a word problem on finding the area

Topic:- Finding Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a rectangle. Area is an important invariant in the differential geometry of surfaces

Question: -

The width of a swimming pool is 10 meters and
length is 30 meters. Then find the area of the
pool.

Solution:-

This geometry help ,will give you the solution of above question.

width of thepool = 10 meters

length of the pool = 30 m

Area of the pool = Area of the rectangle ( as the pool is in the shape of a rectangle) Length

x breadth = 10 x 30

= 300 square meters

So the area of the pool is 300 square meters


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Find the mid point between 2 points

Topic :- Midpoint of 2 points

The midpoint between two points whose coordinates are known will be found. We will also develop a general formula for determining the coordinates of the midpoint and go through an example.
This math help explains ,how to find the midpoint.

Question:

Find the mid-point between

(2,2)and (6,4)

Answer:-

midpoint formula
to points is

  x1+x2          y1+y2
x= -------- , y = -------
    2              2

So ,Let's say.

 ( 2 , 2)   ( 6 , 4 )
   x1  y1     x2  y2


Then the mid point is

       2+6        2+4
   x= ----- , y= ------
        2          2

        8      6
     = ---  , ----
        2       2

     =  4 , 3

So the mid point is (4,3)

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Determine the Attributes of parabola

An Equation of Parabola helps us to find attributes of parabola, after simplification of any given equation we can calculate vertex, focus, directrix etc of the parabola. Here is one such example.

Topic : Parabola

Parabola is a Geometrical figure with standard form x ² = -4ay

Question : Find the vertex, focus, diretrix, and axis of symmetry of the parabola y²+3x-2y-11=0
Solution :

y²+3x-2y-11=0

subtract 3x and add 11 on both the sides

y²+3x-2y-11=0

- 30 + 11 = - 30 + 11
-----------------------------
y²-2y = - 3x + 11

by completing the square method

y²-2y + 1 = - 3x + 11 + 1

(y - 1)² = - 3x + 12

(y - 1)² = - 3(x - 4)

Now x - 4 = 0 so x = 4

and y - 1 = 0 so y = 1

So vertex is (4,1)

Standard form is given by

(y - k)² = 4p(x - h)

so here 4p = -3

p = - 3/4

Focus = (4 + (-3/4), 1) = (4 - 3/4 , 1) = (13/4, 1)

Directix x = 4 - (-3/4)

x = 4 + 3/4

x = 19/4

Axis of symmetry is

x = 4


Solving number of problems like this will help you to solve even difficult problems quickly, for more assistance contact calculus help or geometry help.

A Simple Problem on Finding Integral of a Function

Integral of a Function is very easy to evaluate the value of function. Here is such Integration problem with multi choice answers.

Topic : Integral of a Function

TutorVista helps you to get more multi choice questions and answers and practice the problems.

Problem : The function y(x) satisfying

Choice b is incorrect because of not adding the constant of anti-differentiation to the integral.

Choice c is incorrect because of committing the mistake to write the anti-derivative of 1 / (1 + y²) as cot^-1 y.

Choice d is incorrect because of failing to find the integral correctly.

Hope the Integration of given Function is followed and if you have any more queries write to our calculus help and get your problems rectified.

Question to Find Maximum Distance in the Elliptical Orbit

Topic : Ellipse

Question : Halley's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :

2a = 1,636,484,848miles
so SC = 54,004,000miles
maximum distance from comet to the sun will be DS.
That is when comet comes at D
there is a maximum distance from sun
So SD = CD - SC ; CD = major axis = 1,636,484,848 miles
= 1,636,484,848 - 54004000
= 1582480848miles
So maximum distance is 1582480848miles.

Word Problem to Find Combinations of Tickets

Topic : Word problem

Question : The owner of a movie theater was counting money from1 days sales. he knew that the total of 150 tickets were sold. adult tickets cost 7.50 annd children tickets coast 4.7.5 each if the total recipt for the day were 891.25 how many of each kind of ticket was sold?

Solution :
Number of adult's ticket sold be 'x'
number of children ticket sold be 'y'

the total tickets are 150
So the first equation becomes x+y = 150 ------ (1)

cost of one adult's ticket be 7.50
cost of a child ticket be 4.75

total amount after selling all the tickets makes another equation
7.50x + 4.75y = 891.25 -------- (2)
________________
(x+y = 150) X 7.50
7.50x + 7.50y = 1125
7.50x + 4.75y = 891.25
- _____ -______-______
2.75y = 233.75
divide by 2.75
y = 233.75/2.75
y = 85
x + y = 150
x = 150 - y = 150 - 85 = 65

Problem to Find Unknown Angle of a Triangle

Topic : Angle of a Triangle