13. Case Study - 1 In the picture given below, one can see given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq. m. (a) Based on the information given above, form a quadratic equation in terms of x. (b) Find the width of the sidewalk around the pool. ​

The quadratic equation in terms of x is 4x²-38x+48 = 0 and the width of the sidewalk is 1.5 m.

Given,

The outer edges of the swimming pool are 7m and 12 m.

The width of the sidewalk is x m.

The area of the pool = 36 sq. m

To Find,

The quadratic equation in terms of x, and the width of the sidewalk.

Solution,

Since the width of the sidewalk is x m.

So the dimensions of the pool will be (7-2x) and (12-2x).

Now,

Area of the pool = 36 sq. m

(7-2x)(12-2x) = 36

84-14x-24x+4x² = 36

4x²-38x+48 = 0

4(x-8)(x-3/2) = 0

x = 8, 1.5

The value of x can't be 8 as it will make the dimensions of the pool negative

So, the value of x is 1.5 m.

Hence, the quadratic equation in terms of x is 4x²-38x+48 = 0 and the width of the sidewalk is 1.5 m.

Answer:

The quadratic equation in 'x' is  [tex]2x^2 - 19x +24 = 0[/tex]

Width of the sidewalk = 1.5m

Explanation:

Given,

Area of the pool = 36sq.m.

width of the sidewalk = 'x'm

Length of the pool including the sidewalk = 7m

Breadth of the pool including the sidewalk = 12m

Required to find,

1. Quadratic equation in terms of 'x'
2. Width of the sidewalk

Formula to be used

Area of the rectangle = length x breadth

Length of the pool = 7 -2x

Breadth of the pool = 12 -2x

Area of the pool = (7-2x)(12-2x)

(7-2x)(12-2x) = 36

[tex]84 - 24x - 14x + 4x^2 = 36\\[/tex]

[tex]4x^2 - 38x +48 = 0\\[/tex]

[tex]2x^2 - 19x +24 = 0[/tex]

Hence,

The quadratic equation in 'x' is  [tex]2x^2 - 19x +24 = 0[/tex]

To find 'x'

To solve the quadratic equation by splitting the middle term, we need to find two numbers such that their sum = -19 and product = 48

Two such numbers are = -16 and -3

[tex]2x^2 - 16x - 3x +24 = 0[/tex]

2x (x-8) - 3(x-8) = 0

(2x-3)(x-8) = 0

2x -3 = 0 or x = 8

x = [tex]\frac{3}{2}[/tex] = 1.5 or x = 8

x = 8, is not possible because the length of the pool including the sidewalk is 7m.

So x = 1.5m

Hence,

Width of the sidewalk = 1.5m

Answer:

ssorry i m failed

Step-by-step explanation:

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The value of x would be 24

Correct Question

For what value of x, is the median class of the following frequency distribution be 30-40?

Class Frequency

0-10 3

10-20 5

20-30 11

30-40 10

40-50 X

50-60 3

60-70 2

Given

• class distribution of an observation

To find

• the value of x so that the median class would be 30 - 40

Solution

we are provided with class interval type of distribution and are asked to find the value of x so that the median class of the given observation shall be on 30 - 40

let us make a cumulative frequency distribution of the given data,

Class Frequency cum. freq

0-10 3. 3

10-20 5 8

20-30 11 19

30-40 10 29

40-50 X. 29+ X

50-60 3 32 + X

60-70 2. 34 + X

now for the median class to be 30 - 40,

(34 + X)/2 = 29 ( making an assumption that the

cumulative frequency would exactly be that of the class )

or, 34+ X = 58

or, X = 24

The value of x would be 24

Answer:

Hope this helps you

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Step-by-step explanation:

Use the formula of mode

and simplify and you will get

42.78 as mode

Answer:

Class Frequency

10-20 15

20-30 10

30-40 12

40-50 17

50-60 4

Modal Class= 40-50

Mode= 40+(17-12/2×17-12-4)×10

Mode= 40+(5/18)×10

Mode= 40+(5/9)×5

Mode= 40+25/9

Mode= 40+2.77

Mode= 42.77

Answer:

true

Explanation:

PSU means public sector undertaking. It means that institutions which have 51% share of government and 49% share of private sector.

During PSU all required stakeholders get on boarded and actively participate in project planning and contribute to project's success. Select between true and false.

As we have already studied that the share of government in PSU is 51% and the share of private sector in PSU is 49%. While making any decision in a PSU all required stakeholders get on boarded and actively participate in the planning and contribute to project's success because any plan can make huge profits or huge losses and change ultimately the share of the investors.

#SPJ2