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Serjik [45]
3 years ago
14

A rocket is launched with an initial upward velocity of 320 feet per second from an initial height of 15 feet.

Mathematics
1 answer:
liberstina [14]3 years ago
5 0

Answer:

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

Step-by-step explanation:

The height of the rocket launched from the ground is modelled after the following expression:

h(t) = -16.087\cdot t^{2}+320\cdot t +15 (1)

Where:

t - Time, measured in seconds.

h - Height, measured in feet.

After a careful reading to the statement, we translate all relevant information into the following mathematical inequation:

-16.087\cdot t^{2}+320\cdot t +15\ge 1.039 (2)

After some algebra, we get the equivalent inequation:

-(16.087\cdot t^{2}-320\cdot t -13.961)\ge 0

16.087\cdot t^{2}-320\cdot t -13.961 \le 0

(x-19.936)\cdot (x+0.044)\le 0

Which means that the following conditions must be observed to satisfy the inequation above:

x-19.936\le 0\,\land\,x+0.044\ge 0

x\le 19.936\,s\,\land\,x\ge -0.044\,s

0\,s\le x \le 19.936\,s

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

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3 years ago
A taxi driver had 43 fares to and from the airport last Monday. The price for a ride to the airport is $12, and the price for a
leva [86]

Answer:

(25,18) is the required solution.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of trips to the airport and y represent the number of trips from the airport.

Total number of fares  to and from the airport = 43

Thus, we can write the equation:

x+y = 43

Price for a ride to the airport = $12

Price for a ride from the airport = $10

Total amount collected by the driver = $480

Thus, we can write the equation:

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Solving the two equations, we get,

12x+12y-(12x+10y)=516-480\\\Rightarrow 2y =36\\\Rightarrow y = 18\\\Rightarrow x = 43-18=25

Thus, the driver made 25 trips to the airport and 18 trips from the airport.

The solution can be represented as (25,18)

7 0
2 years ago
Shannon graphed the system of equations.
ehidna [41]
All you need to do is plug -5 into the second equation and you see it is near (-5, -8). When plugged into the top, you get (-5, -27/4) which comes out to ABOUT -6.75 for the Y value. The closest is actually a tie. The first option is .8 from the first and .45 from the second leading in a total distance of 1.25. The second, which is the fellow answer, is 1.2 from the first and .05 from the second, leading to 1.25 away.

The third, which is next closest is 1.8 from the first and .55 from the second leading to a distance of over 2 from the optimal, so only the first two are answers.
3 0
3 years ago
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Answer:

2 RootIndex 4 StartRoot 4 EndRoot

Step-by-step explanation:

we have

64^{\frac{1}{4}}

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substitute

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7 0
2 years ago
Read 2 more answers
1. What is the correct way to write 3,350,000 in scientific notation? * O 3.35 x 10^6 O 3.35 x 10^10 335 x 10^5 O 335 x 10^9
Tomtit [17]

We have the following:

3350000=3.35\cdot1000000=3.35\cdot10^6

therefore, the answer is 3.35 x 10^6

6 0
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