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".

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

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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)


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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 a ≠ b 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  

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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
.

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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.

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) = Ca^x 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) = Ca^x

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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