"Question 3 Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90° 60° … … … (i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion? (ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. (iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
Class 8 Direct and Inverse Proportions Page 213"
Answers
Direct variation:
If two quantities increase or decrease together in such a manner that the ratio of their corresponding values remain constant, we say that the two quantities vary directly.
In other words x and y are said to vary directly if X/y = k , where k is a positive constant.
In direct Proportion
x/y= k
x=ky
So we can find value of k from known values, and then use the formula to calculate the unknown values
Inverse variation:
Two quantities x and y are said to vary inversely or indirectly if an increase in x causes a decrease in y and a decrease in X causes an increase in y in such a way that xy remains constant.
In other words x and y are said to vary indirectly if x y = k, where K is a positive constant.
In inverse Proportion
xy= k
x=k/y
So we can find value of k from known values, and then use the formula to calculate the unknown values
When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x∝ 1/y
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Solution is in the attachment
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Hope this will help you....
hope the both may help you for sure
Step-by-step explanation:
No. of spokes =n
Total angle in the wheel =360
Angle between each spoke =
n
360
Angle between each spoke (n=8)=
8
360
=45
Angle between each spoke (n=10)=
10
360
=36
Angle between each spoke (n=8)=
12
360
=30
Yes, they are inversely proportional.
4=>90
∘
6=>60
∘
8=>45
∘
10=>36
∘
12=>30
∘
