Grade 11 - More exercises.
The hyperbola : answers.
1.1
x is inversely
proportional to y because their product, xy, is a constant : xy = 8
1.2
y becomes
smaller but never becomes 0.
1.3
If one
variable becomes smaller, the other variable becomes greater.
1.4.1
y = 4
1.4.2
x = 2
1.4.3
y = 5
1.4.4
x = 0,4
1.4.5
y is not a real number.
1.4.6
x is not a real number.
1.5
Division
by 0 is not allowed. The product of any number and 0 is 0.
But in
this case the product must be 8. x or y can therefore not be equal to 0.
1.6
The graph
does not intersect the axes and therefore there are no intercepts.
x and y
can not be equal to 0. See 1.5.
2.1
a = 10
b = 5
c = 4
d = 20
2.2
Number of
cookies given is inversely
proportional
to the number of children
because their
product is a constant.
2.3
The graph
is a hyperbola because
the number
of cookies is inversely
proportional to the number of children.
2.4
See
accompanying graph.
2.5
Yes.
2.6
6,66667
children can get 6 cookies each.
It is not an acceptable answer because the number of children must be a whole number.
Fractions of
a child do not exist. They are discrete values.
3.1
a = 60; b = 100 and c = 30.
3.2
Pressure
is inversely proportional to
the volume
of the gas because
their product
is a constant.
3.3
The graph
will be a hyperbola because
pressure is
inversely proportional to
the volume
of the gas.
3.4
No.
The product of any number and 0 is 0.
In this case
the product of pressure
and volume equals
4800.
Therefore p or
v can not be equal to 0.
3.5
See the
accompanying graph.
3.6
p = 4 kPa
3.7
minimum volume = 24 cubic cm.
4.1
a = 3;
b = 30 and c = 0,6
4.2
The speed is
inversely proportional to
the time taken
because the product of
speed and time
is a constant,
60. d = vt
4.3
The graph
will be a hyperbola because
speed
is inversely proportional to time
OR, the product
of speed and time
is a constant.
4.4
See the
accompanying graph.
4.5
Yes.
4.6.1
t = 0,75
; t = 0,3
4.6.2
v = 600
and v = 10
4.7
Yes.
Speed and time are real numbers and can have any value. They are not
discrete values.