Using the vertex, it is found that the maximum height of the punt is of 27.7 feet.
The height of the punt, <u>after x seconds</u>, is given by:
![f(x) = -0.0152x^2 + 1.25x + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-0.0152x%5E2%20%2B%201.25x%20%2B%202)
It is a quadratic equation with coefficients
.
The maximum value is the value of the function at the vertex, hence:
![f_V = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}](https://tex.z-dn.net/?f=f_V%20%3D%20-%5Cfrac%7B%5CDelta%7D%7B4a%7D%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D)
Applying the coefficients:
![f_V = -\frac{b^2 - 4ac}{4a} = -\frac{(1.25)^2 - 4(-0.0152)(2)}{4(-0.0152)} = 27.7](https://tex.z-dn.net/?f=f_V%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D%20%3D%20-%5Cfrac%7B%281.25%29%5E2%20-%204%28-0.0152%29%282%29%7D%7B4%28-0.0152%29%7D%20%3D%2027.7)
The maximum height of the punt is of 27.7 feet.
A similar problem is given at brainly.com/question/16858635
Hello!
As the homework and test are two separate things, selecting an odd or even number on either of them will not affect the probability of selecting an odd or even number on the other.
Therefore, this pair of events is independent.
I hope this helps!
<em>Answer:</em>
<em>4</em>
<em>Step-by-step explanation:</em>
<em>2(6x+4)-6+2x=3(4x+3)+1</em>
<em>=14x+2=12x+10</em>
<em>=14x+2-2=12x+10-2</em>
<em>=14x=12x+8</em>
<em>=14x-12x=12x+8-12x</em>
<em>=2x=8</em>
<em>=2x/2=8/2</em>
<u><em>x=4</em></u>
<u><em></em></u>
Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.
<h3>What is the Volume of a Sphere and a Cylinder?</h3>
- Volume of a sphere = 4/3πr³
- Volume of a cylinder = πr²h
Volume of the bead = Volume of the sphere - volume of the cylindrical hole
= 4/3π(4³) - π(1²)(8)
= 268.08 - 25.13
Volume of the bead = 242.95 mm³
Learn more about volume of sphere on:
brainly.com/question/22807400
31.2% of some number is 28,800. In other words, 0.312x = 28,800. Solve for x by dividing both sides by 0.312 and you get 92,308 as your answer!