Simple conversion

[wakejosh]

If i could get anyone to double check my answers on the following it would be a big help. thanks

On planet Z, the standard unit of length is the foose. Ann the
Astronaut is 5.90 feet tall on
earth. She lands on planet Z and is measure to be 88 foosi
(plural of foose) tall. Her crew
member Rachael is 94 foosi tall. How tall is Rachael in Earth
measurements?

i get 6.3 feet

5.9/88 = 14.92

94/14.92 = 6.3

is this correct? thanks in advance

 

[wakejosh]

Note the expression: y = A/x2. Which statement is most consistent
with this expression?

a. y is less than x
b. if x is halved, y is multiplied by 4
c. y is greater than x
d. if x is doubled, y is multiplied by a factor of 2
e. y is equal to x


I find that A seems to be true,, but the wording on D confuses me a bit.

 

[drpizza]

OOOOPS, give me a moment... I'm rusty with LaTeX

It's always a good idea to write your units down when you're doing calculations. The technique I teach is "multiply by 1"... that is, if the numerator = the denominator, the value of the fraction is one.
$$\frac{3 feet}{36 inches}=1$$ because the numerator equals the denominator.

Now, all you have to do is worry about the units you don't want cancelling out each step of the way.

You could use $$\frac{88 foosi}{6.90feet}$$ as a multiplier, or you could use $$\frac{6.90feet}{88 foosi}$$ as a multiplier (to multiply by 1.

Now, you're starting with $$\frac{94 foosi}{1}$$ If you multiply it like this: $$\frac{94 foosi}{1}*\frac{88 foosi}{6.90 feet}$$, then your units work out to foosi squared per foot. Not what you want.

So, you multiply $$\frac{94 foosi}{1}*\frac{6.90 feet}{88 foosi}$$ And, your units work out to feet.

for what it's worth, "5.9/88" is not "= 14.92". You meant 88/5.9

 

[geoffjb]

On planet Z, the standard unit of length is the foose. Ann the
Astronaut is 5.90 feet tall on
earth. She lands on planet Z and is measure to be 88 foosi
(plural of foose) tall. Her crew
member Rachael is 94 foosi tall. How tall is Rachael in Earth
measurements?

i get 6.3 feet

5.9/88 = 14.92

94/14.92 = 6.3

is this correct? thanks in advance

$$\frac{5.90 feet}{88 foosi} = \frac{x feet}{94 foosi}$$

$$88 foosi\,x = (5.9 feet)(94 foosi)$$

$$x = \frac{(5.9 feet)(94 foosi)}{88 foosi}$$

 

[drpizza]

:) Or you could do it as a proportion as Geoff did... The proportion method is easier for this type of a conversion; my method above works very well if you're converting something like miles per hour to meters per second.

 

[wakejosh]

where did you get 6.9? is that a typo? did you mean 5.9?

anyway, I run the numbers geoff did and I get 6.3 again..so I assum my answer is correct. thanks for the help

 

[geoffjb]

where did you get 6.9? is that a typo? did you mean 5.9?

anyway, I run the numbers geoff did and I get 6.3 again..so I assum my answer is correct. thanks for the help

Yes, your answer's correct.

 

[drpizza]

yes, 6.9 was a typo... or rather, a memory problem. :)

 

[wakejosh]

great thanks.. one other quick question: can I just multiply 3.47 m/s/s by 5 seconds to get my speed after that amount of time? for example:

. A European sports car dealer claims that his car will accelerate
at a constant rate from rest
to a speed of 100 km/hr (28 m/s) in 8.00 s. What is the speed
after the first 5.00 s of
acceleration?

a.44.4 m/s b. 34.7 m/s c. 28.7 m/s d. 17.4 m/s e. 8.7
m/s


First I find the acceleration to be 3.47 m/s^2 now can i just times by 5? If so i get 17.4 m/s Is this correct?