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Alina [70]
3 years ago
12

Hi, I don't feel very confident about my work in this calculus problem and I would appreciate it if anyone else could note any c

orrections or ways to improve my answers. My problem is split into parts A, B, C, and D and my work is in green. Thank you!

Mathematics
1 answer:
Lostsunrise [7]3 years ago
6 0
You're pretty close. It's all in the details.

A. Correct.

B. Correct.

C. Sign error in the boxed answer. -(-0.5) = 0.5
The graph shows c ≈ 1.855. If a is more than that and decreasing, area is increasing. The sign of dA/dt will be positive. (Compare to D)

D. Units are not shown. Numerical value is correct.

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Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

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\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

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