PDF- -CALIFORNIA INSTITUTE OF TECHNOLOGY - calc tech

### Description

#### Session 1

- Part 1

Getting familiar with the functions 1

What are the roots of the polynomial: A

• 3,4 Code: Set Calculator to equation mode: MODE>5>3 for quadratic equation Mode 3 because our polynomial is a 2nd degree equation

### Input the equation coefficients a,b,c: 1 =

• -7 = 1 2 = =

Which of the following is a possible root of the polynomial: A

• 4 Code: NOTE: A root is any value that,

when substituted to the variable(ie x),

• will satisfy the equation

(In our equation 0=0 ) Set the calculator to computation mode: MODE>1 Input ONLY the left side of the equation

### Trial and error,

#### Use the CALCU function

Pag nagtanong ang calculator X

• ? iinput ang mga choices
• ? 3 = output is 240

#### And you will get the answer

repeat the step until you get an output of 0

1,2,3 B

1,2,5 C

1,2,4 D

## And you will get the answer

Code: Set Calculator to equation mode: MODE>5>4 for cubic equation Mode 4 because our polynomial is a 3rd degree equation

Find the value of x and y in the following equations:

-12/19,

16/19 B

-24/19,

-22/19 C

-16/19 D

• 22/19 Code:

Input the equation coefficients a,b,c: 1 =

-7 = 1 4 =

### Set calculator to equation mode: MODE>5>1 for two-variable equation

And you will get the answer

### Input the coefficients of a,b and constant c'of the first equation: 2=3=6=

Solve the values of y in the system of equations: Input the coefficients of a,b and constant c'of the second equation:

• -3 = 5 = 2 = Press the = to get the value of x and press again to get the value of y

And you will get the answer

# The equation has two rational roots,

• both of which are positive

# Find the larger of these two roots

• 4 Code: Same method with number 3

We will be using CALCU function

The calculator should display 0

### And you will get the answer

What is the remainder of the polynomial when divided by A

• 305 Code: Set the calculator to computation mode: MODE>1 Input the left side of the equation Apply the Remainder theorem Use CALCU function and substitute x=5 And you will get the answer

Code: Set the calculator to equation mode: MODE>5>2 Input the coefficients a,b and constant c'of the first,

• second and third equation

Press the equal = button twice to get the value of y

#### Solve for the value of A

• -2i Code: Set the calculator to computation mode: MODE>1 Input the equation in the calculator(as is)
• and you will get the answer

Solve for the value of A

• 91 Code: Set the calculator to computation mode Input the equation in the calculator(as is)

# Solve for the value of x in the equation: A

• 13 Code: Set the calculator to computation mode Input the equation and use the SOLVED function to get the value of x

To get the SOLVED function,

## SHIFT>CALCU>= It should display,

must be 0) And you will get the answer

- PART 2

Set the calculator to computation mode: MODE>1 Input the equation as is but replace k with X

### Find x,

Code: Set calculator to computation mode

## Factor A

### Evaluate A

2290 Code:

type the equation and assign an arbitrary constant to substitute to x and use the CALC function

for example X=8 The calculator will display "2197"

# Second,

substitute 8 to the choices and find which one will be equal to "2197"

## Start with the first choice until you get the value of "2197"

What we do as well in the previous examples like this is called "REVERSE ENGINEERING"

Find the 15th term in the arithmetic sequence: 1,3,5,7

31 Code: 1

### May makikita kayo X and Y column

And X column natin ay ang nth term while sa Y column natin ay ang A

Input sa X column ang 1,2,3(1st term,2nd term,

3rd term)

Sa Y column naman,

iinput ang 1,3,5 (kahit 3 number lang,

• kahit wag na yung 7)

### Which mean the 1st term of the A

• 2nd term is 3 and 3rd term is 7

After niyo mainput,

press AC(don't worry hindi mabubura ang data niyo) Sa problem ang hinahanap ay ang pang 15th term

anu ba ang value ng ika15th term

meaning ang hinahanap ang value sa Y column

• type 15Y-hat

# Ang Y-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>5(Yhat)

while ang X-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>4(X-hat)

take note of this dahil gagamitin natin ito in the next problems

### Then press =

And you will get the answer

### Kung may tanong kayo dito at di niyo makuha pakipost na lang

Find the 12th term in the geometric series: 3,

59,049 B

177,147 C

531,141 D

• 1,594,323 Code:

