1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Daniel [21]
2 years ago
13

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

9 t 2 + 229 t + 346 . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
How high above sea-level does the rocket get at its peak?
Mathematics
1 answer:
Oliga [24]2 years ago
5 0

Answer:

\displaystyle 1)48.2    \:  \: \text{sec}

\rm \displaystyle  2)3021.6 \: m

Step-by-step explanation:

<h3>Question-1:</h3>

so when <u>flash down</u><u> </u>occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

\displaystyle  - 4.9 {t}^{2}  + 229t + 346 = 0

to solve the equation can consider the quadratic formula given by

\displaystyle x =  \frac{ - b \pm  \sqrt{ {b}^{2} - 4 ac} }{2a}

so let our a,b and c be -4.9,229 and 346 Thus substitute:

\rm\displaystyle t =  \frac{ - (229) \pm  \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}

remove parentheses:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}

simplify square:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}

simplify multiplication:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 52441- 6781.6} }{ - 9.8}

simplify Substraction:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 45659.4} }{ - 9.8}

by simplifying we acquire:

\displaystyle t = 48.2  \:  \:  \: \text{and} \quad  - 1.5

since time can't be negative

\displaystyle t = 48.2

hence,

at <u>4</u><u>8</u><u>.</u><u>2</u><u> </u>seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

\displaystyle x _{  \text{max}} =  \frac{ - b}{2a}

let a and b be -4.9 and 229 respectively thus substitute:

\displaystyle t _{  \text{max}} =  \frac{ - 229}{2( - 4.9)}

simplify which yields:

\displaystyle t _{  \text{max}} =  23.4

now plug in the maximum t to the function:

\rm \displaystyle  h(23.4)- 4.9 {(23.4)}^{2}  + 229(23.4)+ 346

simplify:

\rm \displaystyle  h(23.4)  =  3021.6

hence,

about <u>3</u><u>0</u><u>2</u><u>1</u><u>.</u><u>6</u><u> </u>meters high above sea-level the rocket gets at its peak?

You might be interested in
write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.
Brrunno [24]

Step-by-step explanation:

x=y

y=1/z^3

Now,

for equation,

x=y=1/z^3

5 0
3 years ago
Which is a statistical question. How tall is the governor of our state?
serious [3.7K]
 <span>Which is a statistical question. How tall is the governor of our state</span>
3 0
3 years ago
What is the specific method called on #3
IceJOKER [234]

Answer:

subtraction

Step-by-step explanation:

6 0
3 years ago
Find the vertex of the function given below. y = x2 - 4x + 1
DedPeter [7]
The vertex is (2, -3).
Use the formula x= -b/2a to find the x value., which is 2.Then, substitute it into the function, wherever you see an x. Follow order operations and you get y, which is -3.
5 0
3 years ago
Read 2 more answers
HELP
stira [4]
You would just do 5.7-8.1, which is -3.6 degrees Celcius. Hope I helped!
5 0
3 years ago
Other questions:
  • Find inverse function<br>f(x) = -3x + 9​
    12·1 answer
  • TIME REMAINING
    9·1 answer
  • Solve for x 17-x=36 PLSSSS HELPPPPP (A. -53 (B. -19 (C. 19 (D. 53
    13·1 answer
  • Jeff has 2/3 gallon of sherbet he gives each of his friends one 1/12 gallon scoop there is 1/6 gallon left in the carton hiw man
    6·2 answers
  • 1.
    14·1 answer
  • Last year there were 205 ducks living on the pond. This year there are 20% more ducks living on the pond. How many ducks are liv
    9·2 answers
  • Y is less than or equal to
    8·1 answer
  • Given the equation 5x - 7 = 18. What is
    15·2 answers
  • Solve if x = 2, 10 +3(12 ÷ 3x)) = ?
    12·1 answer
  • You are putting together your first post-graduation budget. Your take-home pay will be $2,500 per month. You estimate your month
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!