] = 96

A_{c} = \left[\begin{array}{ccc}36&-6&0\\16&-4&3\\4&2&0\end{array}\right] = - 288

a = \frac{A_{a} }{A} = \frac{24}{-96} = - \frac{1}{4}

b = \frac{A_{b} }{A} = - 1

c = \frac{A_{c} }{A} = 3

<em>y = - </em>\frac{1}{4}<em> x² - x + 3</em>

kondor19780726 [428]3 years ago
4 0

Answer:

y = -1/4x^2 - x + 3

Step-by-step explanation:

(-6,0)

(-4,3)

(2,0)

36a - 6b + c = 0

16a -4b + c = 3

4a + 2b + c = 0

c = -4a - 2b

36a - 6b - 4a -2b = 0

16a - 4b -4a - 2b = 3

32a -8b = 0

12a - 6b = 3

4a - b  = 0

4a - 2b = 1

b = -1

4a + 1 = 0

4a = -1

a = -1/4

c = 1 + 2 = 3

y = -1/4x^2 - x + 3

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25 {x}^{2}  - 36 \\  = ( {5x})^{2}  - ( {6})^{2}  \\

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3 years ago
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3 0
3 years ago
) Set up a double integral for calculating the flux of F=3xi+yj+zk through the part of the surface z=−5x−2y+2 above the triangle
Fynjy0 [20]

The surface (call it S) is a triangle with vertices at the points

x=0,y=0\implies z=2\implies(0,0,2)

x=0,y=2\implies z=-2\implies(0,2,-2)

x=2,y=0\implies z=-8\implies(2,0,-8)

Parameterize S by

\vec s(u,v)=(1-v)(2,0,-8)+v\bigg((1-u)(0,2,-2)+u(0,0,2)\bigg)=(2-2v,2v-2uv,-8+6v+4uv)

with 0\le u\le1 and 0\le v\le1. Take the normal vector to S to be

\vec s_v\times\vec s_u=(20v,8v,4v)

Then the flux of \vec F across S is

\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^1\int_0^1\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^1\int_0^1(6-6v,2v-2uv,-8+6v+4uv)\cdot(20v,8v,4v)\,\mathrm du\,\mathrm dv

=\displaystyle8\int_0^1\int_0^1(11v-10v^2)\,\mathrm du\,\mathrm dv=\boxed{\frac{52}3}

8 0
3 years ago
I need help please ASAP !
Natasha2012 [34]

Answer:

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lkjhgfdsaasdfghjkjhgf

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