The following expression is a perfect square. Find the third term.49y2 + 42y+
1 answer:
Answer:
+ 9
Step-by-step explanation:
Given the expression is a perfect square of the form
(ay + b)² = a²y² + 2aby + b² = 49y² + 42y +
Comparing coefficients of like terms
a² = 49 ( take the square root of both sides )
a = = 7
2ab = 42 ( divide both sides by 2 )
ab = 21 , then
7b = 21 ( divide both sides by 7 )
b = 3, thus
b² = 3² = 9
Hence
49y² + 42y + 9 = (7y + 3)²
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Answer:
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Step-by-step explanation:
We wish to find the area between the curves 2x+y2=8 and y=x.
Substituting y for x in the equation 2x+y2=8 yields
2y+y2y2+2y−8(y+4)(y−2)=8=0=0
so the line y=x intersects the parabola 2x+y2=8 at the points (−4,−4) and (2,2). Solving the equation 2x+y2=8 for x yields
x=4−12y2
From sketching the graphs of the parabola and the line, we see that the x-values on the parabola are at least those on the line when −4≤y≤2.
