Tuesday, August 18

arithmetic reasoning help problems

Arithmetic reasoning help is for students who are preparing for test or competitive exams.We will have 4 options for each question ,in which we have to choose one correct answer.Let's see one of these kind of examples.

Question:-

A doctor can treat 4 cancer patients per hour; however stroke patients need 3 times as much of the doc's time. If the doctor treats patients 6 hours a day and has already treated 10 cancer patients and 3 stroke patients today, how many more stroke patients can the doctor treat?

A.1 B.2 C.3 D. 5

Answer:-

Let's see what is an expert online tutor explain us.

5,5' is the average of 5' and 6': (5 + 6)/2 = 5,5

One would expect that the height of the average is the average of the heights:Height converter will help us with this.

(110 + 170)/2 = 140



HEIGHT WEIGHT
5' 110
6' 170

?

I could just multiply 5x60 to find the LBS of a 5' person, why is this given? I tell you, that's "military math"...

Anyway, let's talk about that doctor:

"4 cancer patients per hour" => one quarter of an hour per cancer patient.

"3 times as much" for stroke patients => three quarters of an hour per stroke patient.

"has already treated 10 cancer patients and 3 stroke patients today" => has already consumed 10 quarters plus 3x3=9 quarters of his time. Makes 19 quarters altogether.

"the doctor treats patients 6 hours a day" => the doctors has 6x4=24 quarters of an hour at his disposal per day.

But he already spent 19 quarters => he has 24-19=5 quarters of an hour still available today.

How many stroke patients fit in 5 quarters of an hour? You already know from above that each stroke patient consumes 3 quarters.

So the answer is "c".

Wednesday, August 12

How to find the equation of a line which is passing through two points

Question:-

Find the equation of line passing through the points(-1,7)and (0,15)

Answer:-
Step 1:-

finding the slope of line = m

                      y2-y1     15-7         8
Formula to find slope ------- = ------- = ------ = 8
                      x2-x1     0-(-1)      0+1

so ,slope of a line is 8

step 2:-

The point slope form of equation (y-y1)=m(x-x1)

We know that (x1,y1) is (-1,7)

and m=8

So (y-7)=m-(x-(-1))

(y-7)=8(x+1)

y-7=8x+8
+7   +7
---------
y=8x+15

step 3:-

The equation of the line becomes

             y=8x+15

For more help on this,you can reply me.

Tuesday, July 21

How to find intersection point of two lines

Topic:-Intersection Point

a point where lines intersect

point - a geometric element that has position but no extension; "a point is defined by its coordinates"

Let's see how to find this intersection point of two lines

Question:-

Find the intersection point of two lines

3x+2y=5 and x+4y=0


Answer:-


Let's say


3x+2y=5 ---------> 1

x+4y=0 ---------->2


Take the equation 2

x+4y=0

x= -4y----->3

Substitute this in equation 1

We get

3(-4y)+2y=5

-12y+2y=5

-10y=5

y= 5/-10

y= - ½

Substitute this in 3

x= -4(-½)

x= 2

So ,The intersection point is

(2,-½)


For more help on this ,you can reply me.

Monday, July 13

a problem on inequality

Topic:-Inequality
What is inequality is defined along with a example in this math help
An inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (See also: equality). Inequality rules are
  • The notation a < b means that a is less than b.
  • The notation a > b means that a is greater than b.
  • The notation ab means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.
In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".
Question:-

Solve the following inequality

y-7 > -12


Answer:-
 y-7 > -12

add 7 on both sides

y-7+7 > -12+7

 y > -5

So y є (-5,∞) is the Answer  
For more help on this ,Please reply me.

Thursday, June 25

problem on Angular speed

Topic :- Angular speed of EarthThe Earth turns toward the east, we see the sky
turning toward the west at this same rate.Then how to find angular speed for it.Let's look at it.

Question:
"Find the angular speed of the Earth's rotation on it's axis",
Answer:-
The earth rotate once about it's axis in 24 hours

That is 2π radians in 24 hours.

Therefore angular speed =


      2π
    ------  rad/hour
      24

    Lets see how to convert in seconds


       2π
  =  ----------
      24*60*60

  = 7.272*10-5rad/sec

So the angular speed of earth is7.272*10-5rad/sec
.
For similar kind of help ,you can reply me.

Wednesday, May 20

A Problem on Volume of a Cube/Geometrical Figure Cube

All the geometrical construction and geometrical figures like cube, cuboid, prism etc come under construction math and construction geometry where you will get more information about these geometrical figures and there attributes.

Topic : Volume of a cube

A Cube is a Geometrical Figure with dimension of equal sides, here is one such example on Cube, to Find length of the side of cube, given volume of cube using indice laws.

