Exercises - Solutions
Exercises - Solutions
 Exercises - Solutions Back to Exercises See also Math Functions at Syntax

1-Algebraic to RPN -Solutions:
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 a)  1 2 3 4 5 + + + +   R: 15 b)  45 98 + 87/  789 9 /  /   R: 0.136927647109 c)  5 3 Yx 467.78 34 Yx      R: 7.5565941485E92 d)  5 ! 3 4 / Yx    R: 36.2565047683  Use:   a [DEL]  to write " ! " e)    7 3 4 / * 5 8 * + 3 -    R:42.25 f)  1 6 81 /   /   R:3.67423461417 g)  9  8  * 3   5   6 Yx   *    4   +  R: 11790.75 h)  45 7 908 * 786 / * .123 *   R: 44.7588549618 i)  78 9 +   R: 9.32737905309 j)  234.89 .3452 Yx  R:6.58297847487

2-Using Equation Writer - Solutions:
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 Screenshot for exercice a Screenshot for exercice c a) 5.16727650751 b) 15.4522603428 c) 1307.8333333333 d) 2.40826422443E36 e) 13.4907375632 f) 3.94822203886 g) 3.31714371843 h) 2.81342968889 i) 2.58734023677 j) 1.25071993425

3-Converting Units - Solutions:
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 a)123 oz = 3486.99134438 g b)8906 m = 5.53393183807 mi c)45.667 YD = 0.0417579048 d)32 ft = 975.36 cm e)150 YD² = 1254191.04  cm² f)1 km² = 247.104393047 acres g)1300 knot = 1496.01328243  mph h)2.34 c = 2525451666.19 kph i)34.5 torr = 4.53947368421E-2 atm j)598 N = 59,800,000 dyn k) 50 atm = 734.797438776 psi l)350 cubic in = 5.7354724  liters (L)

4-Solve and Equation writer - Solutions:
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 E-a)2.04939479441 P-a)(-1.7144088,1.399984);(-1.7144088,-1.399984);  (1.428817701,0) E-b)0 (zero) P-b)(0.42868302, -1.50533700); (0.42868302, +1.50533700)   (-2.897366046,0) E-c) -3.53694581281 P-c) 0,  0,  2 E-d) 2.38395550345 P-d)0.5151138047128 ,  2.14133611566,  3.62619806853 E-e) -3.53694581281 P-e) -5, 2 ,-1

5-Join Similar Terms & Expand - Solutions:
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 a)-861X + 89Y b) X^2 - 2X-35 c) -2X^2 - 9X +145Y d) 9+x^2 + 6X e) 86 -106X +120Y + 908Z f) 4 + Y^2 -4Y g) -77 -2X^4 - X^5 + 32X h) 1 + 3X^2 +X^3 + 3X i) 94 +X^4 + y^9 + 9y j) 12+z^3 -2Z^2 - 11Z

6- Linear System - Solutions:
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 a)   X=-4.258561644  Y=1.289811644;  Z=-3.439212329 b)  X=-0.906382978  Y=-0.608510638  Z=-2.187234043 c)  X=0.274599566  Y=-0.252941424  Z=-6.243480457 b)  X=1.417910448  Y=1.373134328

 7-Solve Stat Fit Data - Solutions: Back to Exercises  a)Linear Fit: -.490566037736 + 1.66037735849X   b)Logarithm Fit:-5.85427750926 + 9.69433026628 LN(X)   c)Exponential Fit:3.18187591457EXP(.150177816434X)   d)Power Fit:1.7474434559X0.943296197549   e)Best Fit: -.490566037736 + 1.66037735849X   f)Predict Value for X=8.85:   y=14.2037735849   f)Predict Value for y=5.43:   y=3.56579545455

8-Solve Taylor Polynomial . Use SYMBOLIC to accessTaylor Polynomial.
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a)  f(x)=sin(x) : X - 1 / 3!*X^3 + 1 / 5!*X^5

b)  f(x)=X^2(x) : X^2

c)  f(x)=tan(x) : X + 2 / 3!*X^3 + 16 / 5!*X^5

d) f(x)=sin(2x) : 2X -8 / 3!*X^3 + 32 / 5!*X^5

9-Plots - Solutions:
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 y=sin(X) - function y=sin(X)cos(X) - function y=sin(X)/X - function y=3sin(3X)- polar '3X2 - 2Y2 + 2' conic col 1= [[0.5][1.1][2][3][3.9]] bar

10 - Equation Library - Solutions
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Solve for the following variables using Equation Library:

a) Solve for F using Coulomb's Law:
use[EQLIB] [ ELETRICITY] [COULOMB'S LAW]

q1=2E- 5 C

q2=7E- 6 C

r=10,000 m
F=1.25825725022E-4_N

b) Find the volume and area of a sphere of radius 5
use[EQLIB] [ SOLID GEOMETRY] [SPHERE]

A=314.1592653cm_^2
V=523.5987755cm_^3

c) Solve for x using  equation X = Xo + Vo.t + 0.5 a.t^2
use[EQLIB] [ MOTION] [LINEAR MOTION]

Xo=5 m

vo = 9 m/s

t=21 s

a=3.2 m/s^2

X = 899.6_m

11-Areas
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a)Y=sin(x) :  A=0.573845990053

b) Y=sin(x): A=0.573845990053

d)  y=5: A=25

12-Matrices - Solutions:
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a)
[[-.7333333333 .33333333333 6.666666666E-2]
[-.13333333333 -.6666666666 .46666666666]
[.666666666666 .33333333333 -.33333333333]]

b)
[
[.16666666666     -.33333333333  -.5     -.75]
[.33333333333   -1.6666666666   -.5      -3.75]
[.33333333333    -1.6666666666   -.5      -4.25]
[-.33333333333    -1.6666666666     1          4]
]
c)
[[.5 -.5 0]
[.25 .25 0]
[.25 .25 -.5]]

d)
[[2 4]
[8 20]]

13-Derivatives and Integrals - Solutions:
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 Differentiate:  a) 5  b) 7 + 32X^7 -22.5X^1.5  c) 4X^3 - 3X^2 + 14X - 5  d)-3x^- 4 -3 X^2 +1.5  e)4.6X-10X^9 Integrate (numeric):  a) 2639.16666666  b) 220543.0555555  c) 1.9766841163 E13    d) y=Sin(2X) dx ,from 2 to 5  A=0.92713954106  e) -175317684.181

14-Evaluate - Solutions:
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Use {X value} | . Press  9 [NXT], after [ | ], in menu and press [ENTER] to evaluate.
Ex:
Evaluate y=Sin(2X)Cos(X) for X=9.87
Write in level 1:
'Sin(2X)*Cos(X)' and press [ENTER]
Continue writting:
{X 9.87}  9 [NXT], press [ | ] in menu and press [ENTER]
It must appear:
R:-.701571149738

Solutions:

a) y=X^5+7 for X=9.23
66996.7728421

b) y=2.345X^2.5 + X^5 +74X for X=5.67
6288.23941576

c) y=207Y^7 + 4X^5 - X^3 +7X^2- 5X  for x=7 and y=8
use {X 7 Y 8} |
434177657
d) y=Sin(2X)Cos(x) for X=9.87
-.701571149738

e) F(w)=3X^2 - X^12 +7Y - 6Z  for X=3,  Y=7  and Z=-9
use {X 7 Y 8 Z -9} |
-531311

15-SIMPLE PROGRAMS - SOLUTIONS:
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