First, we know that when multiplying fractions, we multiply both the numerator and denominator.
so, in 4/9 • 4/5, 4•4 = 16, and 9•5 = 45
so, 4/9 • 4/5 = 16/45. now, we’ll look for the Least Common Factor
factors are numbers that you can multiply together to = another number. the LEAST common Factor is the # that is smallest that you can divide both numbers by, in an equation and get a whole number.
for instance, 3•3 and 1•9 are the only ways to get 9, so, the factors are 1, 3, 9
let’s look for the LCF in 16 and 45. - if we find the ways to get 16, we have: 1•16, 2•8, and 4•4 so, the factors are 1, 2, 4, 8, and 16. this is called FACTORING :)
the ways to get 45 are... 1•45, 3•15, and 5•9, so the FACTORS are 1, 3, 5, 9, 15, & 45. - compare the factors of 16 & 45, none of them are the same besides 1, and we know that dividing these numbers by 1 will not do anything.
because of this, we can not reduce 16/45, so the reduced answer to 4/9 • 4/5 = 16/45
C is the answer, because the statmen placed on this one is true 1&3/4 is actually greater then 3/4 when if you just left that 1 & 3/4 with just a one it would still be greater.
The key to area in polar coordinates is the formula for the area of a sector:
a = (1/2)r²θ
Then a differential of area* can be written as ...
da = (1/2)r²·dθ
Filling in the given function for r, we have ...
da = (1/2)(4cos(3θ))²·dθ = 8cos(3θ)²·dθ
The integral will have limits corresponding to the range of values of θ for one loop of the graph: -π/6 to π/6. So, the area is ...
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* As with other approaches to finding area (horizontal or vertical slice, for example), we assume that the differential element dθ is sufficiently small that we need not concern ourselves with the fact that r is a function of θ.