Answer:
(a) 12 m
(b) 32 m/s
Step-by-step explanation:
(a) The height of the platform is h(0) i.e. the height, h, at time t = 0 secs, since the ball would not have been thrown at that time.
Therefore, h(0) is:
![h(0) = -16(0^2) + 32(0) + 12\\\\\\h(0) = 0 + 0 + 12\\\\\\h(0) = 12 m](https://tex.z-dn.net/?f=h%280%29%20%3D%20-16%280%5E2%29%20%2B%2032%280%29%20%2B%2012%5C%5C%5C%5C%5C%5Ch%280%29%20%3D%200%20%2B%200%20%2B%2012%5C%5C%5C%5C%5C%5Ch%280%29%20%3D%2012%20m)
The height of the platform is 12 m.
(b) The initial velocity when the baseball is thrown will be v(0) that is velocity when t = 0 secs.
We obtain velocity, v, by differentiating height, h, with respect to time:
![v(t) = \frac{dh}{dt} = -32t + 32](https://tex.z-dn.net/?f=v%28t%29%20%3D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20-32t%20%2B%2032)
Therefore, at time t = 0 secs:
![v(0) = -32(0) + 32\\\\\\v(0) = 32 m/s](https://tex.z-dn.net/?f=v%280%29%20%3D%20-32%280%29%20%2B%2032%5C%5C%5C%5C%5C%5Cv%280%29%20%3D%2032%20m%2Fs)
The initial velocity of the baseball when it is thrown is 32 m/s.
Answer:
2 sweatshirts per student
Step-by-step explanation:
I'm not sure whether or not I understood this problem correctly, but I tried my best. Try to make your questions more clear in the future.
($35 per ticket * 16 students) + ($19 per sweatshirt * X sweatshirts sold) = $960
$560 from the sweatshirt + 19X = 960
19X = 960 - 560 = $400
X = 21 sweatshirt sold overall
Number of sweatshirt sold per student = 21/19 = 1.105 ---> 2 per student
Answer:
1 millimeter = 2 meters
Step-by-step explanation:
Scales are used in drawings to represent large buildings and places.
Given
Original width of basketball court = w = 8 meters
Width in drawing = s = 4 millimeters
In order to find the scale we have to divide the original width by the width in drawing.
![Scale = \frac{Original\ width}{Width\ in\ drawing}\\Scale = \frac{8}{4}\\Scale = 2\ meter\ per\ millimeter](https://tex.z-dn.net/?f=Scale%20%3D%20%5Cfrac%7BOriginal%5C%20width%7D%7BWidth%5C%20in%5C%20drawing%7D%5C%5CScale%20%3D%20%5Cfrac%7B8%7D%7B4%7D%5C%5CScale%20%3D%202%5C%20meter%5C%20per%5C%20millimeter)
This means that 1 millimeter represents 2 meters of the original court
1 millimeter = 2 meters
Answer:
10
Step-by-step explanation:
pythagorean theorem
take the sum of the square of each leg and set it equal to the square of the hypotenuse
8² + 6² = x²
64 + 36 = x²
x² = 100
x =
or 10
![\huge{\textbf{\textsf{{\color{navy}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}](https://tex.z-dn.net/?f=%5Chuge%7B%5Ctextbf%7B%5Ctextsf%7B%7B%5Ccolor%7Bnavy%7D%7BAn%7D%7D%7B%5Cred%7Bsw%7D%7D%7B%5Corange%7Ber%7D%7D%20%7B%5Ccolor%7Byellow%7D%7B%3A%7D%7D%7D%7D%7D)
![\frac{2}{x} = \frac{5}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7Bx%7D%20%20%3D%20%20%5Cfrac%7B5%7D%7B3%7D%20)
By doing cross multiplication.
![6 = 5x \\ x = \frac{6}{5} \\ x = 1.2](https://tex.z-dn.net/?f=6%20%3D%205x%20%5C%5C%20%20x%20%3D%20%5Cfrac%7B6%7D%7B5%7D%20%20%5C%5C%20x%20%3D%201.2)
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