When the height is 0 that is when it hits the ground
solve
0=-16t²+25x+3
cant factor so use quadratic formula
for
0=ax²+bx+c
![x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
so for
0=-16t²+25t+3
a=-16
b=25
c=3
so
![x=\frac{-25+/-\sqrt{25^2-4(-16)(3)}}{2(-16)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Csqrt%7B25%5E2-4%28-16%29%283%29%7D%7D%7B2%28-16%29%7D)
![x=\frac{-25+/-\frac{625+192}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Cfrac%7B625%2B192%7D%7D%7B-32%7D)
![x=\frac{-25+/-\frac{817}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Cfrac%7B817%7D%7D%7B-32%7D)
it has to be a positive time
so it will hit the ground after
![\frac{25+\sqrt{817}}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B25%2B%5Csqrt%7B817%7D%7D%7B32%7D)
seconds
Answer:
462 paths from A to B
Step-by-step explanation:
The question is incomplete. However, a possible question is to determine the number of possible paths on the grid map.
The first step is to represent the grid map itself. (See attachment 1)
From the question, we understand that:
- Only right movement is allowed in the horizontal direction
- Only up movement is allowed in the vertical direction
There are a several number of ways to navigate through. However, one possible way is in attachment 2
In attachment 2,
- R represents the right movement
- U represents the up movement
And we have:
and ![U = 6](https://tex.z-dn.net/?f=U%20%3D%206)
The number of possible paths (N) is then calculated as:
![N = \frac{(N + U)!}{N!U!}](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B%28N%20%2B%20U%29%21%7D%7BN%21U%21%7D)
Substitute values for N and U
![N = \frac{(5 + 6)!}{5!6!}](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B%285%20%2B%206%29%21%7D%7B5%216%21%7D)
![N = \frac{11!}{5!6!}](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B11%21%7D%7B5%216%21%7D)
![N = \frac{39916800}{120 * 720}](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B39916800%7D%7B120%20%2A%20720%7D)
![N = \frac{39916800}{86400}](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B39916800%7D%7B86400%7D)
![N = 462](https://tex.z-dn.net/?f=N%20%3D%20462)
<em>Hence, there are 462 possible paths from A to B</em>
One gallon is equivalent to 128 fluid ounces
3 gallons is equivalent to 3*128 fluid ounces
= 384 fluid ounces
One plastic cup can hold 12 guide ounces
So cups needed will be 384/12
32 cups
Answer:
131
Step-by-step explanation:
Using proportion,
If Out of 550 calculators = 6 are defective,
Then out of 12000 calculators = ? are defective
![\frac{12000 calculators}{550calculators} * 6](https://tex.z-dn.net/?f=%5Cfrac%7B12000%20calculators%7D%7B550calculators%7D%20%2A%206)
= 21.8 * 6
= 130.8 ≈ 131
∴ Approximately 131 calculators are defective
Answer:
The answer to number 7 is -1.25
The answer to number 8 is 1.25