Evaluate each expression | -15 |

Mathematics

2 answers:

Nina [5.8K]4 years ago

3 0

Answer:

Step-by-step explanation:

| -15 |

The absolute value means take the positive value of whats inside

| -15 | = 15

Sergio039 [100]4 years ago

3 0

The absolute value of -15 is 15

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What is the height of an equilateral triangle with side lengths of 14?

olganol [36]

If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.
If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.

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4 years ago

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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]

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

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

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