A word problem on algebra linear equations

Equations play a crucial role in modern mathematics and form the basis for mathematical modeling of numerous phenomena and processes in science and engineering.

The international scientific-educational website linear equations explained World presents extensive information on solutions to various classes of ordinary differential, partial differential, integral, functional, and other mathematical equations. It also outlines a thing that solves algebra equations, includes interesting articles, gives links to mathematical websites and software packages, lists useful handbooks and monographs, and refers to scientific publishers, journals, etc. The website includes a dynamic section Equation Archive which allows authors to quickly publish their equations (differential, integral, and other) and also exact solutions, first integrals, and transformations.

Let's see a word problem from 8th grade word problems worksheets.

Question:-

Jack is thinking two positive numbers.one of them is 4 more than the other and the sum of their squares is 208.what are the two numbers?

Answer:-

Let one number be x.

the other number is 4 more ,x+4

given sum of the squares =208

x²+(x+4)²=208

x²+x²+8x+16=208

expanding the 2nd term

2x²+8x+16=208

dividing by 2 as it is common for all terms

x²+4x+8=104

subtract 104 on both sides

x²+4x-96=0

x²+12x-8x-96=0

x(x+12)-8(x+12)=0

(x+12)(x-8)=0

x=-12 or x=8

here we want only positive number ,so x=8

and the numbers are 8 and 12

Problem on pythagoras theorem

From geometry terms and definitions we know that,
Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle in British English). It states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle)
Let's see a heights and distances trigonometry problems

Applying Pythagoras theorem to ΔACF

AF=√(9+9)=√18=√(2*9)=3√2






Now in ΔBAF

BF² = AB²+AF²

= 3²+(3√2)²

= 9+18
BF²=27

BF=√(9*3)= 3√3 units

Similar way we can also find length of base of isosceles triangle

Factors of a Number:

Topic:-Factors of a Number:

Factoring is like taking a number apart. It means to express a number as the product of its factors. Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite).
This algebra help gives us few examples as well.

•A factor of a number N is a number which divides N exactly.

•Example: the factors of 12 are 1,2,3,4,6,and 12

•Note that every number has itself and 1 as its factors.

•When a number is greater than 1 and has just itself and 1 as factors, the number is prime.
Multiples of a Number:

•A number which is the product of a given number and another factor.

•Example: 12 is a multiple of each of the numbers 1,2,3,4, and 6
Example:
5 x 6 = 30
The numbers that are multiplied 5 and 6 are called factors.
The product formed by multiplying the factors that is 30 is called multiple.
30 is a multiple of 6 and 5
Example: Which number is a factor of 16?
_ 8
_ 5
_ 9
Answer: 8

For more help on this ,you can reply me.

How to convert Fahrenheit to Celcius

Topic:-Temperature
Celsius (also known as centigrade) is a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as serve as a unit increment to indicate a temperature interval (a difference between two temperatures or an uncertainty).

Question:-
The temperature in Celcius degrees 'C' can be changed to Fahrenheit degrees 'F' by the formula F = (1/5)*(9C+160). Make C the subject of the formula, then find C when F = 212 degrees.
Answer:-
F = (1/5)*(9C+160)
Multiply both sides with 5, we get
5F = 5*1/5*(9C+160)
5F = 9C+160
5F-160 = 9C
5(F-32) = 9C
C = 5/9*(F-32)
If F = 212 degrees
Substitute F value in above equation, we get
C = 5/9*(212-32)
C = 5/9*180
C = 5*20
C = 100 degrees.

Topic:-Supplementary Angles

Two Angles are Supplementary if they add up to 180 degrees.

They don't have to be together to be supplementary, just so long as the total is 180 degrees.

This math help can help you with a question like

Question:-

What is supplementary angles ,explain with an example ?

Answer:-

two angles are supplementary ,if they add up to 180°
Example-1
Here in the following diagram you can see ιA and ιB are supplemtary angles ,because

ιA+ιB=140°+40°

  = 180°

180° means a straight angle.











So ,ιA and ιB are supplementary angles .

Example 2

Here these two angles also supplementary


ιA+ιB=120°+60°

 = 180°

problem on time and speed

Topic :- Time and Speed


Time problems and speed problems are there in both math and Physics .Here is a simple math problem which help you to understand to how to find time when speed value is given . This problem solved
by using distance formula ,So first we find the distance based on which we get the time .

