48.Electrial restance the el.ectrial restance of a wire, R varies directly as its length. L,and inversely as its crosssectional area. A,If the resistance of a wire is 0.2 ohm when the length is 200 ft and its cross-sectional area is 0.05in^2. what is the resistance of a whose length is 5000 ft with a cross-sectional area of 0.01 in.^2?
R=kLA
where k is some real number. Now the question is how to find k? For this, we just substitute the known values into this equation:
0.2=k∙2000.05
k=0.2200∙0.05=0.00005
Now we can state, that our equation has the following form:
R=0.00005∙LA
Then, the resistance, when length is 5000 ft with a cross-sectional area of 0.01 in^2 is:
R=0.00005∙50000.01=25
Answer: 25 ohm
46.stopping a distance of a care the stopping,d,of of a car after the brakes are applied varies directly as the square of the spee,s, of the car traveling at traveling at speed of 40 mph can stop in 80 ft, what is the stopping distance of a car traveling at 65 mph?
This question is similar. We know, that D varies directly as S^2. Then we can write down the form of our equation:
D=k∙S2
for some real k.
According to the conditions, we know that the following expression is true:
80=k∙402
Hence,
k=80402=0.05
Then,
D=0.05∙S2
And for S=65
D=0.05∙652=211.25
Answer: 211.25 ft
