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HP 9s Powers and Roots
The difference is –0.681534914 =
π
−
π
e
e
< 0, therefore
π
e
>
e
π
.
Answer:
2:
Example
e catheti
d (s figure 1).
Find the hypotenuse of a triangle th
of which are 8 an 15 ee
Solution:
The hypotenuse of a right triangle is given by Pythagoras’ theorem (even
though the Babylonians already knew this relationship!):
2
2
b
a
Hypotenuse
+
=
where
a
b are the two catheti. In this example:
he addition. If the
\
key had been pressed at the end instead, the
and
8O+15O\F
The
\
key is necessary to perform t
calculation performed would have been
2
2
15
8
+
. In fact, we can avoid pressing the
\
key:
M8O+15ONF
is one keystroke shorter, you might prefer using parentheses
for being clearer.
Answer:
Even though the sequence with the
\
key
mbers 8, 15 and 17 is an example of a Pythagorean triple, i.e. integers that can be the
sides of the same right triangle. Some of the simpler sets were already known by the ancient Egyptians.)
ple 3:
17 . (The set of nu
Refer to the HP 9s learning module Polar/Rectangular Coordinate Conversions to learn a faster way of
calculating the hypotenuse.
Calculate
0
0
Exam
Solution:
Although s
e
om calculators return 1, on the HP 9s
0B0\
is an error condition because
is
mathematically an indeterminate (or undetermined) form, much like 0 / 0 or log 0. Press
U
to remove
xample 4:
0
0
the error indicator.
E
se the exponential function to confirm the result.
Calculate
27
0
9
.
−
U
Solution:
A convenie
of computing
y
x
is as
x
ln
y
e
since
x
ln
y
e
e
x
y
=
=
nt way
The HP-35, the world’s first
scientific electronic pocket calc
s
ethod to save valuable space in ROM, which could be
9B
pressed after or while keying in . 27)
x
ln
y
ulator, u ed this m
noticed by the fact that some results were not accurate to the last decimal place (e.g.
9
2
). Therefore,
27
0
9
.
−
can be calculated using the power function (
B
) as follows:
.27=\
(The “Change Sign”“ key,
=
, must be
and also as
9
27
0
ln
.
e
×
−
. To evaluate the latter expression press:
hp calculators
- 3 -
HP 9s Powers and Roots - Version 1.0
