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Charra [1.4K]
3 years ago
14

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What i

s the maximum height that the ball will reach?
Do not round your answe
Mathematics
2 answers:
ahrayia [7]3 years ago
7 0

Answer:

42.25 feet

Step-by-step explanation:

The height function is a parabola.  The maximum value of a negative parabola is at the vertex, which can be found with:

x = -b/2a

where a and b are the coefficients in y = ax² + bx + c.

Here, we have y = -16t² + 52t.  So a = -16 and b = 52.  The vertex is at:

t = -52 / (2×-16)

t = 13/8

Evaluating the function:

h(13/8) = -16(13/8)² + 52(13/8)

h(13/8) = -169/4 + 169/2

h(13/8) = 169/4

h(13/8) = 42.25

pochemuha3 years ago
6 0

Answer:

42.25 feet.

Step-by-step explanation:

The maximum height can be found by converting to vertex form:

h(t) = 52t - 16t^2

h(t) =   -16 (  t^2  - 3.25t)

h(t) = -16 [ (t - 1.625)^2 - 2.640625 ]

= -16(t - 1.625 ^2) + 42.25

Maximum height = 42.25 feet.

Another method of solving this is by using Calculus:

h(t) = 52t - 16t^2

Finding the derivative:

h'(t) = 52 - 32t

This = zero for  a maximum/minimum value.

52 - 32t = 0

t = 1.625 seconds at maximum height.

It is a maximum because  the  path is a parabola  which opens downwards. we know this because of the  negative coefficient of x^2.

Substituting in the original formula:h(t) = 52(1.625)- 16(1.625)^2

= 42.25 feet.

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Answer:

When n=3 and x=−2  the answer is 11.

Step-by-step explanation:

Given:

Let p (n,x) be the function such that

p (n,x) = n + 2x^{2}

To Find:

p (n,x) = p ( 3, -2) = ?

Solution:

p (n,x) = n + 2x^{2}

Substituting n = 3 and x = -2 we get

p (3, -2) = 3 + 2(-2)^{2}

Negative square gives positive number therefore (-2)²=4

p (3, -2) = 3 + 2\times 4

p (3, -2) = 3 + 8\\p (3, -2) = 11

When n=3 and x=−2  the answer is 11.

7 0
3 years ago
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Answer:

that is right

Step-by-step explanation:

because 4×4×4 equals 64 and 6×6 equals 37 so it is 4^3>6^2

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Same here, we do a quick switcharoo on the variables first,

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Answer:

C

Step-by-step explanation:

Firstly, we know that the function must be negative due to its shape. This means that the answer cannot be B

Next we can use the equation x=\frac{-b}{2a} that is used in order to find the vertex of the parabola.

A)

f(x)=-x^2+6x+7\\a=-1,b=6,c=7\\\\x=\frac{-6}{-2} \\x=3

As the vertex is at x=3 on the graph, this one could be a contender.

C)

f(x)=-x^2+6x-7\\a=-1,b=6, c=-7\\\\x=\frac{-6}{-2} \\\\x=3

This also could be the equation

D)

f(x)=-x^2-6x-7\\\\a=-1, b=-6, c=-7\\\\x=\frac{6}{-2} \\\\x=-3

This rules option D out.

For this last step, we can look at where the zeroes would be for each equation. (These values are irrational, so we cannot look at specific number)

A)

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As this equation has a negative value for c, this means that one zero must be positive and the other must be negative.

This means that option A can be ruled out

C)

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