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If x varies directly as y and inversely as z and x = a, y = b and z = c. If y = b2 and z = c2, the value of x is
- a)ab / c
- b)ac / b
- c)bc / a
- d)b2 / a
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If x varies directly as y and inversely as z and x = a, y = b and z = ...
x = ky / z or a = kb / c ;
=> k = ac / b;
Now, x = ky / z or x = kb 2 /c 2
Substituting the value of k,
we get; x = ab/c.
Substituting the value of k,
we get; x = ab/c.
Most Upvoted Answer
If x varies directly as y and inversely as z and x = a, y = b and z = ...
x = ky / z or a = kb / c ;
=> k = ac / b;
Now, x = ky / z or x = kb 2 /c 2
Substituting the value of k,
we get; x = ab/c.
Substituting the value of k,
we get; x = ab/c.
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Community Answer
If x varies directly as y and inversely as z and x = a, y = b and z = ...
Given information:
- x varies directly as y: This means that if y increases, x also increases, and if y decreases, x also decreases.
- x varies inversely as z: This means that if z increases, x decreases, and if z decreases, x increases.
- x = a, y = b, z = c: These are the initial values of x, y, and z.
To find the value of x when y = b^2 and z = c^2, we can use the concepts of direct and inverse variation.
Direct Variation:
Let's assume the direct variation constant as k. This means that x is directly proportional to y, so we can write it as:
x = ky
From the given information, we know that x = a and y = b. Plugging these values into the equation, we get:
a = kb
Solving for k, we find:
k = a/b
Inverse Variation:
Let's assume the inverse variation constant as m. This means that x is inversely proportional to z, so we can write it as:
x = m/z
From the given information, we know that x = a and z = c. Plugging these values into the equation, we get:
a = m/c
Solving for m, we find:
m = ac
Finding the value of x:
Now that we have found the values of k and m, we can find the value of x when y = b^2 and z = c^2.
Plugging y = b^2 and z = c^2 into the equations for direct and inverse variation, we get:
x = k(b^2) = (a/b)(b^2) = ab/b = a
x = m/c^2 = (ac)/c^2 = a
Since both equations simplify to x = a, we can conclude that the value of x when y = b^2 and z = c^2 is a.
Therefore, the correct answer is option A: ab/c.
- x varies directly as y: This means that if y increases, x also increases, and if y decreases, x also decreases.
- x varies inversely as z: This means that if z increases, x decreases, and if z decreases, x increases.
- x = a, y = b, z = c: These are the initial values of x, y, and z.
To find the value of x when y = b^2 and z = c^2, we can use the concepts of direct and inverse variation.
Direct Variation:
Let's assume the direct variation constant as k. This means that x is directly proportional to y, so we can write it as:
x = ky
From the given information, we know that x = a and y = b. Plugging these values into the equation, we get:
a = kb
Solving for k, we find:
k = a/b
Inverse Variation:
Let's assume the inverse variation constant as m. This means that x is inversely proportional to z, so we can write it as:
x = m/z
From the given information, we know that x = a and z = c. Plugging these values into the equation, we get:
a = m/c
Solving for m, we find:
m = ac
Finding the value of x:
Now that we have found the values of k and m, we can find the value of x when y = b^2 and z = c^2.
Plugging y = b^2 and z = c^2 into the equations for direct and inverse variation, we get:
x = k(b^2) = (a/b)(b^2) = ab/b = a
x = m/c^2 = (ac)/c^2 = a
Since both equations simplify to x = a, we can conclude that the value of x when y = b^2 and z = c^2 is a.
Therefore, the correct answer is option A: ab/c.
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