Yoram Isaac Sianz Mathematics Tuitor

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For online WhatsApp coaching in mathematics grade 8 to 12. WhatsApp me on 0975844153

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Factories 4x²-9y²

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Tuitions/ extra lessons for:
- Grade 10 - 12 mathematics
- Grade 8 and 9 math, int. scie and ICT
Location: Botswana road, Mwandi Junction area
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Good evening friends.

Today we will discuss about VOLUME OF A FRUSTUM OF A CONE.

A frustum is the base part of a cone that is formed by cutting the top part of the cone with a plane which is parallel to the base.
To find the volume of a the frustum, you need to calculate the volume of the imaginary full cone before cutting and the volume of the imaginary small cone which was cut off such that when you subtract the volume of the imaginary bigger cone from the imaginary smaller cone you obtain the volume of the frustum. A worked out example will be posted shortly.

Given the geometric progression 20, 5, 1¼,.....
a) find the common ratio
b) n th term
c) the 6 th term
d) the sum of the first 8 terms

Solution
a) common ratio= Term 2/Term 1
C.r= T2/T1
C.r=5/20
C.r=¼
b) n th term implies replacing all variables in the formula Tn=ar^(n-1) except for n, where a is the first term and r is the common ratio.

Tn=20(¼)^(n-1)

c) Tn= ar^(n-1)
T6= 20(¼)^(6-1)
T6= 20(¼)^5
T6= 20(1/1024)
T6= 20/1024
T6= 5/256

d) Sn= a(1-r^n)/1-r
S8=20[1-(¼)^8]/1-¼
S8=20/¾
S8=26⅔

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COORDINATE GEOMETRY GRADE 11
For every slanting line on a Cartesian plane, you get its length by using its two end points coordinates, then you find the square root of the coordinates change in X raised to the power 2 plus the coordinates change in Y raised to the power 2
( AB= √(X2-X1) + (Y2-Y1) )

GRADE 11 COORDINATE GEOMETRY ( Continuity)

We can now derive the equation of a straight line as the square root of change in X raised to power 2 plus change in Y raised to power 2. Thus given a straight line AB it's length is given as follows;

AB=√(X2-X1)²+(Y2-Y1)²
In the example below, the distance between P(-3,3) and R(9, -2) can be solved using the general formula as

AB=√(X2-X1)²+(Y2-Y1)²
PR=√(-3-9)²+(3-(-2))²
PR=√(-12)²+(5)²
PR=√144 + 25
PR=√169
PR= 13