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Therefore the point P is at 3.46 cm from O and it lies on the angle bisector of ∠XOY
<h3>What is an Angle Bisector ?</h3>The ray that bisects the angle into half is called Angle Bisector.
It is given that ∠XOY = 60 degree
the length of OX = 4.5 cm
OY =5 cm
The point M is on OX such that
OM = 2 MX
so The M is at 3 cm from O
The point P lies in the acute angle such that the distance between point P and OX and OY is always same and at 3 cm from M
According to the angle bisector theorem converse states that if a point is in the interior of an angle and is at equal distance from the sides then it lies on the bisector of that angle.
As it can be seen from the image that a point equidistant from the rays , at 3 cm from M will be at
By Pythagoras Theorem
3² +3² = OP²
OP = 2 = 3.46 cm from O
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The sum of the first 8 terms is 2.51 to the nearest hundredth
Step-by-step explanation:
In the geometric sequence there is a constant ratio between each two consecutive terms
The formula of the sum of n terms of a geometric sequence is:
, where
- a is the first term
- r is the constant ratio between the consecutive terms
∵ The sequence is 6 , -5 , 25/6 , .............
∵ -5 ÷ 6 =
∵ ÷ -5 =
- There is a constant ratio between the consecutive terms
∴ The sequence is a geometric sequence
∵ The first term is 6
∴ a = 6
∵ The constant ratio is
∴ r =
∵ We need to find the sum of 8 terms
∴ n = 8
- Substitute the values of a, r and n in the rule above
∴
∴
- Round it to the nearest hundredth
∴
The sum of the first 8 terms is 2.51 to the nearest hundredth
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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