SOLUTION: Find an equation relating the variables for each situation described. (1) z varies directly as b, and z = 4 when b = 16 (2) s2 varies inversely as s1, and s2= -2 when s1 = 1/

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Question 59355: Find an equation relating the variables for each situation described.
(1) z varies directly as b, and z = 4 when b = 16
(2) s2 varies inversely as s1, and s2= -2 when s1 = 1/2
(3) y varies jointly as a and b, and y = -24 when a = 9 and b = -4
(4) m varies directly as n and inversely as p, and p = -3 and m = 1 and n = 1/2
(5) The cost of pipe is directly proportional to its length. If 6 feet of pipe costs $40, find he cost of 10 feet of pipe.
(6) The intensity of light is inversely prorportional to the square of its distance from its origin. An intensity of 100 lumens is registered at a distance of 5 feet. What is the intensity of light registered at a distance of 10 feet?
Answer by funmath(2933) About Me  (Show Source):
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Find an equation relating the variables for each situation described.
:
(1) z varies directly as b, and z = 4 when b = 16
"z varies direclty as b" -->> z=kb
z=4 and b=16 find k:
4=k(16)
4%2F16=16k%2F16
1%2F4=k
Substitute that into the first step:
highlight%28z=%281%2F4%29b%29
:
(2) s2 varies inversely as s1, and s2= -2 when s1 = 1/2
"s2 varies inversely as s1" -->> s2=k/s1
s2=-2 and s1=1/2 find k:
-2=k%2F%281%2F2%29
%281%2F2%29%28-2%29=%281%2F2%29k%2F%281%2F2%29
-1=k
Substitute that into the first step:
highlight%28s2=-1%2Fs1%29
:
(3) y varies jointly as a and b, and y = -24 when a = 9 and b = -4
"y varies jointly as a and b" -->> y=kab
y=-24, a=9, and b=-4, find k
-24=k(9)(-4)
-24=-36k
-24/-36=-36k/-36
2/3=k
Substitute that into the first step:
highlight%28y=%282%2F3%29ab%29
:
(4) m varies directly as n and inversely as p, and p = -3 and m = 1 and n = 1/2
"m varies directly as n and inversely as p" -->> m=kn/p
p=-3, m=1, and n=1/2 find k
1=k%281%2F2%29%2F-3
-3%281%29=-3k%281%2F2%29%2F-3
-3=k%2F2
2%28-3%29=2k%2F2
-6=k
Substitute that into step 1:
highlight%28m=-6n%2Fp%29
:
(5) The cost of pipe is directly proportional to its length. If 6 feet of pipe costs $40, find the cost of 10 feet of pipe.
Let cost be:C and Length be:L
"cost is directly proportional to length" -->> C=kL
C=40, L=6, find k:
40=k(6)
40/6=6k/6
6.667=k
Substitute that into the first step: C=%286.667%29L
Let L=10
C=(6.667)(10)
C=$66.67
:
(6) The intensity of light is inversely prorportional to the square of its distance from its origin. An intensity of 100 lumens is registered at a distance of 5 feet. What is the intensity of light registered at a distance of 10 feet?
Let intensity be:I and distance be:d
"intensity of light in inversely proportional to the square of its distance" -->> I=k%2Fd%5E2
I=100, d=5, find k
100=k%2F%285%5E2%29
100=k%2F25
25%28100%29=25k%2F25
2500=k
Substitute that into step 1:
I=2500%2Fd%5E2
If d=10
I=2500%2F%2810%5E2%29
I=2500%2F100
I=25 lumens
Happy Calculating!!!