## Set the calculator to STAT mode

### MODE 3>5 or MODE3>6 (it's the same for Geometric Progression,

) May makikita kayo X and Y column

And X column natin ay ang nth term while sa Y column natin ay ang G

### Input sa X column ang 1,2,3(1st term,2nd term,

3rd term)

Sa Y column naman,

• iinput ang 3,9,27

#### Which mean the 1st term of the G

• 2nd term is 9 and 3rd term is 27

### After niyo mainput,

press AC(don't worry hindi mabubura ang data niyo) Sa problem ang hinahanap ay ang pang 12th term

anu ba ang value ng ika12th term

meaning ang hinahanap ang value sa Y column

Therefore,

• type 12Y-hat

# Then press =

## What is the sum of the first 20 terms of the sequence: 1,

• 441 Code: 1

Set the calculator to STAT mode: MODE 3>2 (since it is A

#### In the X column,

• input 1,2,3

In the Y column,

• input 1,3,5

After you input the data,

• press AC

# Press SHIFT>LOG(found below the ON KEY)

we will use the SUMMATION function

(SUMMATION symbol is like E) 5

# You will noticed that our summation is from 1 to 21

## If we start the progression from 0,

then that's the time we use 0 to 20

## And it will be like this

• walang Y-hat na symbol e

### What is the sum of the infinite series: 1,

• 6/7 Code: 1

#### Set the calculator to Computation Mode

MODE>1 Since this is an infinite series,

with a common ratio of less than 1,

then the sum is a finite number

### (NOTE: For an infinite series with a common ratio of greater than 1,

• the sum is infinite)

## Input the equation under SUMMATION function and get the sum from 0 to a large value,

So it will be like this

Then press =

• 5462 Code: 1

# Set the Calculator to STAT mode

MODE3>2 (I hope you already know why MODE 3 2) 2

In the X column,

• input 1,2,3

In the Y column,

• input 6,9,12 then press AC

We should get the sum but we don't know how many term does it have

## Therefore,

• our code is 171Xhat

Since 171 is our last term

### And the calculator will display "56" 4

now use the SUMMATION function like in number 26 but this time,

• its 1,56

# What is the 6th term of the infinite series: 1,

1/3125 B

1/15625 C

-1/3125 D

• -1/15625 Code: 1

Set the calculator to Computation mode

Input the general equation of the infinite series and substitute 5 to x using the CALC function to display the 6th term

And press =

#### Rationalize the given equation: A

• (5+10i)/6 C
• (2+i)/3 Code: 1

## Input the equation as it is in the calculator

(NOTE: The imaginary i is found by pressing the ENG key

Then press =

### And you will get the answer

The function discontinous at x=

• either a or b D
• neither a nor b

SESSION 2 PART 1 1

Subtract A

### Code: Pag sinabing discontinous,

mageerror siya sa value na isusubstitute mo or yung tinatawag na MATH ERROR

Pag may lumalabas parin na value positive or negative or even zero,

• continous parin yun
• dapat mageerror siya

Siguro naman kayang kaya niyo na ito

Set the calculator to COMP MODE

• type na equation as it is

press the CALC function and substitute the numbers in the choices and find which one will get an error

The one error is the answer

### During a rain,

• 2mm of water fell

Find how many gallons of water fell on a level 10 acre park

21,381 B

25,381 C

27,381 D

## Alternative solution

• we use the TABLE function

# Type the equation as it is and press = START

? (your number depends on the choices

we start from the lowest which is

### So enter

• -2 then press = END

? (the largest in the choices)

### So enter 2 and press = STEP

? (The variation in the choices)

### Important po ito

kailangan madaanan nung function yung mga choices

#### In this case 2 and

So enter 2 and press =

### Conversion only

V=10 acre (convert acre to m^2)SHIFT>8(for CONV)>11(for acre>m^2)

