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Answer:
see attached
A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6
3t + 4, where t is measured in seconds and h is the height in feet. a) What is the height of the ball after 3 seconds? b) What is the maximum height of the ball? Round to the nearest foot. c) When will the ball hit the ground? d) What domain makes sense for the function?
2 answers:
Answer:
a) 49 ft
b) 66 ft
c) 4 seconds
d) [0, 4] seconds
Step-by-step explanation:
a) Evaluate the function for t=3:
h(3) = -16·3² +63·3 +4 = (-16·3 +63)·3 +4 = 15·3 +4
h(3) = 49
The height of the ball is 49 feet after 3 seconds.
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b) The maximum height of the ball will be found where t=-b/(2a) = -63/-32 = 1.96875.
h(1.96875) = (-16·(63/32) +63)·(63/32) +4 = 63²/64 +4 = 66.015625
The maximum height of the ball is approximately 66 feet.
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c) The ball will hit the ground when its height is zero.
-16t² +63t +4 = 0
Using the quadratic formula, we find the solution to be ...
t = (-63 - √(63² -4(-16)(4)))/(2·(-16)) = (-63 -√4225)/-32 = -128/-32 = 4
The ball will hit the ground after 4 seconds.
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d) The function is only useful for the time period between when the ball is thrown and when it lands, t = 0 to t = 4 seconds.
The domain of t in the interval 0 to 4 seconds makes sense for this function.
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Answer:
Length of rectangle = 24 inches
Width of rectangle = 1 inches
Step-by-step explanation:
Area of rectangle = 24 square inches
Perimeter of rectangle = 50 inches
Formulas:
Area of rectangle =
Perimeter of rectangle =
where represents length of rectangle and
represents width of rectangle.
So, we can get two equations for and
A) [Area]
B) [ Perimeter ]
Simplifying equation B.
Dividing both sides by 2.
Solving for in terms of width.
Subtracting both sides.
∴
Substituting value of in terms of
in equation A.
Using distribution.
Adding both sides.
subtracting both sides
We have a quadratic equation.
We solve for by factor method.
Splitting middle term into two terms such that the sum of the two = and product of two =
Factoring in pairs.
Factoring as a whole
So, we have
and
By adding 24 to one equation and adding 1 to other we get
and
and
So length can be found out by plugging value of in the length equation.
and
Since length is always the longer side of rectangle so, the dimensions of rectangle can be given by.
length = 24 inches (answer)
width = 1 inches (answer)