Answer:
x = 20
Step-by-step explanation:
The angles are same side interior angles so the add to 180
3x-10 + 5x+30 = 180
Combine like terms
8x +20 =180
Subtract 20 from each side
8x+20 -20 =180-20
8x = 160
Divide by 8
8x/8 =160/8
x = 20
Question:
Find the point (,) on the curve
that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:

Step-by-step explanation:
can be represented as: 
Substitute
for 

So, next:
Calculate the distance between
and 
Distance is calculated as:

So:


Evaluate all exponents

Rewrite as:


Differentiate using chain rule:
Let


So:



Chain Rule:




Substitute: 

Next, is to minimize (by equating d' to 0)

Cross Multiply

Solve for x


Substitute
in 

Split

Rationalize



Hence:

Answer:
RD≅ TA
Step-by-step explanation:
RD≅ TA is not true statement as they are not corresponding sides.