PPT for educational technology II

2. Jointly Proportional.
When we say z is jointly proportional
to a set of variables, it means that z is
directly proportional to each variable
taken one at a time. If z varies
jointly with respect to x and y, the
equation will be of the form z = kxy
(where k is a constant).

3. Examples:
1. If z varies jointly x and y when z=12, x=9 and y=3.
Find the equation of variation.
Sol’n:
z=kxy
12=k(9)(3)
12
27
=
27𝑘
27
k=
4
9
∴ The equation of variation is z=
𝟒
𝟗
xy.

4. 2. If p varies jointly as q and squared of r, and p = 225
when q = 4 and r = 3, find p when q = 6 and r = 8.
Sol’n:
p=kqr2 p=kqr2
225=k(4)(3)2 p=
25
4
(6)(8)2
225=k(4)(9) p=
25
4
(6)(64)
225
36
=
36𝑘
36
p=
25
4
(384)
k=
25
4
p=
9600
4
p=2400

5. 3. The volume of a cone varies jointly as its
height and the square of its radius. A cone
with a radius of 6 inches and a height of 10
inches has a volume of 120π cubic inches.
Find the volume of a cone having a radius of
15 inches and a height of 7 inches.
Sol’n:
v=khr2 v=khr2
120𝜋 = k 10 6 2 v=
𝜋
3
(7)(15)2
120𝜋
360
=
360𝑘
360
v=
1575𝜋
3
7in
k=
𝜋
3
v=525𝜋 cubic inches 15 in

6. Activity(Board work)
Column A Column B
“a varies jointly as b and c”
1. Translate the statement
above into mathematical
equation.
2. If a=6, b=6 and c=2.
What is k?
3. What is a when b=9 and c=2?
“ area(a) varies jointly as length(l) and
width(w)”
4. Translate the statement
above into mathematical
equation.
5. If area is 12cm2, length is 2 and width is 4, then what is k?
6. What is a when l=8cm and w=3cm?
j. a=
𝑘
𝑏𝑐
u.
1
2
a. 36cm2
e. 9
d. k=
3
2
h. a=kbc
n. a=klw

7. Answer:
_ __ __ __ __ __
1 2 3 4 5 6

8. Direction: Answer and illustrate what is being
asked. Encircle the final answer.(NR×5)
1. Kinetic energy varies jointly as the mass and
the square of the velocity. A mass of 8 grams and
a velocity of 5 centimeters per second has a
kinetic energy of 100 ergs. Find the kinetic
energy for a mass of 6 grams and a velocity of 9
centimeters per second.
2. Wind resistance varies jointly as an object’s
surface area and velocity. If an object traveling at
40 mile per hour with a surface area of 25 square
feet experiences a wind resistance of 225
Newtons, how fast must a car with 40 square feet
of surface area travel in order to experience a
wind resistance of 270 Newtons?

9. Assignment:
In your study guide page 216
answer activity numbers
5and 6. Write it in a one
WHOLE sheet of paper.