The vertex of the graph for the function g(x) = (x- 3)^2 + 9 is located 3 units to the right and 9 units upwards compared to the vertex of the function f(x) = x^2.
According to the details provided in the question, m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°. Since ∠2 is congruent to ∠9 (alternate interior angles), we establish that m∠2 = m∠9 = 41°. Utilizing the angle sum property, we have m∠8 + m∠9 + m∠10 = 180°, leading to m∠8 + 41 + 109 = 180°. Thus, m∠8 equates to 30°. From the triangle's angle sum, m∠2 + m∠7 + m∠8 = 180°, resulting in 41 + m∠7 + 30 = 180°. Consequently, m∠7 calculates to 109°. Also, m∠6 + m∠7 = 180°, so m∠6 comes to 71°. Given that m∠5 + m∠4 = 180°, we have m∠4 = 86°. Lastly, using the triangle angle sum theorem again, m∠4 + m∠3 + m∠9 = 180°, so m∠3 calculates to 53°. Thus, through the angle relationship, m∠1 + m∠2 + m∠3 = 180°, leading to m∠1 = 86°.
Let's apply u-substitution:
In the substitution process:dx=u du. then the integral transforms to:
=u-ln(u+1)=
. Next, we will adjust the limits:
=4-ln(5)-2+ln(3)=
2+ln(0.6)=2-0.51=1.49
Total: 737.38 + 618.57 equals 1,355.95, which is Choice A.