## It will give an answer 40468

#### Then multiply it to

• 002 m(given in the problem) and it will display 80
• 93712 in m^3

#### Convert this to Liters

• 1 m^3 = 1000L

# And it will display 80937

12 in L

Finally convert this to gal

## Find the possible factors of A

• (x-2) B
• (2x+3) D

all of the above Code: Para masabing factor siya,

kailangan ang y=0 pag isusubstitute natin yung root of x

We use CALC function

### Set the calculator to MODE 1

Type the equation as it is and press CALC

## Get the root of the choices and substitute

• ? enter 2 if y=0,
• then possible root siya

### Try the next one

• ? enter 1/2,
• if y=0,
• then possible root siya

# Try the last one

• ? enter
• -3/2 if y=0,
• then possible root siya

## Determine the area of the triangle bounded by the straight lines x+2y-7=0,

3x-4y-1=0,

• and 2x-y+6=0
• units B
• units C
• units D

units Code: First get the point of intersection

• use the EQN function

### MODE 5>1 For the first two equation,

• type: 127 3
• -4 1 then press = =

Therefore the point of intersection of this is x=3,

• and y=2

Then try the next equation

• -6 Then press = =

and y=-4 try the last combination of equation

• -6 Then press = =

and y=4 Then we use the determinant function to get the area of the triangle

## Set the calculator to MATRIX

MODE 6 and press AC

What important in this is kailangan natin madaan yung DIM or dimension ng matrix

#### So press SHIFT>4>1>1>1 and enter 321

• -1 4 1 then press AC

To get the determinant press SHIFT>7(det)>SHIFT>4>3(since we enter our data in MatA

### Remember the area of a triangle given the vertices is 0

• 5 times the determinant

# Therefore multiply it to 0

• 5 and get its Abs value

# Find the center of the circle that is circumscribed about the triangle whose vertices are (-3,1),

• (3,1) and (5,3) A
• (-3,9) B
• (3,-9) C
• (-3,-9) D

(3,9) Code: Substitute x and y in the general equation of circle

### In the first point you will get the equation

• -3D-E+F=-10 The second point will give you 3D+E+F=-10 The third point will give you 5D+3E+F=-34

#### Therefore we have 3 equations,

3 unknown

Use the EQN 2 and enter

-10 3 1 1

-10 5 3 1

• -34 And you will get D=6,

and F=-10 And write it in the general form

Ito ang shortcut para makuha ang center

### In the x column enter 1,2 In the y column enter 2,5 then press AC

Use the SUMMATION FUNCTION

# Therefore our center (h,k) is at (-3,9)

Find the value of y of the parabola whose axis is vertical and passes through (-1,0),

• (1,8) and (4,y) A
• 6 Code: We use STAT 3( for parabola) in this case

# In the x column enter

-1,5 and 1

### In the y column enter 0,0,

and 8 then press AC Find the value of y when x = 4

therefore 4(y-hat) or And you will get the answer

Find the sum of an A

• : 2,5,8
• where n=25
• 975 Code: Use STAT 2(for A

#### Find the sum of a G

• : 2,3,4
• where n=10
• 84 Code: Same method with #9 BUT use STAT 6(for G

) Then use the SUMMATION function to get the sum

### And you will get the answer

In how many ways can a picture be painted by using three(3) or more of the seven(7) different colors

• 120 Code: Set the calculator to COMP MODE

# We use the COMBINATION function

It will be found by pressing SHIFT > ÷ ( nCr ) And type the equation just like this: And you will get the answer

#### SESSION 2 PART 2 Starting in this Part,

di ko na iisa-isahin kung anu pipindutin niyo para madali tayo

Kung may tanong kayo at di niyo makuha,

• pakipost na lang

Evaluate A x B

# Find the decimal equivalent of A

32677 B

36277 C

23677 D

• 26377 Code: Convert niyo lang sa decimal

# Additional TIP: Kung hindi na kasya sa calculator at sobrang haba ng BIN mo,

• iconvert mo muna sa OCT
• 101=5 110=6 001=1 111=7 101=5

#### Set to OCT and type the OCT equivalent,

• 56175 And press DEC and you got the answer

### Tandaan daanan lagi si DIM

SHIFT>4>1 Itype ang matrix and that's it

DON'T use divide,

#### And it will be like this

Find dy/dx if

To get the slope,

simply get the first derivative of the equation

### And you will get the answer

Find the slope of the equation A

Gagawa tayo ng equation from the figure,

since may given tayo na r and Code: Pag Trigonometric/Inverse,

• i-set ang calcu sa RADIAN MODE

### Then we must come up with Using Pythagorean theorem:

• po natin diyan,
• pi po yun

# If y = 4tanh x + sinh 2x,

what is the slope of the curve when x = 2

• 2 Code: TANDAAN: Slope = first derivative =

And derive with respect to theta

## Substituting the given and using the d/dx function of the calcu,

• it will be like this:

#### Next we must get From the figure,

• we have and equating it to x,

we have: Substituting the given and getting the derivative of x with respect to theta,

• we have:

4x-y=2 B

4x-y=-2 C

• x+4y=9 D
• x+4y=-9

# Determine the current at the end of 2 seconds

• 10 A Code: Simple get the first derivative of this with x=2 (2 seconds) and you will get the answer

A 1800-gallon tank of water drains from the bottm in 30 min

### According to Torricelli's law,

the volume of water remaining in the tant after t minutes is

#### Code: When you are getting the slope of the line using the first derivative,

what you are getting is the slope of the tangent line

To get the slope of the Normal Line,

you get the negative reciprocal of this

get the first derivate(Tangent slope) of the given equation with x=1(given in the problem)

### Then get the equation using STAT 2

#### And press AC

Get A and B

SHIFT>1>7> and SHIFT>1>7>2 Remember,

• in the calculator,

the equation of STAT 2 is y=a+bx

Substitute a and b in the equation and you will get the answer

# The charge in coulombs that passes through a wire after t seconds is given by the function

where How fast is the water draining from the tant after 20 minutes

-40 gpm B

-30 gpm C

-20 gpm D

• -10 gpm Code: Simply get the derivative of the equation with x=20 (20 minutes)

#### And you will get the answer in gpm

Find the value of x when the function y=lnx/x is at maximum value

Code: For maxima/minima,

the first derivative should be equal to 0

Try or test all the choices using CALC function if dy/dx=0 with x = x to use CALC function while getting the derivative

• and press CALC x

## I-note ito

i-substitute ang limits sa choices

Wag intindihin ang constant "C"

• remember,
• upper limit minus lower limit

lets say for example sa choice A

# Happy integrating

0 e 1 1/e

Kung anu sa choices ang nag equal to 0,

• yun ang sagot

• (2,2) D

1) Code:

### Code: Remember,

in solving Trigonometric or inverse trigonometric,

# Pag nakita niyo na parehas yan,

• i mean 4x,4x
• 9x,9y and so on,
• ang shortcut niyan is 0
• 9x(center): therefore,
• 9 x (2,2) = answer

Find the area of the region bounded by ,

• the x-axis,

and the vertical lines x=0 and x=4

• units B

16/3 sq

17/3 sq

• units D

units Code: First get the limits from the equation it self

Use EQN 3

• hirap e

# Ayun bale alternating po yan

Then integrate using the limits

# Ang you will get the answer

88 Code:

### Kaya po negative yung isa kasi dumaan po sa negative half cycle

And you will get the answer

# Determine the area of the region bounded by the curve and the x-axis,

• units B
• units C
• units D

37/12 sq

units Code: Get the limits from the equation

# Di ko na siya ibibigay

### Shortcuts lang lahat ito

Ang shortcut dito ay distance formula(two points)

### First get the functions of y=f(x) When x=0,

• x=pi/4 Then y=0,
• 34 Then use the distance formula

# And you will get the answer

The speed of the particle is given by

90 ft C

# Code: Get the limits from the equation when d=7

Use EQN 4

• -7 Get the real number and that is your lower limit

### Get the limits from the equation when d=99

Use EQN 4

• -99 Get the real number and that is your upper limit

#### Then integrate the equation using your lower and upper limit

And you will get the answer

Code: Choice one from the choices and Convert the equation to y=f(x)

Differentiate using your calculator with x=1(as given) and you will get the value of dy/dx Substitute x,

y and dy/dx to the equation in the problem and see if it is equal to 2

If yes,

## Code: Get the roots

Use EQN 4

• 1 0 0 8 You will get one real root and two complex roots

# Choose your favorite number for C and x and substitute it to your choice

And solved for y

i-differentiate ang iyong napiling equation with x=(kung ano ni-substitute mo sa una,

be consistent) You will get the y' Then susbtitute in the given equation y'-y=2

• if 2=2 Therefore,
• napili mo ang tamang answer

Will be posted soon

SESSION 2 PART 4 31

## Find its half life

19 hr B

49 hr C

89 hr D

• 16 hr Code: Dahil sa ito ay radioactive,

nagiincrease ito exponentially

## Which means kung exponentially ito,

• gagamitin natin ang STAT 5

Code: Pag temperature ang pinaguusapan use STAT 5

## Sa x column natin is the time(min) and in y column it's either "Ts-T" or "TTs" (temperature)

### It depends kung sino malaki kung si T or si Ts

T = Object temperature Ts = surrounding/environment temperature gets

# Since malaki ang Ts natin which is Ts-T

therefore ang gagamitin natin ay

X-----|-----Y(Ts-T) 0-----|-----(70-18) 1-----|-----(70-31) After natin ma-input ang data,

