A word problem on Radius of Earth

In geometry help, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

More generally — in geometry, science, engineering, and many other contexts — the radius of something (e.g., a cylinder, a polygon, a mechanical part, a hole, or a galaxy) usually refers to the distance from its center or axis of symmetry to a point in the periphery: usually the point farthest from the center or axis (the outermost or maximum radius), or, sometimes, the closest point (the short or minimum radius). If the object does not have an obvious center, the term may refer to its circumradius, the volume finding radius increasing rate of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter (which is usually defined as the maximum distance between any two points of the figure).

The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.

Question

An airplane reaches an altitude of 3 miles above the earth .Assuming a clear day and that a passenger has binoculars , how far can that passenger see ?(Hint : The radius of the earth is approximately 4000 miles)


Answer

Cosθ = OB/OA = 4000/4003 = 0.999 = cos(2.56)

So θ = 2.56˚

∟BOC = 2θ = 5.12˚= 0.0893 radians

Now arc BC = 4000 . ∟BOC

= 4000 . 0.0893 = 357.2 miles


The passenger can see a circular region of diameter 357.2 miles

word problem on one variable equations

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use. The concepts of constants and variables are fundamental to all modern mathematics, science, engineering, and computer programming.Varying, in the context of mathematical variables, does not mean change, but rather, dependence on the values of other variables in the expression in which the variable occurs, or dependence of the value of the expression on that of the variable. However, in some languages other than English, one distinguishes between "variables" in functions and "unknown quantities" in equations ,same way we also can go for linear equations in two variables
Question:-

You are serving 3 different entrees at a party.If 100 are having beef ,175 are having pasta,and 45% are having chicken then how many guests are expected at the party?

Answer:-

let's look at answers to algebra equations with variable terms on both sides

Let the total number of guests be 'x'

add all the given data

x = 100+175+(45% of x)

x = 100+175+(45x/100)

x - (45x/100) = 100+175

55x/100 = 275

by using cross product ,we get

x=500

So total 500 members are expected in the party

we can solve more word problems from free exam papers

simple probability problem on colors

Probability, or chance, is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later.

Here is a simple probability problems from 4th grade math algebra word problems with solution


Example :-

We have find the following probabilities of
different colors in this picture.

P(red)=1/3

p(green)=4/9

p(white)=0

p(green or yellow)=2/3

p(not yellow)=7/9

p(blue)=0

a probability of an event A is represented by a real number in the range from 0 to 1 and written as P(A), p(A) or Pr(A)^[6]. An impossible event has a probability formula of 0, and a certain event has a probability of 1. However, the converses are not always true: probability 0 events are not always impossible, nor probability 1 events certain. The rather subtle distinction between "certain" and "probability 1" is treated at greater length in the article on "almost surely

Algebric Problem on Numbers

Topic:Number Problem

In mathematics, an algebraic number is a complex number that is a root of a non-zero polynomial in one variable with rational (or equivalently, integer) coefficients. Numbers such as π that are not algebraic are said to be transcendental, and are infinitely more numerous within the complex number field.
Let's see algebra calculator online variables on following definition and problem
The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. or numeric and algebraic operations

Question:

Solve the problem given below:

9 + (9 - 8 + 3)⁴

Answer:


For similar problems on this free math answers will guide you

How to solve a probability problem

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In simple terms it refers to a chance. In mathematics we can see the concept has a given exact meaning in probability theory, that is used extensively in such areas of study as mathematics, science, statistic, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

Here is a simple example for you:

Question:

Assume that your friend, Omar, had two job interviews, and now estimates he has
a 40% chance of getting the first job, and also a 40% chance of getting each job.
What are his chances of getting at least one job offer?
What are his chances of getting neither job?
What are his chances of getting offered both jobs?

Answer:

Chances of getting each job = 40% = .4

So chances of not getting the jobs = 1- .4 = 6


Now chances of getting at least one job includes the

chances of getting any one job and chances of getting both.


