Alternate interior angles can always add to 180

1 answer:

7 0

Two angles are said to be supplementary when the sum of the two angles is 180°. ... All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

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Help please thank you

anyanavicka [17]

Answer:(3,3) eery year

Step-by-step explanation:

4 0

3 years ago

Please help solve this question been stuck for a while

damaskus [11]

Answer:

7.7

Step-by-step explanation:

To find the intersection points of the line and the circle we have to set up a system with their equations and solve. The system would look like this:

$\left \{ {{x=1 } \atop {x^2+y^2=16}} \right.$

To solve, substitute 1 for x in the second equation to get:

$1^2+y^2=16$

Solving, we get:

$y=\sqrt{15}, y=-\sqrt{15}$

Therefore, the two points of intersection are $(1,\sqrt{15} )$ and $(1,-\sqrt{15})$ . The distance between these two points (the length of the chord in the circle) is $2\sqrt{15}$ which is 7.745966692414... which is 7.7 rounded to the nearest tenth.

Hope this helps :)

6 0

3 years ago

Work out the balance for £4500 invested for 2 years at 4% per annum

Anika [276]

the amount you are looking for is £4860

hope this helps. good luck with the rest.

3 0

3 years ago

Find the flux of the vector field F = 〈e-z,4z,6xy) across the curved sides of the surface S = {(x,y,z): z= cos y, lys π, 0sxs4}

Len [333]

I'll go ahead and assume you meant to say that S is the surface given by

$S = \left\{(x,y,z) \mid z = \cos(y)\text{ with } 0\le y\le \pi\text{ and }0\le x\le4\right\}$

This immediately gives us a parameterization for the surface,

$\vec r(x, y) = \left\langle x, y, \cos(y)\right \rangle$

The upward-pointing normal vector to this surface is then

$\vec n = \dfrac{\partial\vec r}{\partial x} \times \dfrac{\partial\vec r}{\partial y} = \left\langle0,\sin(y),1\right\rangle$

Then the flux of $\vec F(x,y,z) = \left\langle e^{-z}, 4z, 6xy\right\rangle$ across S is

$\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \int_0^4\int_0^\pi \vec F(x,y,\cos(y))\cdot\vec n\,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi \left\langle e^{-\cos(y)},4\cos(y),6xy\right\rangle \cdot \left\langle0,\sin(y),1\right\rangle \,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi (4\sin(y)\cos(y)+6xy)\,\mathrm dy\,\mathrm dx \\\\ = 2 \int_0^4\int_0^\pi (\sin(2y) + 3xy)\,\mathrm dy\,\mathrm dx = \boxed{24\pi^2}$