Please help me on how to solve this question, it is really confusing, pleaseeeee

Mathematics

1 answer:

mezya [45]3 years ago

6 0

D is halfway between A and B

so the coordinates of D are (2,2)

E is halfway between A and C so the coordinates of E are (-1,1)

now you need to find the gradient/slope of DE and BC using the formula:

y2 - y1 ÷ x2 - x1

Gradient of DE:

SUB IN COORDINATES OF D AND E

1-2 ÷ -1-2

therefore the gradient of DE is 1/3.

Gradient of BC:

SUB IN COORDINATES OF B AND C

- 2 - 0 ÷ - 3 - 3

therefore the gradient of BC is -2/-6 which simplifies to 1/3.

therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient

You might be interested in

Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k, S is the hemisphere x2 + y2 + z2

Alenkinab [10]

By Stokes' theorem, the integral of the curl of $\vec F$ across $S$ is equal to the integral of $\vec F$ along the boundary of $S$ , call it $C$ . Parameterize $C$ by

$\vec r(t)=2\cos t\,\vec\imath+2\sin t\,\vec\jmath$

with $0\le t\le2\pi$ . So we have

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_C\vec F\cdot\mathrm d\vec r$

$=\displaystyle\int_0^{2\pi}(10\sin t\cos 0\,\vec\imath+e^{2\cos t}\sin0\,\vec\jmath+2\cos t\,e^{2\sin t}\,\vec k)\cdot(-2\sin t\,\vec\imath+2\cos t\,\vec\jmath)\,\mathrm dt$