Question:-
Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
Answer:-
Let the time taken by the second cyclist to catch up the first be 'x' hours.

Then the time taken by the first to reach than the point wil be (x+3) hours.

Speed of the second cyclist=10 miles/hour.

So the distance covered =speed*time
= 10 * x = 10x miles

Speed of the first cyclist = 6 miles/hour

So distance covered = 6(x+3)
=(6x+18) miles

Now distnce covered by both are same .

So

10x = 6x+18
-6x   -6x
------------------
4x  =  18

4x     18
---- = ----
4      4

   18     9        1
x= ---- = ---- = 4----
   4     2         2

So the time taken by the second
cyclist = 4 hours 30 minutes

I hope you liked it ,For math help ,you can reply me

Question on Circles, Finding unknown values of attributes of the circle

Circle is a geometrical figure with basic attributes diameter, radius, circumference, arc, chord etc. Below is a Geometry construction for the circle and to find unknown attributes value.

Topic : Circle and its attributes

Tangent is a straight line which just touches the circumference of the circle at a single point.

Question : Given VQ is tangent to the circle O at Q, QS is a diameter of the circle O, arc PQ = 115⁰, angle RPS = 36⁰

Find a) angle R ; b) angle S ; c) arc SR ; d) arc QR ; e) angle QPR ; f) angle QPS ; g) angle QTP











Solution :











Given : mPQ = 115⁰
‹RPS = 36⁰

a) ‹R
Since QS is the diameter,
So ‹QRS = 90⁰
(as angle in a semi circle is a right angle)

b) ‹S
As mPQ = 115⁰
So ‹PSQ = 1/2 * (115⁰) = 57.5⁰
(angle subtented by an arc at any point on the circle is half of the angle subtented by it at the center)

c) mSR
given ‹SPR = 36⁰
So mSR = 2(36) = 72⁰

d) mQR
now mQS = 180⁰
mQR = mQS - mSR
mQR = 180⁰ - 72⁰
mQR = 108⁰

e) ‹QPR
mQR = 108⁰
So ‹QPR = 1/2*(108) = 54⁰

f) ‹QPS
‹QPS = 90⁰(as QS is the diameter)

g) ‹QTP
mQP = 115⁰
so ‹QSP = 1/2 *(115⁰) = 57.5⁰
now in triangle PTS
‹QTP = 180⁰ - (‹TPS + ‹PST)
‹QTP = 180⁰ - (36⁰ + 57.5⁰)
‹QTP = 180⁰ - 93.5⁰
‹QTP = 86.5⁰

Well these are the bits of circle, to get more examples and get practiced, contact geometry help.

A Simple Word Problem on Finding an Integral of an Expression/Temperature vs Time problem

Here is a Multi choice word problem on Temperature and Time to Evaluate the temperature by Integration. Also converting the value into degrees. You can find similar set of questions at TutorVista Blogs.

Topic : Integration.

Calculation in the solution will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table
Time Temp
N -----63
1 ----- 65
2 ----- 66
3 ----- 68
4 ----- 70
5 ----- 69
6 ----- 68
7 ----- 68
8 ----- 65
9 ----- 64
10 ---- 62
11 ---- 58
M ----- 55

Then the average temperature for the 12-hour period is

a. 71
b. 76
c. 65
d. 66

Solution :
Choice c is correct.

We are looking for the average value of a continuous function (temp.) for which we know values at discrete times that are one unit apart.
We need to find
Average (f) = 1/(b-a)_a∫^bf(x)dx
Without having a formula for f(x)
The integral, however can be approximated by the Trapezoidal Rule, taking h=1

T = h/2(y₀ + 2y₁ + 2y₂ + ..... + 2y₁₁ + 2y₁₂)

= 1/2 (63 + 2*65 + 2*66 + ...... + 2*58 + 2*55)

= 782

average (f)approximately 1/(b-a)T = 1/12*782 = 65.17
Therefore, the average temperature =65 degrees

Choice a is incorrect because of the error in considering the interval between noon to midnight as 13 hours instead of 12 hours.

Choice b is incorrect because of the error in considering the interval between noon to midnight as 11 hours instead of 12 hours.

Choice d is incorrect because of error in calculating the trapezoidal approximation T as 792 instead of 782.

If you have any queries related to this problem or Integration, please do write to us and you will surely get help from calculus help

Question to Find Percentage of Discount on a Calculator Price

Topic : Sales and Price

Question : Peter bought a calcuator on sale for $40 the calculators retail price is $60 what is the percent discount?

