I thought I saw this one earlier and there were people answering. Guess not.
h(t) = 5 + 98t - 4.9t²
h(0) = 5 meters
h(5) = 5 + 98(5) - 4.9(5)² = 372.5 meters
h(10) = 5 + 98(10) - 4.9(10)² = 5 + 980 - 490 = 495 meters
h(15) = 5 + 98(15) - 4.9(15²) = 372.5 meters
h(20) = 5 meters
I'll leave the graphing to you, plot those points
(0,5), (5,372,5),(10,495),(15,372.5) (20,5)
and connect the dots
It's coming down pretty fast at 5 feet up 20 seconds. That last bit is 5/495 or 1% of the trip, so probably double the average speed of around 50m/s so 100msec or .05 sec to go 5 meters.
So it's in the ground at about 20.05 seconds after launch.
Answer: 20.05 meters
Answer:
15
Step-by-step explanation:
Answer: The equation has a positive y-intercept
This is because the constant is +10
Answer:
12 units
Step-by-step explanation:
The first segment, RS, is along the grid line y=4 from x=-1 to x=5, a total distance of 5-(-1)=6 grid units.
The second segment, ST, is along the grid line x=5 from y=4 to y=-2, a total distance of 4-(-2)=6 grid units.
The total length of the trail is the sum of the lengths of the first and second segments, so is 6+6=12 units.
_____
It can help to plot the points on a graph so you can better see what it is you're being asked to find.
We have been given that a jeweler has 5 rings, each weighing 12 g, made of an alloy of 20% silver and 80% gold.
Upon melting all 5 rings, the weight of the material will be 12*5=60 grams.
We have been given that the alloy contains 20% silver and 80% gold. Further, let us assume that x grams of silver are added to the melted material so that it has 64% gold and 36% silver.
Therefore, we can set up an equation:
![\text{Amount of gold before mixing}=\text{Amount of gold after mixing}](https://tex.z-dn.net/?f=%5Ctext%7BAmount%20of%20gold%20before%20mixing%7D%3D%5Ctext%7BAmount%20of%20gold%20after%20mixing%7D)
Therefore, we get an equation:
![80\%\text{ of 60 gram}=64\%\text{ of (x+60) gram}](https://tex.z-dn.net/?f=80%5C%25%5Ctext%7B%20of%2060%20gram%7D%3D64%5C%25%5Ctext%7B%20of%20%28x%2B60%29%20gram%7D)
![0.80*60=0.64(x+60)\\48=0.64x+38.4\\0.64x=9.6\\x=\frac{9.6}{0.64} \\x=15](https://tex.z-dn.net/?f=0.80%2A60%3D0.64%28x%2B60%29%5C%5C48%3D0.64x%2B38.4%5C%5C0.64x%3D9.6%5C%5Cx%3D%5Cfrac%7B9.6%7D%7B0.64%7D%20%5C%5Cx%3D15)
Therefore, 15 grams of silver must be added to the melted material in order to reduce the gold content to 64%.