Answer:
<m=79
<n=66
Step-by-step explanation:
The exterior angle is equal to the sum of the non-adjacent interior angles.
Hello :
let A(0,3,2) and (Δ) this line , v vector parallel to (<span>Δ).
M</span>∈ (Δ) : vector (AM) = t v..... t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector <span>perpendicular
to the plane : n </span>⊥ v .... n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v .... vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) <span>perpendicular to (1,1,1)
</span>because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
Easy, use these two formulas, to find Markdown:
Markdown=Original-New
and
Markdown%=

So, plug in what you know.
Markdown= $30-$20.10
M=$9.90
Now, Markdown%
Markdown%=

M%=0.33*100
M%=33
Thus, there was a 33% markdown.
Answer:
CD = 6.385 units
Step-by-step explanation:
Given triangle ABC with right angle at C.
And AB = AD + 6 .
Now, consider the triangle ABC.
⇒ cos(∠BAC) =
(cosФ = adj/hyp)
cos(20) =
.
0.9397 =
(since AB = AD + 6 and AC = AD + CD)
⇒ 0.9397 AD + 5.6382 = AD + CD
⇒ CD = 0.0603 AD + 5.6382. →→→→→ (1)
⇒ sin(∠BAC) =
(sinФ = opp/hyp)
sin(20) =
.
⇒ BC = AB sin(20) . →→→→→(2)
Now, consider the triangle BCD,
sin(∠BDC) = 
⇒ sin(80) = 
CD = 
From (2), CD =
.
⇒ CD = AB (0.3473)
⇒ CD = (AD + 6) (0.3473)
⇒ CD = 0.3473 AD + 2.0838 →→→→→→(3)
Now, (1) →→ CD = 0.0603 AD + 5.6382
(3) →→ CD = 0.3473 AD + 2.0838
⇒ 0.0603 AD + 5.6382 = 0.3473 AD + 2.0838
0.287 AD = 3.5544.
⇒ AD = 12.3847
⇒ From (1), CD = 0.0603(12.3847) + 5.6382
⇒ CD = 6.385 units