Chances of getting any one job = 2x(.4x .6) = .48

Chances of getting both = .4x .4x = .16

So required probability = .48 + .16 = .64 or 64%

Now chances of getting neither job = 1 -chances of getting at least one job

                              = 1 - .64 = .36 or 36%

Chances of getting both jobs offered = .4 * .4 = .16 or 16%

a word problem on Sets and relations

Topic:-Sets and Relations

A set is a group or collection of objects or numbers, considered as an entity unto itself. Sets are usually symbolized by uppercase, italicized, boldface letters such as A, B, S, or Z.
Each object or number in a set is called a member or element of the set.

Examples include the set of all computers in the world, the set of all apples on a tree, and the set of all irrational numbers between 0 and 1.

Let's see a word problem on this.

Question:-

In an elementary school, students know atleast one of the languages, French and Spanish. 125 students know French, 75 students know Spanish and 50 of them know both French and Spanish. How many students are there in the school?

Answer:-

Let:

n(F) = number of students who know French

n(S) = number of students who know Spanish

Here

n(F) = 125, n(S) = 78, n(F n S) = 50

We have to find n(F u S)

We know that n(F u S) = n(F) + n(S) - n(F n S)
= 125 + 75 - 50
= 150 (Answer)

For more help on this ,you can reply me.

How to find slope of two points

Topic:- Slope
Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between two points on the line. It is also always the same thing as how many rises in one run.

To find slope of two points when there is two points given ,we have to use the slope formula .


Question :-

Find the slope of (2,4) (3,7)

Answer:-

This math help is to find the slope

Let us assume that,

( 2 , 4 ) ( 3 , 7 )
x1   y1   x2  y2


The formula for slope is

 y2-y1
----------
 x2-x1

 7- 4
-------
 3- 2

  3
-----
  1

= 3 is the slope

For more help on this ,Please reply me.

Basic algebra problem

Topic:- Introduction to algebra

This Algebra help is a branch of mathematics concerning the study of structure, relation, and quantity.
Here we are giving a simple algebra problem as part of introduction to algebra

Question:-

x+78.07+44.49=204.37

Find the value of 'x'?

Answer:-

 Given
       x +78.07+44.49=204.37
          -----------
            add
  
       78.07
      +44.49
     ----------
      122.56

  
    so x+122.56=204.37

    subtract 122.56 on both sides

      x+122.56= 204.37
       -122.56=-122.56
     ---------------------
           x  = 81.81


So the answer is 81.81

For more help in algebra ,Please reply me

A Word problem on Surd with Algebraic Expression

Surd with an algebraic expression can be simplified as shown in the example below.Finding cube root and square root are basic of surd.

Topic : Solving a surd

In the problem shown below explains how to find square root of any algebraic expressions. For more problems on surd please see indice math.

Question : Suppose that N= √x + 4 models the number of cases of an infection, inmillions, of a disease x years from now.
(a) Approximately how many cases of the infection will there be 16years from now?
(b) In approximately how many years will there be 6 million cases?

(a) Solution :

Given x = 16.
So, number of cases of infection will be found as:
N = √x + 4
= √16 + 4
= 4 + 4
= 8

So, There will be approximately 8 cases of the infection 16 years from
now.

(b) Solution :

Given N = 6
So, number of cases of infection will be found as:
N = √x + 4
=> 6 = √x + 4
=> 6 – 4 = √x
=> 2 = √x
=> √x = 2

Squaring both sides we get
x = 2²
=> x = 4

So,In 4 years, there will be 6 million cases.

For more assistance please drop your comments and math help will get back to you with required answers.

Question on Differentiation using First Principle

Here is a problem on Differentiation using First Principle and resultant applying limits.


Topic : First Principle of Differentiation


A simple problem on first principle of differentiation.


Question: Differentiate by first principle.

-12x² -11x - 1 and given function [f(x+h)- f(h)]/h

Solution :





















Above Differentiation using first principle will be an best and simple example to solve similar kind of problems, if you have any queries do write to calculus help.

