Answer:
1. UW // TX
2. VX // UY
3. UW ≅ TY ≅ YX
4. YW =
TV
5. TX = 2 UW
6. ∠TXV ≅∠WUY
Step-by-step explanation:
The line segment joining the midpoint of two sides of a triangle is parallel to the third side and equal to half its length
In Δ XVT
∵ U is the midpoint of VT
∵ W is the midpoint of VX
∵ XT is the 3rd side of the triangle
→ By using the rule above
∴ UW // TX ⇒ (1)
∴ UW =
TX
→ Multiply both sides by 2
∴ 2 UW = TX
∴ TX = 2 UW ⇒ (5)
∵ Y is the midpoint of TX
∴ TY = YX =
TX
∵ UW =
TX
∴ UW ≅ TY ≅ YX ⇒ (3)
∵ U is the midpoint of VT
∵ Y is the midpoint of XT
∵ VX is the 3rd side of the triangle
→ By using the rule above
∴ UY // VX
∴ VX // UY ⇒ (2)
∴ UY =
VX
∵ W is the midpoint of VX
∵ Y is the midpoint of XT
∵ TV is the 3rd side of the triangle
→ By using the rule above
∴ YW // TV
∴ YW =
TV ⇒ (4)
∵ 2 Δs UYW and XVT
∵ UY =
XV
∵ YW =
VT
∵ WU =
TX
∴
=
=
= 
→ By using the SSS postulate of similarity
∴ ∠TXV ≅∠WUY ⇒ (6)
Answer:
a) the slope is 2/-1 or just -2
b) the slope is 1/1 or just 1
Step-by-step explanation:
You can find slope (rise/run) by picking a point on the graph. For example on question a I chose the point (-2, 1) i then counted how far my run was, which is 2, and my rise (or how far down it went) was -1. Therefore my slope was 2/-1 or just -2.
The surface is parameterized by

and the normal to the surface is given by the cross product of the partial derivatives of
:

It looks like you're given

Then the normal vector is

Now, the point (2, 2, 0) corresponds to u and v such that

and solving gives
, so the normal vector at the point we care about is

Then the equation of the tangent plane is



Answer:
11 x1 + 16 x2 + 25 x3 = 971
15 x1 + 22 x2 + 8 x3 = 1,104
9 x1 + 12 x2 + 17 x3 = 730
Step-by-step explanation:
Right on edg.
Lin is older by 3 years. 5-2=3