Provide an appropriate response.Find the error in the following "proof" that the area inside the lemniscate 
and then find the correct area. A = 
= 
= 
= 0
What will be an ideal response?
The error is in the limits of integration. There are no points on the curve corresponding to values of ? such that 
or 
since 
is negative on these intervals. The correct area is a2.
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Determine whether the polynomial is a perfect square trinomial, a difference of squares, or neither.x2 - 4
A. Perfect square trinomial B. Neither C. Difference of squares
Solve the problem.The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation for the new graph.
A. y = x2 + 5 B. y = x2 - 5 C. y = (x + 5)2 D. y = (x - 5)2
Solve the problem.When light travels from one medium to another-from air to water, for instance-it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence ?i is the angle in the first medium; the angle of refraction ?r is the second medium. (See illustration.) Each medium has an index of refraction-ni and nr, respectively-which can be found in tables. Snell's law relates these quantities in the formula ni sin?i = nr sin ?rSolving for ?r, we obtain ?r = sin-1 src="https://sciemce.com/media/4/ppg__tttt0506191043__f1q5g2.jpg" alt="" style="vertical-align: 0.0px;" height="174" width="173" />
What will be an ideal response?
Find ?r for fused quartz (ni = 1.46), ethyl alcohol (nr = 1.36), and ?i = 8.5°.
Write in logarithmic form.32 = 9
A. log3 2 = 9 B. log2 9 = 3 C. log9 3 = 2 D. log3 9 = 2