Y=square root of x
All the others would be a straight line with an unchanging slope (meaning they're linear). Y=rootx is not linear.
I hope this Helps!
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.
<u>M</u><u>e</u><u>t</u><u>h</u><u>o</u><u>d</u><u> </u><u>1</u><u> </u><u>:</u>
replace x and y by their value 1 and 3
3 = 4(1) - 1 = 4-1 = 3
2(1) + 3 = 2 + 3 = 5
correct
<u>M</u><u>e</u><u>t</u><u>h</u><u>o</u><u>d</u><u> </u><u>2</u><u> </u><u>:</u>
y = 4x - 1
2x + y = 5
y = 4x - 1
y = -2x + 5
y - y = 4x - 1 - ( -2x + 5 )
0 = 4x - 1 + 2x - 5
6x - 6 = 0
6x = 6
x = 6/6 = 1
y = 4x - 1
y = 4(1) - 1
y = 3
correct
By Hand
Step 1:
Put the numbers in order.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 2:
Find the median.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 3:
Place parentheses around the numbers above and below the median.
Not necessary statistically, but it makes Q1 and Q3 easier to spot.
(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).
Step 4:
Find Q1 and Q3
Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.
(1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.
Step 5:
Subtract Q1 from Q3 to find the interquartile range.
18 – 5 = 13.