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State whether the following statements are true or false. Justify your answer. a) The level curves of x/yz=are hyperbolas. b) 2222)0,0()y,x(yxyxlim+−→does not exist. c) The set }0z,0y,0x|)z,y,x{(<>>is a domain in 3R. d) The work done by the Force )x,y()y,x(F−=in moving a particle along the boundary of the ellipse 36y4x922=−+is 6. e) The function xyze)z,y,x(f=is integrable over ].1,0[]1,0[]1,0[××
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 30 liters per minute. There are 500 liters in the pond to start.

Let W
represent the amount of water in the pond (in liters), and let T
represent the number of minutes that water has been added. Write an equation relating W
to T
, and then graph your equation
Write a linear first-order differential equation and work out its general solution.
Compute the appropriate regression equation for the following data:
2 18
4 12
5 10
6 8
8 7
11 5

Where X is the independent variable and Y is the dependent variable.
Also find the correlation coefficient between X and Y and infer about the
relationship between X and Y.
If you increase the dimensions of a square pyramid by 6 times, how much larger will the new surface area be?
Consider a random sample (WOR) of two industries from a population of 5
industries having yearly turnover as follows:

Industry Turnover (in lakhs)
1 2000
2 2400
3 1800
4 3000
5 2600

Enumerate all possible samples (WOR) of size two and show that the sample
mean gives an unbiased estimate of population mean
Find the slope of the line bisectng the angle from the line through (2,3) and(10,9) to the line (3,15) and (10,9).
Answer please its 'asap'
1. show that points(2,-3), (5,0), (2,3), and (-1,0), are the vertices of a square.
2. the distance (x,1) is 2 square root of 5 units from (2, 3), find x.
3. what are the coordinates of the point 3 units from the Y-axis and at distance square root 5 from (5,3)?
4. what is the equation of a line through (7,-3) and perpendicular to the line whose inclination is Arctan 2/3.
5. show that lines 2x + 3Y - 2 =0, 3X - 2Y + 23 =0 and X - 5Y = 12 = 0 are the sides of an isosceles triangle.
1.Show that if d ≠ 0, then d | (-a) and -d | a.
2.Show that it is false that a>b implies a|b.
3.Is 980637 divisible by 7? Show.
4.Determine whether of the following are divisible by 3, 5, 7, 9, or 11 using the methods described int he text:
A. 1969
B. 28350
C. 1421
D. 17303
E. 116424
F. 1089
5.Classify each of the following as true or false:
A. 6 is a divisor of 24.
B. 40 is a multiple of 8.
C. 0 divides 10.
D. 13 is a factor of 33.
E. 12 divides 6.
6.Show that 23n -1 is divisible by 7.
7.Show that 5n - 1 is divisible by 4.
Q. Define the following terms
Conditionally convergent series
Completeness property