Question : The volume of a cube is given by V = s3, where s is the length of a side. Find the length of a side of a cube if the volume is 700 in3.Round the answer to three decimal places.

Solution :

Given V = 700 in3

Also, volume of a cube is given by

V = s3

=> 700 = s3

=> s3 = 700

=> s = cuberoot(700)

=> s = 8.697

Length of a side of cube = 8.697 inches.

Monday, May 4

Word problem on Function and gas concentration as its dependencies

Functions are denoted as shown in the figure where there will be dependencies of one variable value to another.

Topic : Functions and variables values.

Variables, co-efficient are the terms found in functions.

Problem : The table lists future concentrations of a certain green house gas in parts per billion (ppb), If current trends continue.

a) Let x = 0 correspond to 2010 and x = 20 correspond to 2030. Find C and a so that f(x) = Cax models the data.

b) Estimate the gas concentration in 2021.

Year ------ Gas(ppb)
2010 ------ 0.74 (when x = 0)
2015 ------ 0.86
2020 ------ 0.99
2025 ------ 1.15
2030 ------ 1.34 (when x = 20)

Solution :

a) We have function ,
f(x) = Cax

x = 0 ; f(0) = Ca0 = C*1 = C

So f(0) = 0.74 ; C = 0.74

and x = 20 ; f(x) = C a20 = 0.74 a20

f(20) = 1.34 (from the table)

So 1.34 = 0.74 a20 ; a20 = 1.34/0.74 = 1.8108

So a = 1.0301


b) To find gas concentration at the year 2021, we have to find f(21)

f(21) = Ca21 = 0.74 (1.0301)21

= 0.74 * 1.8641

= 1.37943

So f(21) approximately 1.38

Therefore gas concentration at 2021 will be 1.38

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If you have any queries related to this problem please do write to us and our algebra help will be happy respond.

Thursday, April 9

Question on Integrating Factor Method for Solving Differential Equation

Topic : Integrating Factor

Question : Explain Integrating Factor Method for Solving Differential Equation

Solution :
Suppose we have this equation to solve:
dy + y = x

dx
In this case we cannot separate the variables and introducing a new variable doesn't help either. So we need to use an entirely different method, known as Integrating Factor Method.
Here's the typical equation for which we can use this method:

dy + yP(x) = Q(x)
dx

Here the functions P(x) and Q(x) can be any functions of x, in the example above they were 1 and x respectively.
Step One: calculate the integral of the function P(x).
Step Two: the integrating factor, which we'll call IF, is defined as the exponential of this, i.e. it's defined by :

Integrating Factor = IF = e^(∫P(x) dx)
Step Three: the solution to the equation is given by:
y(x) = 1/IF ∫Q(x) IF dx
Now let us understand this using an example-
dy + y = x
dx

So P(x)=1 and Q(x)=x. The integrating factor is therefore ex, since the integral of 1 is x. (No need for a constant of integration, that's because if you do put one in it will cancel out later on anyway)
So, we can write down the solution y(x) of the equation using the "mysterious" formula given in Step Three:

y(x) = 1/IF ∫Q(x) IF dx
In this case that's:
y(x) = 1/e^x ∫xe^x dx
We can do that integral using integration by part. The result is:
y(x) = e^(-x) (xe^x - e^x + c)
which implies to
y(x) = x - 1 + ce^(-x)

Friday, April 3

Problem to Solve Simultaneous Equations by Substitution Method

Topic : Substitution Method

Problem : Solve using Substitution Method.
y - 2x = - 6
2y - x = 5

Solution :


Monday, March 30

Question to Find Factors of a Function

Topic : Functions

Question : Given f(x) = 2x³ - 5x² + 12x - 5 Find all zeros, if
p : ± 1, ± 5
q : ± 1, ± 2
p/q = ± 1/2 , ± 5/2

Solution :

Tuesday, March 24

Question on Linear Equation

Topic : Linear Equation

Question : Sue wants to buy a new printer that costs $189. She has $125 saved. She has a job that pays $8 an hour. How many hours must she work to earn enough to buy the printer?

Solution :
The cost of the printer is $189.
She has saved $125.
Also, she is paid $8 an hour to do a job.
We need to find the number of hours she works to buy the printer.
Let us assume “x” to be the number of hours she works to buy the printer.
8x + 125 =189
Now, subtract 125 on either side of the equation.
8x + 125 – 125 = 189 – 125
8x = 64
Divide by 8 on either side of the equation.
8x/8 = 64/8
x = 8
Therefore, the number of hours she works to buy the printer is 8.

