Explanation:
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 ...
_____
* 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.
Answer:
x = 31 °
Step-by-step explanation:
90 = 58 + x
x = 90 - 58
x = 31 °
Answer:
See explanation below.
Step-by-step explanation:
Let's say,
x = number of tokens required to play one game of ping pong
y = number of token required play one game of pinball
Using the data given, the system of equations are:
Solving the system of equations using substitution method will give us:
So, one game of ping pong required 1 token, whereas one game of pinball required 4 tokens.
1/12 + 1/6x = 3/4...multiply everything by common denominator of 12
1 + 2x = 9
2x = 9 - 1
2x = 8
x = 8/2
x = 4 <== he can play 4 rounds
Answer:
If we are working in a coordinate plane where the endpoints has the coordinates (x1,y1) and (x2,y2) then the midpoint coordinates is found by using the following formula:
midpoint=(x1+x22,y1+y22)
Step-by-step explanation:
