Answer: The projectile reaches its maximum height after 20 seconds.
Step-by-step explanation:
Given the function:
![h(t) = -16t^2 + 640t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E2%20%2B%20640t)
You can following formula (which gives the x -coordinate of the vertex of the parabola) in order to find after how many seconds the projectile takes to reach its maximum height:
![x=t=-\frac{b}{2a}](https://tex.z-dn.net/?f=x%3Dt%3D-%5Cfrac%7Bb%7D%7B2a%7D)
In this case you can identify that the values of "a" and "b" are:
![a=-16\\b=640](https://tex.z-dn.net/?f=a%3D-16%5C%5Cb%3D640)
Then, substituting values into the formula, you get the following result:
![t=-\frac{640}{2(-16)}\\\\t=20](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7B640%7D%7B2%28-16%29%7D%5C%5C%5C%5Ct%3D20)
Therefore,based on this, the conclusion is: The projectile reaches its maximum height after 20 seconds.
7^2 I think is the write answer
Answer:
x = -6 , -2
Step-by-step explanation:
Find factors of x² and 12, in which, when combined, will give 8x:
x² + 8x + 12 = 0
x 6
x 2
(x + 6)(x + 2) = 0
Check. Use the FOIL method:
First, combine the first terms: x * x = x²
Next, combine the outside terms: x * 2 = 2x
Then, combine the inside terms: 6 * x = 6x
Finally, combine the last terms: 6 * 2 = 12
Combine like terms: x² + (2x + 6x) + 12
x² + 8x + 12
Solve for the solutions. Set each parenthesis equal to 0:
(x + 6)(x + 2) = 0
(x + 6) = 0
(x + 2) = 0
Isolate the variable x. Subtract 6 & 2 from both sides for their respective equation:
x + 6 = 0
x + 6 (-6) = 0 (-6)
x = 0 - 6
x = -6
x + 2 = 0
x + 2 (-2) = 0 (-2)
x = 0 - 2
x = -2
x = -6 , -2
~
Answer:
x = 18
Step-by-step explanation:
To write a proportion, we need to write down the data we have.
Shorter side of rectangle 1 = 6
Longer side of rectangle 1 = 13
Shorter side of rectangle 2 = x
Longer side of rectangle 2 = 39.
A proportion representing this would be: ![\frac{6}{13} = \frac{x}{39}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B13%7D%20%3D%20%5Cfrac%7Bx%7D%7B39%7D)
Solving this proportion for x, we would have:
![\frac{6}{13} =\frac{x}{39}\\x=\frac{6(39)}{13} \\x= \frac{234}{13} \\ x=18](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B13%7D%20%3D%5Cfrac%7Bx%7D%7B39%7D%5C%5Cx%3D%5Cfrac%7B6%2839%29%7D%7B13%7D%20%5C%5Cx%3D%20%5Cfrac%7B234%7D%7B13%7D%20%5C%5C%20x%3D18)
Therefore, the shorter side of the second rectangle is 18.