Solution :
Discount in Price = 60 - 40 = $20
So discount percentage = discount price /Retail Price * 100
= 20/60 * 100
= 100/3
= 33.33%

Problem on Trigonometry Equation and Proof for the Identities

Topic : Trigonometry Identites

Simplify.

Problem on Trigonometric Equations

Topic : Trigonometric Equation

Problem : Solve 3Sin θ Cos θ – 2 Cos θ = 0 and 0 ≤ θ ≤ 2π

Solution :

3Sin θ Cos θ – 2 Cos θ = 0
Taking Cos θ as common
Cos θ (3Sin θ - 2) = 0
Cos θ = 0 or 3Sin θ – 2 = 0
3 Sin θ – 2 = 0
3Sin θ = 2
Sin θ = 2/3 (2/3 = 0.66 = 41.8º ~ 42º)
Sin θ = Sin 42º
θ = n π + (-1)ⁿ 42º
when n = 0 , θ = 42º
when n = 1 , θ = π - 42º = 138º

Let’s solve Cos θ = 0
Cos θ = Cos π/2
The formula for Cosine is :
If Cos x = Cos y
Then x = 2nπ ± y

So here it will be θ = 2nπ ± π/2
When n = 0, θ = 2(0)π ± π/2 = ± π/2
But only + π/2 lies in 0 ≤ θ ≤ 2π
So x = π/2

When n = 1, θ = 2(1)π ± π/2 = 2π ± π/2 = 2π ± π/2 = (4π ± π)/2 = 3π/2, 5π/2
But x = 3π/2

Now the further values of n will give angles greater than 360º

So θ will be 42º, 90º, 138º, 270º

Problem on Simple Linear Equation

Topic : Linear Equation

Problem : Solve y = 3y - 12

Solution :

A Simple Integration Problem

Topic : Integration

Problem : Integrate x /√(1 - x^4)

Solution :

Question to Find Interior angle of a Triangle

Topic : Interior angle of triangle

Question : Find the interior angle of the triangle if sum of all the angles is equal to 171º.

Answer :

Each interior angle = (n-2) *180º / n = 171º
180ºn - 360º = 171ºn
+360º = +360º
180ºn = -171ºn + 360º
-171ºn = -171ºn
---------------------
9ºn/9º = 360º/9º
n = 40º

Question on Similar Triangles

Topic : Similar Triangles

Question : Define and Mention the Properties of Similar Triangles

Solution :
Triangles are similar if they have the same shape, but can be different sizes.
Properties of Similar Triangles
1. Corresponding angles are the same
So in the figure above, the angle P=P', Q=Q', and R=R'.
2. Corresponding sides are all in the same proportion
Above, PQ is twice the length of P'Q'. Therefore, the other pairs of sides are also in that proportion. PR is twice P'R' and RQ is twice R'Q'.
Formally, in two similar triangles PQR and P'Q'R' :
PQ / P’Q’ = QR / Q’R’ = RP / R’P’

Question on Sales and Profit

Topic : Sales and Profit

Question : Jill is paid $991 per week, plus also receives 15% commission on sales made during the week. If Jill recives a $3965.35 paycheck this week, how much did Jill have in sales?

Solution :

Given per week = $991

commission on sales made = 15%

Given total amount received = $3965.35

Let x be the total sales

Therefore,

$991 + x times 15% = 3965.35

15% x = 3965.35-991 = 2974.35

x = (2974.35 x 100)/15 = 19829

The total number of sales = $19,829 (Answer)

Question to Find an Exponential Function

Topic : An Exponential Function

Question : Write as an exponential function



Solution :
x
y = 4(1.7)
ln y = ln 4 + x (ln(1.7))
= 1.3862 + x (0.5306)

So we have






Hope the Solution did the needful.

Question on Finding Unknown Value of a Variable

Topic : Reservoirs Word Problem

Question : During a drought, east reservoir which began the month 6 ft. below full, is dropping at a rate of 4 inches per day. west reservoir which began the month 4 feet below full is dropping at a rate of 6 inches per day. use a table or solve an equation to find when the reservoirs will be the same amounts below full.

Answer :
East reservoir = X - 72 -
West Reservoir = X - 48 -
when both are
X - 72 - 4T = X - 48 - 6T
2T = 24
T= 12 days,
So the aswer is 12 days(x can be any value)

Hope the above answer is useful for you.