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S varies directly as R varies and T varies inversely as R varies. At a time R = 20, S = 40 and T = 10. If R is changed to 10, then the value of T will be:
- a)20
- b)10
- c)40
- d)80
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
S varies directly as R varies and T varies inversely as R varies.At a ...
►S α R; so, S= k1R----(i) and
►Tα1/R; so,T = k2 /R----(ii).
Also given R = 20, S = 40 and T = 10.
►Tα1/R; so,T = k2 /R----(ii).
Also given R = 20, S = 40 and T = 10.
►Solving the two equations we get k1 = 2 and k2 = 200.
►Now when R changes to 10, putting values of R & k2 in (ii) we get T = 20.
Hence option A.
Hence option A.
Most Upvoted Answer
S varies directly as R varies and T varies inversely as R varies.At a ...
Given:
S varies directly as R varies
T varies inversely as R varies
Direct Variation:
In direct variation, two variables are directly proportional to each other. This means that as one variable increases, the other variable also increases, and as one variable decreases, the other variable also decreases.
Inverse Variation:
In inverse variation, two variables are inversely proportional to each other. This means that as one variable increases, the other variable decreases, and vice versa.
Let's solve the problem step by step:
Step 1: Find the constant of variation for S and R
Since S varies directly as R, we can write the equation as:
S = k*R
where k is the constant of variation.
To find the value of k, we can use the given values when R = 20 and S = 40:
40 = k*20
k = 2
So, the equation for S in terms of R is:
S = 2R
Step 2: Find the constant of variation for T and R
Since T varies inversely as R, we can write the equation as:
T = k/R
To find the value of k, we can use the given values when R = 20 and T = 10:
10 = k/20
k = 200
So, the equation for T in terms of R is:
T = 200/R
Step 3: Find the value of T when R is changed to 10
Using the equation T = 200/R, substitute R = 10:
T = 200/10
T = 20
Therefore, when R is changed to 10, the value of T will be 20.
Hence, the correct answer is option A) 20.
S varies directly as R varies
T varies inversely as R varies
Direct Variation:
In direct variation, two variables are directly proportional to each other. This means that as one variable increases, the other variable also increases, and as one variable decreases, the other variable also decreases.
Inverse Variation:
In inverse variation, two variables are inversely proportional to each other. This means that as one variable increases, the other variable decreases, and vice versa.
Let's solve the problem step by step:
Step 1: Find the constant of variation for S and R
Since S varies directly as R, we can write the equation as:
S = k*R
where k is the constant of variation.
To find the value of k, we can use the given values when R = 20 and S = 40:
40 = k*20
k = 2
So, the equation for S in terms of R is:
S = 2R
Step 2: Find the constant of variation for T and R
Since T varies inversely as R, we can write the equation as:
T = k/R
To find the value of k, we can use the given values when R = 20 and T = 10:
10 = k/20
k = 200
So, the equation for T in terms of R is:
T = 200/R
Step 3: Find the value of T when R is changed to 10
Using the equation T = 200/R, substitute R = 10:
T = 200/10
T = 20
Therefore, when R is changed to 10, the value of T will be 20.
Hence, the correct answer is option A) 20.
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S varies directly as R varies and T varies inversely as R varies.At a time R = 20, S = 40 and T = 10.If R is changed to 10, then the value of T will be:a)20b)10c)40d)80Correct answer is option 'A'. Can you explain this answer?
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