Zero and Negative Integral Exponents

1. Zero and
Negative
Integral
Exponents

17. Inverse variation
The statement, “y varies inversely
to x,” translates to y = k/x, where k
is the constant of variation.

18. Express each of the following statements as a
mathematical equation.
1. The number of pizza slices p
varies inversely as the number
of persons n sharing a whole
pizza.

19. Express each of the following statements as a
mathematical equation.
2. The number of pechay plants
n in a row varies inversely as
the space s between them.

20. Express each of the following statements as a
mathematical equation.
3. The number of persons n
needed to do a job varies
inversely as the number of
days
d to finish the job.

21. Express each of the following statements as a
mathematical equation.
4. The length l of a rectangular
field varies inversely as its
width w.

22. Express each of the following statements as a
mathematical equation.
5. The density d of air varies
inversely as the volume v of
water in the atmosphere.

23. Find the constant of variation and write the equation
representing the relationship
between the quantities:
x 2 4 6 8
y 36 18 12 9

24. Find the constant of variation and write the equation
representing the relationship
between the quantities:
x 1 2 3 4
y 2 1 2/31/2

25. More examples
1. Find the equation and solve
for k: y varies inversely as x and
y = 6 when x = 18.

26. More examples
2. Find the equation and solve
for k: y varies inversely as x and
y = 12 when x = 5.

27. More examples
3. Find the equation and solve
for k: y varies inversely as x and
y = 10 when x = 2/5.

28. Activity
Section

29. Express each of the following statements as a
mathematical equation
1. The rate r at which a person types a
certain manuscript varies inversely as
the time t spent in typing.
2. The cost c per person of renting a
private resort varies inversely as the
number n of
persons sharing the rent.

30. Find the constant of variation and write the equation
representing the relationship between the quantities:
x 3 6 9 12
y 2 1 2/3 1/2
3.
4.
x 7 5 3 1
y 5/7 1 5/3 5

31. 5. y varies inversely as x and y =
18 when x = 3.
6. y varies inversely as x and y =
12 when x = 2/3.

32. If y varies inversely as x and y = 10 when
x = 2, find y when x = 10.
Example 1.

33. If y varies inversely as x and y = 3 when x
= 4, find y when x = 6.
Example 2.

34. If p varies inversely as the square of q
and p = 3 when q = 4, find p when q = 16.
Example 3.

35. If w varies inversely as y and w = 2 when
y = 3, find w when y = 6
Example 4.

36. The number of days needed in repairing
a house varies inversely as the number
of men
working. It takes 15 days for 2 men to
repair the house. How many men are
needed to complete the job in 6 days?
Example 5.

37. At 60 kilometers per hour it takes Loida
10 hours to travel from her house to
their house in
the province. How long will it take her if
she travels at 80 kilometers an hour?
Example 6.

38. Solve for the indicated variable in each of the
following.
1. If m varies inversely as n and m = 8
when n = 3, find m when n = 12.
2. If y varies inversely as x, and y is 10
when x = 5, find y when x = 7.
3. If a varies inversely as b and a = 12
when b = 8, find a when b = 6.
4. If w varies inversely as x and w is 10
when x = 5 find w when x = 25.

39. Solve for the indicated variable in each of the
following.
5. Two college students decided to rent an
apartment near the school where they
are studying. The nearest and cheapest
apartment costs Php 5,000 a month,
which they find too much for their
monthly budget. How many students will
they need to share the rent with so that
each will pay only Php 1,250 a month?

40. Solve for the indicated variable in each of the
following.
6. Norman is figuring out a way to reach
Baguio at the shortest possible time.
Using his car, he can reach Baguio in 6
hours at an average speed of 70 km per
hour. How fast should he drive in order to
reach Baguio in 5 hours?

41. Thank
You