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dangina [55]
2 years ago
15

A six-foot-tall basketball player shoots a ball towards the basket and misses. The height in feet of the ball up off the floor o

f the court as it travels through the air can be modeled by the function: h(x)=-16x^2+48x+6 where x is the number of seconds the ball is in the air after the shot is taken. When does the ball reach its maximum height? What is the maximum height of the ball? How much time will pass in seconds from the start of the shot to the ball hitting the floor? Answer all three questions to receive full credit.
Mathematics
1 answer:
enot [183]2 years ago
8 0

Answer:

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

 Step-by-step explanation:

<u>Step(i):</u>-

Given h(x) = - 16 x² + 48 x +6   ...(i)

Differentiating equation (i) with respective to 'x'

h ^{l} (x) = - 16 (2 x) +48 (1)   ...(ii)

Equating Zero

- 3 2 x + 4 8 = 0

- 32 x = - 48

    x = 1.5

<u><em>step(ii)</em></u>:-

The maximum height of the ball 'x' = 1.5

Again Differentiating equation (ii) with respective to 'x'

h ^{ll} (x) = - 16 (2 x) < 0

The maximum height 'x' = 1.5

h(x) = - 16 x² + 48 x +6  

h(1.5) = - 16 (1.5)² +4 8 (1.5) +6

         =   42

The maximum height at x = 1.5 is  = 42

<u><em>Final answer</em></u>:-

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

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3 years ago
An object is launched vertically upward from a 25 foot platform and is modeled by the function s(t)=−16t2+11t+25.
ch4aika [34]

Correct option:

d. 1.64

<h2>Explanation:</h2>

An object is launched vertically upward from a 25 foot platform and is modeled by the following function:

s(t)=-16t^2+11t+25

So this is the equation of a parabola because the object is a projectile so it follows the Projectile Motion.

The object fall back to the ground when s(t)=0 so:

-16t^2+11t+25=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ t_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ a=-16 \\ \\ b=11 \\ \\ c=25 \\ \\ \\ t_{12}=\frac{-11\pm \sqrt{11^2-4(-16)(25)}}{2(-16)} \\ \\ t_{12}=\frac{-11\pm 41.48}{-32} \\ \\ t_{1}=\frac{-11+ 41.48}{-32}=-0.95s \\ \\ t_{2}=\frac{-11- 41.48}{-32}=1.64s

Since time can't be negative, we only choose the positive value. therefore:

<em>The object fall back to the ground after 1.64 seconds</em>

<em></em>

<h2>Learn more:</h2>

Projectile motion: brainly.com/question/12554459

#LearnWithbrainly

4 0
3 years ago
Why is it valid to say that both a function and its inverse describe the same relationship
liberstina [14]
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Looking at ordered pairs of the function and its inverse would look like this:

(2,4) on the original function becomes (4,2) on the inverse. 

While the graph of a function and its inverse are noticeably different an important thing to note is that it is merely a reflection across the line y=x. 

So even though they appear different you are looking at the same relationship just as y vs. x instead of x vs. y
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Expression for the quotient of b divided by the difference of two minus 3
uysha [10]

Answer:

The required expression is

                                     \frac{b}{2 - 3}  = - b

Step-by-step explanation:

 

Difference of two minus three = 2-3

Quotient of b divided by the difference of two minus three is

                                             \frac{b}{2-3} = \frac{b}{-1} = - b

Therefore, the required expression is

                                                  \frac{b}{2-3}  \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ \  - b

7 0
3 years ago
The price of a watch was increased by 7% to £1350. What was the price before the increase? Give your answer to the nearest penny
frutty [35]

Answer:

1261.68

Step-by-step explanation:

1350 = the increased watch price= 107% of the original

1350= 1.07x

1261.68224299

Check:

7% of 1261.68224299 is 88.317757

1261.68224299 + 88.317757 = 1349.9 = 1350

Round:

1261.68224299  

To the penny= to the hundreth= 1261.68

3 0
3 years ago
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