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:
There are no solutions
Step-by-step explanation:
4/5 ( 20x + 5 ) = 16x - 2
Distibute on the left:
( 4/5 x 20 x ) + ( 4/5 x 5 ) = 16x - 2
16x + 4 = 16x - 2
Subtract 16x from both sides:
4=-2
Add 2 to each side:
6=0
No solutions
Answer:
441
Step-by-step explanation:
Answer:
8.9 in.
Step-by-step explanation:
Area of triangle = (1/2) b. h
40 = (1/2) x*x
80 = x^2
square root (80) = x
x=> 8.944.... inch
Rounding off you get 8.9 in.
All percentages can be expressed as fractions or decimals. To find a percentage of a number, we multiply the percentage with the number. In this case:
3/100 * 16/1 = 48/100 = 0.48
Or:
0.03 * 16 = 0.48
Her new hourly wage would be $16.48
