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Triss [41]
2 years ago
15

n="absmiddle" class="latex-formula"> and $\overline{CZ}$ are angle bisectors of triangle ABC that meet at I as shown below, with CY = 4, AY = 6, and AB = 8. Find BZ.

Mathematics
1 answer:
erica [24]2 years ago
6 0

Answer:

  BZ = 64/23 = 2 18/23

Step-by-step explanation:

The angle bisectors divide the triangle into proportional parts, so we have ...

  CB/CY = AB/AY

  CB = CY(AB/AY) = 4(8/6) = 16/3 . . . . multiply by CY and evaluate

and ...

  BZ/CB = AZ/AC

  BZ = AZ(CB/AC) . . . . multiply by CB

But we have ...

  AZ = 8 -BZ, so this becomes ...

  BZ = (8 -BZ)(16/3)/(10)

  BZ(1 +8/15) = 64/15 . . . . add the BZ term on the right to both sides

  BZ = (64/15)(15/23) = 64/23 . . . . divide by the coefficient of BZ

BZ = 64/23 = 2 18/23

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Pavel [41]

Answer:

588 english tst ok alright

3 0
3 years ago
Read 2 more answers
G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =
Svetach [21]
Presumably you should be doing this using calculus methods, namely computing the surface integral along \mathbf r(u,v).

But since \mathbf r(u,v) describes a sphere, we can simply recall that the surface area of a sphere of radius a is 4\pi a^2.

In calculus terms, we would first find an expression for the surface element, which is given by

\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k
\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j
\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k
\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u

So the area of the surface is

\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u
=-2\pi a^2(\cos\pi-\cos 0)
=-2\pi a^2(-1-1)
=4\pi a^2

as expected.
6 0
3 years ago
Randy buys a pair of shoes that were originally priced at $147. He receives a 35% discount and pays 8.5% sales tax. How much doe
maksim [4K]
Begin by subtracting 35% from 100%, giving 65% which is equivalent to 0.65
Then multiply
147 * 0.67 =  98.49
Now for a sales tax you would want to multiply by 108.5% (or 1.085) as you are paying the previous price and them some
98.49 * 1.085 = <span>106.86165
You can round to the second decimal place since you can't have a monetary value less than a penny
your answer would be $106.86
</span> 

3 0
3 years ago
Given AVXY and AVWZ, what is WW?<br><br> helpppp pls
Yuliya22 [10]

Answer:

Step-by-step explanation:

VZ = 44-27.5 = 16.5

ZY/VY = ⅝

WX = ⅝ of VX

VX = 36×8/5 = 57.6

VW = VX - WX = 21.6 units

7 0
2 years ago
Can someone help fast ??
VARVARA [1.3K]
Use this website wwww.abcs 123.com for the answer blrddd
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