Question

plz help me, i'll medal and fan

Answer 1

Distances in space are measured in light-years. The distance from Earth to a star is 4.1 x 10^13 kilometers. What is the distance, in light-years, from Earth to the star (1 light-year = 9.46 x 10^12 kilometers)?

Answer 2

@BrAnDoN_AAS @Lyrae @Krissy3039 plz hellppp

Answer 3

and this plzzzz

Answer 4

@princeharryyy plzzzzzzz

Answer 5

@mtori_12

Answer 6

Have you seen cancellation like this before in fractions?
\[\frac{2}{7} \times \frac{7}{3} = \frac{2}{3}\]
Because the 7 is common in both the numerator (top) and denominator (bottom) of the resulting product, the 7s cancel out and you're left with 2/3 in the final product. The same can be done with units (in your problem, kilometers and light years).

Rewrite the problem such that the unit you want at the end (in this case, light years) ends up on top (the numerator).
\[4.1\times 10^{13} \ \text{kilometers} \times \frac{1 \ \text{light year}}{9.46 \times 10^{12}\ \text{kilometers}}\]
Notice how, like the example above, the kilometers unit cancels out and we're left with light years, which is what the problem asks for.

Answer 7

i still dont get it

Answer 8

In your second problem, you have to remember these exponent rules.
\[x^{-n} = \left( \frac{1}{x} \right)^n\]
^ When raised to a negative exponent, you can flip the inside (in this case, x) and make the exponent positive.
\[\left( a^b \right)^c = a^{b \times c} = a^{bc}\]
^ When a number raised to an exponent (a^b) is raised to an exponent (c), you can multiply the exponents before raising the base to that product (b x c) to evaluate.

To start you off:
\[\left( \frac{xy^2}{x^{-3}y^3} \right)^{-4} = \left( \frac{x^{-3}y^3}{xy^2} \right)^{4}\]

Answer 9

So for the kilometers to light year problem:
What are we given/what are we starting out with? We're told the distance in kilometers, so I write that down first.
\[4.1 \times 10^{13} \ \text{kilometers}\]
Now, is there a quantity (a conversion factor) that allows us to change from kilometers (the given unit) to light years (the desired unit)? We're given that in the last sentence of your problem:
\[1 \ \text{light year} = 9.46 \times 10^{12} \ \text{kilometers}\]
Why was I able to write this quantity as a fraction as I did in the previous post? Think about this: a fraction where the numerator (top) and denominator (bottom) are both equal would equal 1, right?
\[\frac{1}{1} = \frac{5232}{5232} = \ldots = 1\]
I can then rewrite out conversion factor as follows:
\[1 = \frac{9.46 \times 10^{12} \ \text{kilometers}}{9.46 \times 10^{12} \ \text{kilometers}} = \frac{1 \ \text{light year}}{9.46 \times 10^{12} \ \text{kilometers}}\]

Answer 10

Now we have two quantities:
the given parameter
\[4.1 \times 10^{13} \ \text{kilometers}\]
the conversion factor
\[\frac{1 \ \text{light year}}{9.46 \times 10^{12} \ \text{kilometers}}\]
I can try multiplying it like this
\[4.1 \times 10^{13} \ \text{kilometers} \times \frac{9.46 \times 10^{12} \ \text{kilometers}}{1 \ \text{light year}}\]
But what would that give us? The units (if we followed through with the multiplication) would work out to be \[\frac{\text{kilometers}^2}{1 \ \text{light year}}\]
^ which is not what we want.

What if I flip the conversion factor over such that kilometers is on the bottom?
\[4.1 \times 10^{13} \ \text{kilometers} \times \frac{1 \ \text{light year}}{9.46 \times 10^{12} \ \text{kilometers}}\]
Notice that if I multiplied straight through, the units would end up as follows:
\[\frac{\text{kilometers} \times \text{light year}}{\text{kilometers}}\]
In this case, because there is a common term (the unit kilometers) in the top and bottom, this unit cancels, leaving us with our desired unit: light years.

Answer 11

are you against giving me the actual answer?

Answer 12

Are you against trying things out yourself? I've essentially given you the answer by working it out and explaining it to you. All you have to do is plug the numbers into the calculator.

Answer 13

thats the problem, i don't have a calculator and i have to have this assignment turned in in like 3 minutes.

Answer 14

13**
but now like 6 minutes

Answer 15

You seem to be on a computer...
4.334 light years

Answer 16

thank you very much(:
and oh, im sorry,i didnt even think about using a calculator online.