Question on Percentage Word Problem

Topic : Percentage

Question : Jonah had 84 baseball cards. He threw 25% of them away. How many did he throw away?

Solution :
Johan threw 25% of 84 balls
25/100 x 84= 1/4 x 84=21 balls

Question on Calculating Mid Point and Distance between the mid points in a Geometrical Figure

Topic : Mid Point and Distance Between Mid Points

Let M and N be the mid points of TR and TV

We use mid point formula to find coordinates of M and N ,

From figure x1 = 1, y1 = -4 and x2 = 9 , y2 = 8

Substitute in mid point formula,

M = (1+9/2, -4+8/2) = (5,2)

Similarly coordinates of N = (9+13/2 , 8+2/2) = (11,5)

Now we use distance formula to find MN

M = (5,2) and N =(11, 5)

x1 = 5 and y1 = 2

x2 = 11 and y2 = 5

substituting the values in distance formula we get

MN = √(11 - 5)² + (5 - 2)²

= √4² + 3²

= √45

= 3√5

Problem to To Convert the Given Polar CoOrdinates to Rectangular CoOrdinates

Topic : Convertion of polar coordinates to rectangular coordinates

Question : Convert the given polar co ordinates to rectangular co ordinates.

Solution :

Simple Problem on Solving a Linear Equation

Topic : Linear Equation
Problem : Solve for x, x + 1 = 3
Answer :
x + 1 = 3
x = 3 -1
x = 2
So Value of x = 2
For verification you can substitute value of x in linear equation given.
Since 2 + 1 = 3 the value obtained is correct.

Verifying Continuity of a function r(t)

Topic : Limits and Continuity

Question : Determine whether r(t) is continuous at 0. Explain your reasoning.

r(t) = e^t(i) + j + Cosec t (k)

Solution :

r(t) is continuous at 0, if each of its components are continuous at 0 then,

Problem on Factorization

Topic : Factorization

Problem : Factorise -2w^4 +1250

Solution :
-2w^4 +1250
taking -2 as common
-2(w^4 -625)
-2[(w^2)^2 - (25)^2]
Applying the formula
a^2-b^2 = (a+b)(a-b)
we get -2[(w^2+25)(w^2-25)]
-2[(w^2+25)(w^2-5^2)]
Again applying the formula
for (w^2-5^2)
we get
-2[(w^2+25)(w+5)(w-5)]

Question on Equilibrium using Trignometric Expressions

Topic : Equilibrium of Suspended Strings

Question : A particle A, of weight W, is suspended by two strings AB and AC. AB is inclined at 30degrees to the vertical and AC at angle P to the vertical. The tension in AB and AC are 40N and 60N respectively. Calculate the value of W and P.

Solution :

Since the system is in equilibrium,
60 Sin P = 40 Sin 30º ------- (1)
and 60 Cos P + 40 Cos 30º = W-----(2)

From (1) we get,
60 Sin P = 40 *(1/2)

60 Sin P/60 = 20/60
Sin P = 1/3

P = Sinˉ¹(1/3)

P= 19.469º


From (2) we get,
W = 60 Cos P + 40 Cos 30º

= 60 Cos (19.469º) + 40 Cos 30º

= 60 . 0.943 + 40 . 0.866

= 56.58 + 34.64

= 91.22N

So P = 19.469º

W = 91.22N

Problem on Finding Geometrical Figure's unknown Quantity

Topic : Geometrical Figure





Question : Find the area of triangle ABC where
angle ABC = 35 degrees
angle BCA = 110 degrees
angle CAB = 35 degrees
AND, length BC = 4 cm



ANSWER:





















Description Step1 : b = AC = BC because triangle ABC is isosceles
Triangle ABC are isosceles because angle ABC=angle BAC=35 degree



Description Step2 : sin 70 degrees = h/4
0.9369=h/4
h = 0.9369*4 = 3.759



Step3: Area = 0.5*b*h = 0.5*(4)(3.759) = 7.518 cm2

Definition of Expanded Form of any Numbers

Topic : Expanded Form

Question : Definition for Expanded Form, Explained with an Example.

