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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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Bad White [126]

Answer: −(b+4)(2b−3)

Step-by-step explanation:

1. Factor out the negative sign.

−(2b^2+5b−12)

2. Split the second term in 2b^2+5b−12 into two terms.

−(2b^2+8b−3b−12)

3.Factor out common terms in the first two terms, then in the last two terms.

−(2b(b+4)−3(b+4))

4. Factor out the common term b+4b+4b+4.

−(b+4)(2b−3)

5 0
3 years ago
Please help thank you.
Mnenie [13.5K]

Answer:

Option D

Step-by-step explanation:

Whenever we take a square root of a number the ± sign is with it like here in the question

x^2=20\\\\Apply\ square\ root\ on\ both\ sides\\sqrt{x^2}=\sqrt{20}  \\\\The\ square\ cancels\ out\ with\ the\ root\x=\sqrt{20}

And then x = ±4.47 which means x has two values one is +4.47 and the other is -4.47 so Option D is our answer.

7 0
2 years ago
You have one type of nut that sells for $4.50/lb and another type of nut that sells for $8.00/lb. You would like to have 28 lbs
-Dominant- [34]

Answer:

I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.

Step-by-step explanation:

Since I have one type of nut that sells for $ 4.50 / lb and another type of nut that sells for $ 8.00 / lb, and I would like to have 28 lbs of a nut mixture that sells for $ 7.80 / lb, to determine how much of each nut will I need to obtain the desired mixture, the following calculation must be performed:

8 x 0.95 + 4.5 x 0.05 = 7.825

8 x 0.94 + 4.5 x 0.06 = 7.79

0.94 x 28 = 26.32

26.4 x 8 + 1.6 x 4.5 = 218.4

218.4 / 28 = 7.8

Thus, I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.

7 0
2 years ago
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in
exis [7]
2x + y = 10
2x + 3y = 22

Please consider marking this answer as Brainliest to help me advance, and let me know if you need any clarifications.
4 0
3 years ago
30. Each interior angle of a regular polygon is 4 times each exterior ang
kifflom [539]

Answer:

(a) the size of each exterior angle  360/10=36

(b)  the number of sides of the polygon.​ 10

Step-by-step explanation:

Each interior angle of a regular polygon is 4 times each exterior angle

∴sum of interior angles: (n-2)*180=4*360

n-2=8

n=10

(a) the size of each exterior angle  360/10=36

(b)  the number of sides of the polygon.​ 10

5 0
2 years ago
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