• press AC

#### Since ang kinukuha natin dito ay equation,

therefore kukunin natin ang value ng A and B

I hope and assume na you know it already kung paano at saan ito kukunin since naturo ko na ito sa naunang session/part

# Ang x column natin ay ang time(hr) and y column natin ay quantity

#### X-----|-----Y 0-----|-----10 2-----|-----9

After makuha ang A and B,

alam natin na ang equation sa STAT 5 ay

since time in its half life ang hinahanap,

• press AC then find

# A thermometer reading is brought into a room where the temperature is

• 1 min later,

### I-substitute ang A and B,

x=t and y=Ts-T since yun ang ginamit natin(y=70T)

#### At the surface of the earth,

Assume the earth to be a sphere of radius 6,371 km,

• compute the mass of the earth

BUT F=mg,

• assume m = Therefore,

41 Code:

## Use STAT 1 and follow the formula,

• and you will get the answer

## Find the value of A

8 + 8i C

• 4 + 4i Code: Ang pwede lang po sa ating calcu ay cube at square ng complex

## Pwede pong ganito:

cancels' out Or pwede din ito:

And you will get the answer

Calculate the form factor of a periodic voltage having the following values for equal time intervals changing one value to the next: 0,

Determine the argument of the result of A

4 Code:

115 ohms

• 15 degrees C B
• 65 degrees C C
• 25 degrees C D
• 45 degrees C Code: STAT 2 X column = temp

### Y column = Resistance

---x--- |

• ---Y-----100 |

---30 |

### Sa next part na

Marami pa naman ito

The resistance of a wire is 126

• 48 ohms at 100 degrees C and 100 ohms at 30 degrees C

### Determine the temperature when the resistance is

What is the present worth of two 10,000 pesos payment at the end of the 3rd and 4th year if the annual interest is 8% compounded quarterly

264 Code:

Ang formula po talaga nito ay where: F = future worth P = present worth i = interest rate m = number of compounding(quarterl,

• semi-anually,
• annually etc)
• t = time(years,month,

etc) Kung alam niyo kung paano computin sa long method,

• then go

:D Then ito po yung sa CALCU TECHNIQUE: First kukunin natin ang P ng 3rd and 4th year

## STAT 5 or 6 X column = mt(ito yung naka-raised sa formula) Y column =

• indeterminate D
• infinity

----- X

----- |

----- Y

--------12

• ----- | 10,000

----- | 1

• 02(10,000) bakit po 12
• ? kasi mt=(4)(3) bakit po 13
• ? kasi next year
• +1 year gets
• bakit 10,000 lang,
• akala ko yung formula

? ginagamit lang natin yung formula on the next year

I-type lang ang equation Press CALC

? Wag po natin i-substitute as x=0 dahil magmaMATH error po yan

# Then press '='

And you will get the answer

Then get the present worth: Second,

kukunin natin ang present worth sa 4th year

Same lang din ito sa 3rd year

Ang pinagkaiba lang yung mt

----- X

----- |

----- Y

• ---------16----- | 10,000
• -----17----- | 1
• 02(10,000) Then get the present worth: Finally get the sum of the present worth in the 3rd year and 4th year

And you will get the answer

# SESSION 3 PART 1 Differential Calculus

• indeterminate D

infinity Code: Same method lang po sa #1

napaisip ka ngayon kung paano infinity

### Ano po ba ang infinity

? Ito ay isang malaking number

So press CALC

? infinity = 1000 or kahit anong malaking number basta wag lang magMAMATH error

## And you will get the answer

• 2 Code: Same method as #1
• 3 Code: Same method lang din sa #1

Pero wag kalimutan na ilagay sa rad mode ang calcu

Code: Same method as #4

infinity Code: Same method lang din as #4

# Palitan ang x ng malapit sa 1

• either 1

Find the derivative of A

This time I assume na marunong na ang lahat at pamilyar na kayo sa mga steps at function na ginagawa natin

Don't forget: Always use rad mode in trigonometric and inverse trigonometric equations