Answer :

Expanded form is a way to write a number that shows the sum of values of each digit of a number.

Expanded form is a way of writing numbers so that all that is hidden

about them comes out into the open.

The simplest way to write numbers in expanded form is to write them

sort of in English.

For 4,017, this becomes 4 thousands and 0 hundreds and 1 ten and 7

ones. This can be made to look like math by changing the words to math

symbols.The expanded form for 4,017, then, is:

4 x 1000 + 0 x 100 + 1 x 10 + 7 x 1

The expanded form shows what each digit is worth (for example, the 4

is worth 4 x 1000, which is the same as 4 thousands, which equals

4000).

Here is another example.

12,345 becomes 1 ten thousand and 2 thousands and 3 hundreds and 4 tens

and 5 ones. Changing the words to math symbols, 12,345 in expanded form

is:

1 x 10,000 + 2 x 1,000 + 3 x 100 + 4 x 10 + 5 x 1

Standard form is the reverse of expanded form. You begin with expanded

form and change it to the way we normally write numbers.

For example, 3 x 1,000 + 5 x 100 + 7 x 10 + 4 x 1 can be changed to

3 thousands and 5 hundreds and 7 tens and 4 ones. This becomes:

3000 + 500 + 70 + 4

Question to Find Span of Given Vectors

Topic : Matrix

Questions : Find the span of the given vectors.
There are three column matrices givenfirst matrix is
1
0
-1
second matrix is
-1
1
0
third matrix is
0
-1
1
find the span of the given vectors (1) algebraically and (2)geometrically

Answer :

1) the 3 vectors (1.0.-1), (-1,1,0) (0 -.1,1) are linearly dependent.. You will find the determinant of matrix=0
2) Further you will find that any 2 among these 3 will span the third
To show the above equate any one of the above say
(1,0,-1) = a( -1,1,0) + b( 0,-1.1) you get a= b= -1 and the system to be consistent.
Another method is write the matrix , perform row operations and find the rank to be 2
Now to what is the subspace generated in R^3 take any pair
x( 1,0,-1) + y( -1,1,0) = (x-y, y, -x)
this means such of those points in R^3 which meet the condition x+y+z=0
will be the subspace
but this equation represents a plane.
So algebraic siginificance is subspace and geometric significance is plane

Word Problem on Quantity of a Substance

Topic : Word Problem on Quantity of a Substance

Question : A soda production line fills bottles with "a" liters of product. A bottle is placed under a nozzle and a valve is opened which dispenses the soda under a pressure. The soda is dispensed as the valve opens and accelerates at a constant rate "r" from 0 liters per second to "b" liters per second in "c" seconds. After "c" seconds, the soda is dispensed at the constant rate of "b" liters per second. When the valve closes, the soda flow decelerates.
from "b" liters per second to 0 liters per second at the constant rate "-r" in "c" seconds.
Find the time "T" it takes to fill a bottle of "a" liters with b.

Answer :

During the the first c seconds the rate of filling forms an arithmetic progression.
r,2r, 3r,……b. b is also a multiple of r and as the rate is reached after c seconds
b=cr or r =b/c ………(i)

Also the quantity filled in litres during this period is the sum to c terms of the AP.
Quantity filled in first c seconds =c/2{2r + (c-1)r}, which when simplified
= c(c+1)r/2

Same way we can take the amount filled in the last c seconds when the filling rate
Decelerates as c(c +1)r/2.

Total amount filled in the first c and the last c seconds that is
2c seconds = c(c+1)r. Substituting r = b/c from (i) we get
Amount filled in 2c seconds = b(c+1)


Now to find the amount filled during the constant speed we subtract this from a.

a – b(c+1) = a-bc-b litres.

This is filled at a constant speed b litres per second so the time taken
= (a-bc-b)/b = a/b –c -1 seconds.

When the 2c seconds (first c + last c) to this time
Total time taken to fill = a/b –c -1 + 2c = a/b + c – 1 seconds.