Briefly Explain How to Find Sum of Geometric Progression

Topic : Geometric Progression

Question : Explanation to Find How to Find Sum of terms in Geometric Progression

Solution :

Question to Prove Rectangle Inscribed the Circle Properties

Topic : Rectangle Inscribed the Circle

Question : If RTCE is a rectangle, then show that RC is the diameter of the circle.









Solution :
Since ∟RTC = 90º
So measure of arc REC = 180
mREC = 180º
This shows that the arc REC is half of the circle as the total measure of circle is 180º X 2 = 360º

That means arc REC forms a semi circle
Hence RC passes through the center of the circle or we can say that RC is the diameter of the circle.
Hence proved.

Question to Draw Box Plot for a Collection of Data

Topic : Box Plot

Question : In a survey of the cafeteria food at Metropiolis Middle School, 50 students were asked to rate how well they liked the lunches on a scale of 1 to 10, with 1 being the lowest rating and 10 being the highest rating. The box plot was made from the collected data.
What percent of the students in the sample rated the cafeteria food between 5.75 and 9

Solution :








First Quartile = Q1 = 5.75
That is 25% of students lie between 3 and 5.75
Second Quartile = Q2 = 6.5
That is 50% of students lie between 3 and 6.5
Third Quartile = Q3 = 8
That is 75% of the students lie between 3 and 8
100% of students lie between 3 and 9
So the % of students who lie between 5.75 and 9 = 100% - 25% = 75%
and Answer is 75%

Question on Finding the area of a Field

Topic : Area of Rectangle

Question : A farmer wants to use 1000 meters of fencing to enclose 3 sides of a rectangular field. What dimensions should be used to maximize the area of the field, and what is the maximum area of the field?

Solution :

Equation of Circle Passing Through Point (-1,-9)

Topic : Equation of Circle

Question : Write the Standard from of the equation of the circle that passes through the given point (-1,-9) and whose center is the origin.

Solution :
The Standard equation of the circle with center at origin (0,0) is x² + y² = r²
r being its radius as x² + y² = r² passes through (-1,-9) we have
(-1)² + (-9)² = r²
or
r² = 1 + 81 = 82
So the required circle is x² + y² = 82

Problem on Simultaneous Equation

Topic : Simultaneous Equation

Question : Solve and find the value of x and z
x + z = 22
x +6z = 50

Solution :
x + z = 22---------------(1)
x +6z = 50--------------(2)

Subtracting second equation from first equation
we get, -5z = -28
divide both sides by -5
So z = 5.6

Substitute the value of z in equation (1)
x+5.6 = 22
x=22-5.6
x= 16.4

So the value of x = 16.4 and z = 5.6

Problem on Square Roots

Topic : Square Roots

Question : Solve:
(x – 2)^2 = 4

Solution :
Taking square roots on both the sides, we get
(x – 2) = ± rad(4)
Case (i)
x – 2 = 2
Add 2 on both the sides of the equation
x – 2 + 2 = 2 + 2
x = 4
Case (ii)
x – 2 = -2
Add 2 on both the sides of the equation
x – 2 + 2 = -2 + 2
x = 0
The solutions are x = 0, 4