Answer:
Oh gosh. Im not positive but I think it would be 43:25. Please dont get mad at me if its wrong!
Step-by-step explanation:
I am so sorry if its wrong but im not very sure :-(
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).
Answer:
Step-by-step explanation:
common difference d=3-1=2
first term a=1
an=a+(n-1)d
2n-1=1+(l-1)2
2n-1=1+2l-2
2n-1=2l-1
l=n
(i used l for number of terms)
number of terms=n

Answer:
40 mph
Step-by-step explanation:
One hour includes 60 minutes
8/60=0.13(3 repeating)
You only need 15 minutes of time
0.13(3 repeating)*15=2
8+2=10 miles
15 minutes is 1/4 of an hour
10*4=40 mph
Answer:

Step-by-step explanation:
We are asked to divide our given fraction:
.
We will simplify our division problem using rules of exponents.
Using product rule of exponents
we can write:


Substituting these values in our division problem we will get,

Using power rule of exponents
we will get,


Using quotient rule of exponent
we will get,


Using product rule of exponents
we will get,


Upon canceling out
we will get,

Using power rule of exponents
we will get,


Therefore, our resulting quotient will be
.