Malcolm started with a board that was 5 3/4 feet long. He then cut off a section that was 1 feet long. How much of the board is
1 answer:
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Answer:
A = 36.8°
B = 23.2°
a = 7.6
Step-by-step explanation:
Given:
C = 120°
b = 5
c = 11
Required:
Find A, B, and a.
Solution:
✔️To find B, apply the Law of Sines
Plug in the values
Cross multiply
Sin(B)*11 = sin(120)*5
Divide both sides by 11
Sin(B) = 0.3936
B =
B = 23.1786882° ≈ 23.2° (nearest tenth)
✔️Find A:
A = 180° - (B + C) (sum of triangle)
A = 180° - (23.2° + 120°)
A = 36.8°
✔️To find a, apply the Law of sines:
Plug in the values
Cross multiply
a*sin(23.2) = 5*sin(36.8)
Divide both sides by sin(23.2)
a = 7.60294329 ≈ 7.6 (nearest tenth)
Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be , the first and second derivatives are, respectively:
First Derivative
Second Derivative
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
(Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
The highest altitude that the object reaches is 576 feet.