Which expression is eq to (125^2/125^4/3)

Mathematics

1 answer:

sweet [91]2 years ago

5 0

Answer:

Step-by-step explanation:

So the denominator can be simplified to 5⁴ → $(5^3)^\frac{4}{3}$ and then the 3's cancel out and we are left with 5⁴

Now our new fraction is $\frac{125^{2} }{5^{4} } = \frac{15625}{625}$ which then simplifies to 25

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What is the value of tan (-2pi/3)?

wolverine [178]

This revolves around exact trig values - no easy way to say this, you just need to memorise them. They are there for sin cos and tan, but I will give you the main tan ones below - note this is RADIANS (always work in them when you can, everything is better):

tan0: 0
tanpi/6: 1/sqrt(3)
tanpi/4: 1
tanpi/3: sqrt(3)
tanpi/2: undefined

Now we just need to equate -2pi/3 to something we understand. 2pi/3 is 1/3 of the way round a circle, so -2pi/3 is 1/3 of the way round the circle going backwards (anticlockwise), so on a diagram we already know it's in the third quadrant of the circle (somewhere between pi and 3pi/2 rads).
We also know it is pi/3 away from pi, so we are looking at sqrt(3) or -sqrt(3) because of those exact values.

Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).

4 0

3 years ago

Read 2 more answers

Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .