Mindy is driving 32mi / h as she nears an elementary school. A first grade student runs into the street after a soccer ball, and
1 answer:
Answer:
11 meters is her approximate reaction distance.
Step-by-step explanation:
Speed of the car of Mindy = 32 mile/hour =
1 mile = 1609.34 m
1 hour = 3600 seconds
Duration for her reaction last after student runs into street in front of her =
Distance covered three -quarters of a second = d
d = 10.73 m ≈ 11 m
11 meters is her approximate reaction distance.
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Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = 90° → A + B = 90° - C
→ C = 90° - (A + B)
Use the Double Angle Identity: cos 2A = 1 - 2 sin² A
→ sin² A = (1 - cos 2A)/2
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use the Product to Sum Identity: cos (A - B) - cos (A + B) = 2 sin A · sin B
Use the Cofunction Identities: cos (90° - A) = sin A
sin (90° - A) = cos A
<u>Proof LHS → RHS:</u>
LHS: sin² A + sin² B + sin² C
Given: 1 - cos (90° - C) · cos (A - B) + sin² C
Cofunction: 1 - sin C · cos (A - B) + sin² C
Factor: 1 - sin C [cos (A - B) + sin C]
Given: 1 - sin C[cos (A - B) - sin (90° - (A + B))]
Cofunction: 1 - sin C[cos (A - B) - cos (A + B)]
Sum to Product: 1 - sin C [2 sin A · sin B]
= 1 - 2 sin A · sin B · sin C
LHS = RHS: 1 - 2 sin A · sin B · sin C = 1 - 2 sin A · sin B · sin C
