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3 years ago

The school principal decided to put a small fence around the hopscotch area

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

6 0

She can make a 6x7 or a 7x6 area

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) 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

4 years ago

How do simplify 4(x-3)+5(x-3)

vesna_86 [32]

Answer:

9x-27

Step-by-step explanation:

4(x-3)+5(x-3)=4x-12+5x-15=4x+5x-12-15=9x-27

4 0

3 years ago

Jonathan bought a table and some chairs at a furniture store.

Naily [24]

Answer:

It must be the cost of the one table.

Step-by-step explanation:

It's logic. 25x is the cost of the (unknown) number of chairs.

The total Amount he spent is the cost of the chairs <u>plus</u> what he spent on the table.

4 0

4 years ago

A drawer contains 6 red socks, 5 white socks and 9 blue socks. Without looking, you draw out a sock

umka2103 [35]

Answer:

2/20

Step-by-step explanation:

because 9+5+6=20 and if you draw 2 red socks then that would be yur numerator

3 0

3 years ago

Find all possible solutions to the following: x2 =1.96 (1 point)

11111nata11111 [884]

Answer:

Step-by-step explanation:

x²=1.96

x²-1.96=0

(x+1.4)(x-1.4)=0

x=1.4 and -1.4

3 0

3 years ago