Thursday, March 19

Solved variable Saparable form of Differential Equation

Topic : Variable Saparable Form

Question : Solve dy/dx = (x-1)/(y+2)

Solution :
dy/dx = (x-1)/(y+2)
(y+2) dy = (x-1) dx
∫(y+2) dy = ∫(x-1) dx
y²/2 + 2y = x²/2 - x + c1 (c1 is the constant)

Monday, March 16

Problem on Simple Differentiation

Topic : Simple Differentiation
Problem : Solve y = x² + 4e^x
Solution :
y = x² + 4e^x
dy/dx = d(x²)/dx + 4d(e^x)/dx
dy/dx = 2x + 4e^x

Wednesday, March 11

Word Problem on Sine Rule

Topic : Sine Rule

Question :
Lookout station B is located 7 miles due east of station A. The bearing of a fire from A is S 8degree50’ W and the bearing from B is S 28degree20’ W. Determine the distance from the fire to B(to the nearest tenth of a mile)

Solution :


Figure is as shown in the figure according the question



From Sine Rule

a / Sin A = b / Sin B = c / Sin C

a = c Sin A / Sin C
a = 7 * Sin (90º + 8º 50’) / Sin (90º - 28º 20’)
a = 7 * Sin (98º 50’) / Sin (19º 30’)

a = 20.72miles

Monday, March 9

Question on Ratio/Proportionality

Topic : Ratio /Proportionality

Question : Are the ratios 25g: 30g and 40Kg: 48Kg in proportion?

Solution :
25g: 30 g = 25/30 = 5:6
40Kg: 48Kg = 40/48 = 5:6
So 25: 30 = 40:48
Therefore, the ratios are in proportion
25:30: : 40:48.

Wednesday, March 4

Question on Linear Equation

Topic : Linear Equation

Question : 9 added to thrice a whole number gives 45. Find the number.

Solution :
Step 1. Let the required number be X.
Step 2 Thrice the whole number is 3X
Step 3 Nine added to 3X is 3X + 9
Step 4 3X + 9 = 45
Step 5 3X = 45 -- 9
Step 6 3X = 36
Step 7 X = 36/3
Step 8 X = 12
The required number is 12

Wednesday, February 25

Question on Finding Resultant and Direction of a Moving Article

Topic : Trigonometry

Question : Airplane is moving with speed 400knot due East and wind 50knot due North East . Find the resultant and direction .

Solution :

400 ->E
50 ->NE
Angle between East and North direction is 45º
Hence angle between 400 and 50 is 45º



We have a formula for the resultant of two forces (velocities) P and Q

R² = P² + Q² +2PQCosθ, θ being the angle between P and Q

P = 400; Q = 50; θ = 45

R² = 400² + 50² + 2(400)(50)Cos45
= 160000 + 2500 + 40000 * 0.7071
= 190784

So resultant R = √(190784) = 436.788 = 436.8

To find the direction :

The angle Φ is in between R and P

Q Sin θ
So tan Φ = --------------------
P + Q Cos θ

50 Sin 45
tan Φ = ------------------------- = 0.0812 => Φ = tanˉ ¹ 0.0812 => 4.65
400 + 50 Cos 45

Here Φ is the angle between R and P
and Φ = 4.65 , if resultant motion is away due East.

That is same as
90 – 4.65 due North
So 85.35 ≈ 85.4 due North

Hence Solution is 436.8 due 85.4º North

Hope the Answer and Explanation will be helpful for you.

Thursday, February 5

Question to Find Area of Triangle

Topic : Area of Triangle
Question: In any ∆ ABC a²Sin2B+b²Sin2C =
A) Area of the triangle

B) Twice the Area of the triangle
C) Thrice the Area of the triangle
D) Four times of the Area of the triangle

Solution :
In the data any triangle is mentioned.
Therefore let us take equilateral triangle having side 1 unit.
That is a=b=c=1, A=B=C=60º.
Area of the equilateral triangle is = [(√3)/4]a²=[(√3)/4]x1=(√3)/4.
value of the expression given =1²xSin120+1²xsin120=[(√3)/2]+[(√3)/2]= √3------(1)

Option A): Area of the Triangle=(√3)/4, but value of expression = √3 These two are not equal. Hence Option A is not correct
Option B): Twice the Area of the triangle=2x[(√3)/4]=(√3)/2, but the value of expression is √3. Hence option B is incorrect
Option C):Thrice the Area of the triangle = 3x[(√3)/4], but the value of the expression is √3. hence option C also incorrect.
Option D): Four times of the Area of the triangle=4x[(√3)/4]= √3, this is also equal to the value of the expression shown in ---(1).

Hence Option D is the correct choice of the above question.


Hope the Answer and Explanation will be helpful for you.