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Fantom [35]
3 years ago
14

An object is launched directly in the air at a speed of 48 feet per second from a platform located 12 feet above the ground. The

position of the object can be modeled using the function f(t)=−16t2+48t+12, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Mathematics
1 answer:
anastassius [24]3 years ago
6 0

9514 1404 393

Answer:

  48 ft

Step-by-step explanation:

For the quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the given quadratic, which defines a parabola opening downward, the axis of symmetry defines the time at which the maximum height is reached.

  t = -48/(2(-16)) = 1.5

Then the maximum height is ...

  f(1.5) = (-16·1.5 +48)1.5 +12 = (24·1.5) +12

  f(1.5) = 48

The maximum height the object will reach is 48 feet.

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Use the Law of Sines to solve the triangle. (Let b = 47.7 yd. Round your answers for a and c to two decimal places.)
klio [65]

Answer:

C = 68.667°

a = 123.31 yd.

c = 114.90 yd.

Step-by-step explanation:

The missing image for the question is attached to this solution.

In the missing image, a triangle AB is given with angles A and B given to be 88° 35' and 22° 45' respectively

We are them told to find angle C and side a and c given that side b = 47.7 yd.

A = 88° 35' = 88° + (35/60)° = 88.583°

B = 22° 45' = 22° + (45/60)° = 22.75°

The sum of angles in a triangle = 180°

A + B + C = 180°

C = 180° - (A + B) = 180° - (88.583° + 22.75°) = 68.667°

The sine law is given as

(a/sin A) = (b/sin B) = (c/sin C)

Using the first two terms of the sine law

(a/sin A) = (b/sin B)

a = ?

A = 88.583°

b = 47.7 yd.

B = 22.75°

(a/sin 88.583°) = (47.7/sin 22.75°)

a = (47.7 × sin 88.583°) ÷ sin 22.75°

a = 123.31 yd.

Using the last two terms of the sine law

(b/sin B) = (c/sin C)

b = 47.7 yd.

B = 22.75°

c = ?

C = 68.667°

(47.7/sin 22.75°) = (c/sin 68.667°)

c = (47.7 × sin 68.667°) ÷ sin 22.75°

c = 114.90 yd.

Hope this Helps!!!

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Step-by-step explanation:

Step two:

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