1) surface area = 18m^2 * pi * 26m = <span>8424pi m^2</span>
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
We see that the points of the graph of the function never attain a y-value of 0. Thus f is never equal to 0 for real numbers, hence we can disqualify all the necessary answers already (only answer not against this is 2). Nevertheless, we can show that this is the right answer. The graph is called a parabola, so it is represents a second order polynomial. These polynomials have either 2 real or 2 complex solutions. Since this does not have real solutions (at the lowest point of that polynomial the y-value is 4) the correct answer is b).
Answer:
Step-by-step explanation:
32.04 pounds is the answer
