OK these two problems are driving me crazy and they are my last ones.?

Question

I have spent 2 hours on these please help.

Hat sizes are determined by measuring the circumference of one's head in either inches ore centimeters. Use ratio and proportion to complete the following table.

Hat size Head Circumference Head Circumference

(to nearest 1/5 inch) (to nearest centimeter)

7 1/2 23 3/5 60

7 3/8 Answer:? Answer?

I am confused please tell me what I need to do in order to solve the problem.

The last one is I need help on is:

The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 50 mph can stop in 140f, how many feet will it take the same car to stop when it is travelling 80 mph?

It will take ___ ft?

simplify your answer. Type an integer or a fraction.

Answer 1

1.

To find the correct ratio, divide the new hat size by the original hat size.  Since the hat size is decreasing, then so will the circumferential measurements:

Ratio of hat sizes: New/Old = (7 3/8)/(7 ½) = 59/60.

The circumference of the hat in inches in centimeters will be in the same ratio as the two hat sizes.

New circumference in inches:

(118/5)∙(59/60) = (59/5)∙(59/30) = (59)²/150 = 3481/150 ≈ 23.2066 ≈ 23 1/5.

Notice the circumference in inches went down because the hat size did.

Use the same ratio for the centimeters:

New circumference in centimeters:

(60)∙(59/60) = 59

So here are your answers:

Hat Size: 7 3/8

Head Circumference (Inches): 23 1/5

Head Circumference (Centimeters): 59

2.

This is  a relationship involving squared quantities, not linear quantities, which the other answerers don't seem to have picked up on.  We can find the new stopping distance, D', by simply performing this ratio calculation:

S'²/S² = D'/D

(S'²/S²)(D) = D', where S' is the new speed, S is the original speed, D' is the new stopping distance, and D is the original stopping distance.

Now we plug in our values into the equation above:

(80)²/(50)² = D/140

(6400/2500)(140) = D

358.4 ft.

As a check against this, there is another way of solving this problem.

Since this is a direct variation problem, then we can find what is called a constant of variation, or constant of proportionality which relates the precise increase, or decrease, between the units which are being related as they change.  We can write the relationship between the stopping distance and the square of the speed like this:

D = kS², where D is the stopping distance, k is the constant of variation, and S is the speed of the car.  

We are given that D = 140 when S = 50.  So we plug those into the equation above to find k:

D = kS²

D/S² = k

140/(50)² = k

140/2500 = k

14/250 = k

What the figure above translates into is that the car requires 14 ft to stop for every 250 (m/h)² that the car is traveling.  So every increment of 250 (m/h)² causes an increase of 14 ft in the stopping distance.  Likewise, every decrement of that velocity squared reduces the stopping distance by 14 ft.

Now that we know k, we can plug that into the equation for distance to find D when S = 80 mph:

D = (14/250)(80)²

D = (14/250)(6400)

D = (14/25)(640)

D = 358.4 ft.

Notice that the same stopping distance results no matter what method we use.  So our analysis seems to be correct.  To the closest integer, it will take 358 ft. for the car to stop.

Answer 2

Hat Size    in inches      in cm

7 1/2            23 3/5         60

7 3/8            23 1/5         59

if the car traveling 50 mph can stop in 140 ft,

then the same car traveling 80 mph can stop in 224 ft

Answer 3

I didn't calculate it but here's the way to do it.

For the first answer: Since the question says to use ratio and proportion, you have to figure out the proportions for the first set of measurements, and then you can figure out the unknowns in the second set. You already have the hat size (7 3/8), so you can use that as your starting point.

Find out the proportion of 7 1/2 to 23 3/5 (aka 7 1/2 divided by 23 3/5). After you figure that out, use that number and multiply it by the hat size for which you're trying to find the other measurements (7 3/8).  Then you can do the same for the second part. The proportion of 23 3/5 to 60 (aka 23 3/5 divided by 60) and multiply that number by the second number that you just figured out.

For the second question, you have 50 mph and 140 feet. It'll look something like this: 50 mph of vehicle= 140 feet to stop. Then you have 80 mph and unknown, which would look like 80 mph of vehicle= x feet to stop. To find out what x is, you have to figure out how many feet it takes to stop per mph. You do this by dividing 140 by 50. After you get that answer, you can multiply that number by the 80 mph, and you'll get what x is.

hope you understand. gl