help me it's so difficult !!?

Question

1. The current in a circuit is inversely proportional to the resistance. The current is 20 amperes when the resistance is 5 ohms. What will the current be if the resistance is 16 ohms?

2. A truck leaves Cincinnati traveling east at 35 mph. One hour later, a car leaves Cincinnati also traveling east at 40mph. How far from Cincinnati will the car catch up with the truck?

3. A chemical supply company has a 30% sulfuric acid solution and a 70% sulfuric acid solution. How many liters of each should be used to obtain 100 liters of a 40% solution?

Answer 1

1)

let current = I
let resistance = R

given:
I = k * (1/R)
I = 20 Amps, R = 5 Ohms
I = ? Amps, R = 16 Ohms

Use the 1st set of I & R (given) to find the value of k (constant of proportionality)
I = k * (1/R)
k = I / (1/R)
k = IR
k = (20 Amps)(5 Ohms)
k = 100 Amps*Ohms

Use R = 16 Ohms & newly found k = 100 Amps*Ohms to find I = ? Amps.
I = k * (1/R)
I = (100 Amps*Ohms) (1 / 16Ohms)
I = (100/16) Amps
I = (25/4) Amps
I = 6.25 Amps
I = 6 Amps (1 significant figure)

Therefore I = 6 Amps.

-----

2)

let x = distance from Cincinnati where the car catches up with the truck

When the car starts travelling, the truck has already travelled 35 miles (in the 1 hour headstart).

In the same amount of time:
the truck has to travel (x - 35) miles, while
the car has to travel x miles.

v = d/t ==> t = d/v

for the truck:
t = (x-35)miles / 35mph

for the car:
t = (x)miles / 40mph

Equate the truck & car's times.
(x-35)miles / 35mph = (x)miles / 40mph

Looks a little messy, so we'll do the math without the units.

(x-35) / 35 = (x) / 40
(x-35) * 40 = (x) * 35
40x - 35*40 = 35x
40x - 35x = 35*40
5x = 1400
x = 280 miles
x = 2.8 * 10^2 miles (2 significant figures)

Therefore the car will catch up with the truck 2.8 * 10^2 miles east of Cincinnati.

-----

3)

let C = # litres of 30% solution needed
let G = # litres of 70% solution needed

C + G = 100 L
C = 100L - G

Percent solutions are defined as # grams /100mL.
So a:
40% solution would have 40 grams /100mL, or 400 grams/1L, or 40000 g/100L.
30% solution would have 30 grams /100mL, or 300 g/ 1L.
70% solution would have 70 grams/ 100mL, or 700g/1L.

Lets equate the # grams per 100 litres.
40000 g = (300g/1L)*C + (700g/1L)*G

But C = 100L - G

40000 g = (300g/1L)*(100L-G) + (700g/1L)*G

Looks a little messy, so we'll do the math without the units.

40000 = (300/1)*(100-G) + (700/1)*G
40000 = (300)*(100-G) + (700)*G
40000 = 30000 - 300G + 700G
10000 = 400G
G = 10000/400
G = 25L (2 significant figures)

C = 100L - G
C = 100L - 25L
C = 75L (2 significant figures)

Therefore you would use 75L of the 30% solution, and 25L of the 70% solution, to obtain 100L of a 40% solution.

-----

Answer 2

q2 - 280 miles east (as long as they take the same route)

40-35 = a 5 mph faster travelling speed

35/5 = 7

After 7 hours the car will be (40*7) 280 miles away

The truck was on the road for an hour longer so its (35*8)=280 miles east of Cincinnati

Answer 3

1. I2 = I1x R1/R2 = 20 x 5/16 = 6.25 A

2. The distance travelled by both should be the same.
s1 = s2
v1 t1 = v2 t2
35 t1 = 40 (t1-1)
5 t1 = 40
t1 = 8
s1 = v1 t1 = 35 x 8 = 280 miles

3. Let the two supply solution's amount be x and y, respectively (in litres)

x + y = 100
x = 100 - y ...(1)

0.3x + 0.7y = 0.4(x+y) = 40...(2)

substitute (1) into (2)
0.3(100-y) + 0.7y = 40
30 - 0.3y + 0.7y = 40
0.4y = 10
y = 25
x = 75

Answer 4

If the current is inversly proportional, then it will be 5/16 'th of the value it had at 5 ohms.

7 hours (it's not math, it's horsesense)

If you work this one out yourself, you might have a fighting chance of passing you next exam. If not, you're doomed.


Doug

Answer 5

the variation is inverse
therefore the product is constant
20*5=x*16
x=100/16amps

2.the relative velocity is 5 mph
(difference as the direction is the same)
distance=35 miles
time=distance/speed=35/5=7 hrs

3. 0.3x+0.7y=(x+y)*0.4
i.e. 3x+7y=4x+4y
=>-x+3y=0
x+y=100
adding 4y=100 y=25 and so x=75
so he has to mix
75 ml of 30% and 25 ml of 70%

Answer 6

we'd want to make certain the circumstances and circumstances triumphing to grin or to make others to grin. smiling in maximum confusing circumstances are not from now on straightforward and likewise in an ungainly concern making others smile too confusing. besides to minimize the failings, we may be able to objective on both.

Answer 7

(3)25L of the 70% sol'n and 75L of the 30% sol'n.

0.30(100-x)+0.70x=0.40(100)
30-0.30x+0.70x=40
0.40x=10
x=25
100-x=75

check:

0.30*75+0.70*25=40
22.5+17.5=40
40=40 :)

Answer 8

Do you have to show your work or not.

Answer 9

Do your own homework!!

Answer 10

ur 1st answer is 6.25A