## SHIFT>INTEGRAL then i-type ang equation

#### At maglagay ng value ng x

Youre favorite number

#### I preferred 5

Set x=5 Makakakuha tayo ng answer

Then mula sa choices,

isubstitute lang ang 5 sa x at makakauha tayo ng sagot

Say A2 (answer #2) Kung A1 = A2 then tama ang napili niyo sa choices

• 1 + cos x D
• - cos x Code: Same method with #7

Find the derivative of y if A

Find the derivative of y if tan y = x

• sec x tan x C

# Code: Same lang sa #7

I hope you get it

That's what you called reverse engineering

### Then yun,

• same method na lang as #7

### Find the derivative of y if A

Find the first derivative of y if A

## Kung hindi niyo alam ito,

basa muna kayo sa mga naunang example

### NOTE: Pag parehas ang sagot,

#### USE 2 or 3

Find the second derivative of y if A

Quote: So,

mano-mano ito since walang shortcut pag second derivative

## Sa board exam may ganyan

So let's test kung marunong pa kayo sa mano-mano

#### Find the third derivative of y = x ln x

-1/(x^2) C

-1/(x^3) D

• -1 Quote: So,

mano-mano ito since walang shortcut pag third derivative

## So let's test kung marunong pa kayo sa mano-mano

### Find the derivative of y if A

change to function of x then use d/dx function

# Find the first derivative of y if A

• y / (x+y) B
• -y / (x+y) C
• y / (x+2y) D
• -y / (x+2y) Quote: Same lang sa #14

### Find the partial derivatives with respect to x of the function A

• xy-5y D
• 2xy Quote: Mag-iisip ka ng value ng y and then kapag dinirivative mo,
• equal siya dun sa value ng y

# Substitute 4 in the equation

The equation now becomes 16x-20+6 or 16x14

### Then use (d/dx)(16x-4)

Ang x natin dito ay always 1

So kung anong nakuha niyo answer diyan,

kailangan mag equal siya dun sa answer

## The function A

• is discontinous at

Quote: Use d/dx function then x=x and press CALC

## Find the slope of the tangent line to the graph of the function at the point where x=3

Quote: same with #18

#### Find C so that the line y = 4x + 3 is tangent to the curve y = x^2 + C

• 7 Quote: Remember: m1=m2 (tangent/parallel) m1=
• -1/m2 (normal/perpendicular) And y=4x+3 should be tangent to y=x^2+C First,

get the first derivative or slope of y=4x+3

### Use d/dx with x=1,

• therefore the slope is 4

equate y' = y' (y=4x+3) = (y=x^2+C) 4 = 2x and x = 2

# Therefore,

our pt is (2,11) Substitute this to Y = x^2 + C to get the value of C

# If y=4cos x + sin 2x,

what is the slope of the curve when x = 2 radians

share ko lang din ng CALCU TECHNIQUE sa Laplace Transformation:

Examples:

### Find the laplace transform of f(t) = cosh 5t a

• (5 / s^2

- 25) b

• (5s / s^2

- 25) c

• (s / s^2 + 25) d
• (s / s^2

Sana po nakatulong sa nyo kahit paano

### God Bless "Knowledge are meant to be shared,

• not to be kept"

Steps: By calculator technique (FX991ES+): Let t = x a

Press the Integral sign sa calculator (yung nasa baba ng alpha button) b

### Type mo (e^-9x) (cosh 5x) c

#### Then yung limit po,

• ilagay nyo po 0 to 9 d

Para po malaman mo kung anu yung laplace transform nya sa choices,

trial and error from the choices,

• just change "s" to 9

Like for this example,

letter d'yung may kaparehas na sagot

## Find the inverse laplace of [3(s^2-2)^2] / 2s^5 a

• (3/2) + 3t^2 + (t^4/4) b
• - (t^4/4) c

- (3/2)

• - 3t^2 + (t^4/4) d
• - 3t^2 + (t^4/4) Steps: By calculator technique (FX991ES+): Let t = x & s'= 9 a

### From this example,

reverse process po ang gagawin

158537 b

## From the given choices,

trial and error po uli ang gagawin

### Sa question,

• letter "d" po yung sagot c

• then press =

# Medjo matagal nga lang po lumabas yung sagot

Ang sagot po dapat ay

#### Last edited by robgab

• 11th Aug 2012 Sat at 20:32
• #183 9th Aug 2012 Thu,
• ## Calcium Chloride Handbook

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