a. Parameterize 
by
with 
.
b/c. The line integral of 
over is
d. Notice that we can write the line integral as
By Green's theorem, the line integral is equivalent to
where 
is the triangle bounded by , and this integral is simply twice the area of . is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
Answer & Step-by-step explanation:
This can be proven with the SAS theorem (side-angle-side)
With a perpendicular bisector, the line it bisects is cut directly in half. This creates two equal sides:
and it creates two 90° angles:
∠
∠
And because of the reflexive property of congruence:
Side-Angle-Side.
:Done
Answer:
The greatest common factor of 23 and 50 is 1
Step-by-step explanation:
Answer:
Commision may be defined as a percentage cut which an employee, broker, vendor, retailer or other persons within a sale chain receive from an employer or production firm for selling a good or offering a successful service based on agreed terms by both parties. ;
$18700
Step-by-step explanation:
Given :
Commision pattern :
5% on first $200,000
6% on remaining amount
Amount of commission on $345000
0.05 * 200000 = 10,000
0.06 * (345000 - 200000) = 8700
Total commission :
10,000 + 8700 = 18,700
For these questions it is asking you to convert different measurements.
For the first part,
You must convert 10 kilometres to meters
Or 500 meters to kilometres
For this example I will covert 500 meters to kilometres
1000 meters = 1 kilometer
So 500 meters is 0.5 kilometres or half a kilometer
So on the first day you ride 10 kilometres and increase by 0.5 kilometres a day that means you increase by 1 kilometer every two days
The question is asking how many days until you get to 15 kilometres well
15-10=5
5x2 =10 so the answer to the first part is 10 days
In the second part you have to convert again I am going to convert kilometres to meters this time
We know 1km = 1000m
So you times the kilometer by 1000 to get the meters
0.75 x 1000 = 750
So you start with 7500 and increase by 750 every day
The question asks you the total after 3 days so we must find out each day and add them up
1st day: 7500
2nd day: 7500+750=8250
3rd day: 8250+750=9000
Now we must add them together so
7500+8250+9000=24750
So the answer to this part is 24750 meters
The last part is asking you to compare the programs so let’s start with training program A
20-10=10
10x2= 20
So A is 20 days
Training program B:
We know from previous questions that on the third day you do 9000 meters so we must carry on from there
4th day: 9000+750=9750
5th day: 9750 +750=10500
6th day: 10500 + 750=11250
7th day: 11250 + 750 = 12000
As you can see there is a pattern here on the 3rd day we are on 9000 and on the 7th day we are on 12000 that means it has increased by 3000 in 4 days this is because 750 x 4 = 3000
This means we know 18000 is the 15th day
We will carry on from here
16th day: 18000+750=18750
17th day: 18760+750=19500
18th day: 19500+750=20250
Here we have gone over 200000 which is 20 km on the 18th day meaning training program B is quicker
