C. Solve for the indicated variable in each of the following.
1. If y varies inversely as x and y = 3 when x = 4, find y when x = 6.
2. If r varies inversely as s and r= 100 when s = 27, find the value of r when s = 45.
3. If p varies inversely as the square of q and p = 3 when q = 4, find p when q = 16.
4. If y varies inversely as x and y = -2 when x = -8, find x when y = 2.
5. If w varies inversely as y and w = 2 when y = 3, find w when y = 6.
Answers
Given : y varies inversely as x and y = 3 when x = 4,
To Find : y when x = 6.
Solution:
y varies inversely as x
=> y ∝ 1/x
=> xy = K ( K is constant)
y = 3 when x = 4,
=> 4(3) = K
=> K = 12
=> xy = 12
x = 6
=> 6y = 12
=> y = 2
r varies inversely as s
=> rs = k
=> 100(27) = 2700 = k
s = 45.
=> 45r = 2700
=> r = 60
p varies inversely as the square of q
=> pq² = k
=> 3(4)² = p(16)²
=> p = 3/16
y varies inversely as x
=> xy = k
=> (-8)(-2) = x(2)
=> x = 8
w varies inversely as y
=> wy = k
=> 2(3) = w(6)
=> w = 1
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Answer:
1.M=2
2.Y=50/7
3.A = 16
4.W= 2
5.Y= 10/13
Step-by-step explanation: