S is directly proportional to M^3. It is given that S=36 for a certain value of M. Find the value of S when this value of M is
(a) doubled
(b) reduced by 40%
S=k*M^3
so if M is doubled, S must go up by 8 (2^3)
so if M is changed to .4, S must be down by .6^3=.216
answers:
a) 36*8
b) 36*.216
To find the value of S when the value of M is doubled, we first need to understand the concept of direct proportionality. In a direct proportion, as one quantity increases, the other quantity also increases by a certain factor.
In this case, we are told that S is directly proportional to M^3, which means that as M increases, S will increase by a factor of M^3.
Let's denote the initial value of M as M1 and the corresponding value of S as S1. We are given that S1 = 36 for M1.
(a) Doubling the value of M means that the new value of M, denoted as M2, will be 2 times M1. Now, we can use the concept of direct proportionality to find the value of S2.
Since S is directly proportional to M^3, we can write the equation:
S1/M1^3 = S2/M2^3
Substituting the given values, we get:
36/M1^3 = S2/(2M1)^3
Simplifying further, we get:
36/M1^3 = S2/8M1^3
Cross-multiplying, we have:
36 * 8M1^3 = S2 * M1^3
288M1^3 = S2 * M1^3
Canceling out M1^3 on both sides, we have:
288 = S2
Therefore, when the value of M is doubled, the value of S becomes 288.
(b) When the value of M is reduced by 40%, the new value of M, denoted as M3, will be (100% - 40%) = 60% of M1.
Now, we can use the same concept of direct proportionality to find the value of S3.
Using the equation:
S1/M1^3 = S3/M3^3
Substituting the given values, we get:
36/M1^3 = S3/(0.6M1)^3
Simplifying further, we get:
36/M1^3 = S3/(0.216M1^3)
Cross-multiplying, we have:
36 * 0.216M1^3 = S3 * M1^3
7.776M1^3 = S3 * M1^3
Canceling out M1^3 on both sides, we have:
7.776 = S3
Therefore, when the value of M is reduced by 40%, the value of S becomes approximately 7.776.