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?

Answers

Answer 1

Answer:

[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]

[tex] \rm \displaystyle 2)3021.6 \: m[/tex]

Step-by-step explanation:

Question-1:

so when flash down 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:

[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]

to solve the equation can consider the quadratic formula given by

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

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

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

remove parentheses:

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

simplify square:

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

simplify multiplication:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]

simplify Substraction:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]

by simplifying we acquire:

[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]

since time can't be negative

[tex] \displaystyle t = 48.2 [/tex]

hence,

at 48.2 seconds splashdown occurs

Question-2:

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

[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]

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

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

simplify which yields:

[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]

now plug in the maximum t to the function:

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

simplify:

[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?


Related Questions

Which of the following exponential functions represents the graph below

Answers

9514 1404 393

Answer:

  D

Step-by-step explanation:

The exponential function is decreasing everywhere, so the base of the exponent must be less than 1. Only one answer choice fits.

For the function f(x) = -12x^2 + 6x - 8 find the equation of the tangent line at x= -1

Answers

Let, f(x) = y = -12x^2+6x-8

Substitute x = -1 in f(x) we get y = -26

y = -12x^2+6x-8

Differentiate ‘y’ w.r.t ‘x’ we get

dy/dx = -24x+6

By putting value of ‘x’ we get

dy/dx = 30

Slope(m)=dy/dx = 30

Equation of tangent => (y - y1)=m(x - x1)

Here, x1= -1 and y1 = -26 and m = 30

So, (y - (-26)) =30(x - (-1))

y+26=30(x+1)

y+26=30x+30

30x - y + 4 =0 is the equation of tangent at x = -1

Answer:

y=30x+4

Step-by-step explanation:

(1.00)^365

What type of math problem is this and how to explain it, please?

Answers

Step-by-step explanation:

(1.00)³⁶⁵

=1

1 power any natural number is 1

Answer:

1

Step-by-step explanation:

(1.00)^365

it means to multiply (1 .00) 365 times

which of the following is not a pythagorean triple?

Answers

Answer:

A

Step-by-step explanation:

7^2+8^2 does NOT equal 9^2

A. (7,8,9)


Did the test just now.

Does this graph represent a function? Why or why not?

Answers

A. Yes because it passes the vertical line test
yes bc it passes the vertical test

Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 511 human resource​ professionals, each was asked about the importance of the age of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
a) it is flawed because it is a census.
b) it is flawed because it is not statistically significant.
c) it appears to be sound because the data are not biased in anyway.
d) it is flawed because it is a voluntary response sample.

Answers

Answer:

c) it appears to be sound because the data are not biased in anyway.

Step-by-step explanation:

From the information given regarding the sample selection method , the size, the larger sample from which the survey subject were selected, we can conclude that the data is sound and not in anyway biased. The subject were selected from a reputable market research firm, which means the subjects were chosen from a larger sample which is reliable and not just a voluntary pool of subjects. Also, the selection process is randomized. Based on these, there are no flaws which are likely to cause the introduction of bias into the sample selected. Hence, the data is sound and not in any way biased.

Can someone help me?

Answers

Answer:

1. True, because when performing the calculations in both sides of the equation, we find that the left value is indeed the same as the right value

4-3+5 = 1+5 = 6

-6+8+4 = 2+4 = 6

6=6, so the sentence is correct

2+5 = 19-12 => 7=7, true

5-4-3-2-1 = 30-34-1 => -5=-5, true

2(x+5)-4x = 3(x-2)-5x+16

=> 2x+10-4x = 3x-6-5x+16

=> -2x+10 = -2x+10, true

Step-by-step explanation:

the other two sentences lead to false

4/5 + 1/5 = 2 - 1 - 1, => 5/5 = 1 = 0, false

2(x+8) = 2x-8, => 2x+16 = 2x-8 => 16=-8, false

if m=17 and b=6,find m

Answers

Answer:

M) = 17

Step-by-step explanation:

You stated the answer right there. I think the question is missing more info but for now M=17

graph the function g(x)=-4x-1

Answers

here is the answer

mark me in the brainlist

thanks

Answer to the question

Answers

Answer:

x = 48.

Step-by-step explanation:

AE and EC are equivalent. Subtract 9 from 921, and divide by 19 to get the value of x, which is 48.

Write a function to describe the following scenario.
A taxi driver charges a $5 flat fee to
enter the car and $0.50 per mile.
What is the total cost of a taxi ride?
y = [?]x + [?]

Answers

Answer:

y = $0.50x + $5. $7 if you went 4 miles

Step-by-step explanation:

$0.50 will be the coefficient for the variable x since the amount changes based on how many miles you ride. $5 will be the amount you are charged just for getting into the taxi and doesn't change depending on how many miles you go.

[tex]y=0.50x+5[/tex]

I used x = 4 for the number of miles travelled.

[tex]y=0.50(4)+5[/tex]

[tex]y=2+5[/tex]

[tex]y=[/tex] $7 total cost

Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)

Answers

[tex] \large{ \boxed{ \tt{OUR \: ANSWER : \underline{ \$ \: 583.3125}}}}[/tex]

Well , You can solve this question using two ways. I'm gonna use the both ways to make you clear and the one which you can easily understand , pick up that way and start solving another question as similar as this one.

[tex] \large{ \tt{❃ \: FIRST \: METHOD }} : [/tex]

This method is related to the unitary method. Let's start :

We're provided - Amount Kelly earns per hour for gardening = $ 12.75 and we're asked to find out the amount she earn if she worked 45.75 hours this month.

We know , Kelly probably earns more money if she worked 45.75 hours comparison to if she worked 1 hour. So You just multiply 45.75 & 12.75 , you would get $ 583.3125 and that's your final answer.

[tex] \large{ \tt{❃ \: SECOND \: METHOD}} : [/tex]

This method is related to the proportion. If you haven't learned about it yet , use the above way to solve the similar type of questions. Let's start :

Let Kelly earns X dollars if she worked 45.75 hours this month. [ Now , See the attached picture ]

Here , we can see the time is increased which implies that money will surely be increased. Such type of proportion is called direct proportion.

Here , the ratio of time ( in hours ) = 1 : 45.75 and the ratio of amount ( in dollars ) = 12.75 : x . Now , Set up an equation and solve for x :

[tex] \large{ \tt{ ❁ \: \frac{1}{45.75} = \frac{12.75}{x}}} [/tex]

[tex] \large{ \tt{↦ \: 1 \times x = 45.75 \times 12.75}}[/tex]

[tex] \large{ \tt{↦x = \$ \: 583.3125}}[/tex]

Hence , She earned $ 583.3125 .

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

how to what.nnnnkkadjkdjdadljadjldjlkajlljklk

Answers

Answer:

??

Step-by-step explanation:

How can she find the coordinates of the new point without graphing the point?

Answers

How can she find the coordinates of the new point without graphing the point?

If you know the coordinates of any two points on a straight line, you can compute its slope without looking at its graph. Every point has two coordinates: an x-value and a y-value, which are expressed as an ordered pair (x, y). The x value indicates the horizontal location of a point.

☆彡Hanna

#CarryOnLearning

find the polynomial of minimum degree, with real coefficients, zeros at x=-4+1i and x=8, and y intercept at -408

Answers

Answer:

(x-8)(x+4-i)=x^2+4x-ix-8x-32+8i=x^2-(4+i)x-32+8i

y=x^2-(4+i)x-32+8i

Check:

D=16+8i-1+128-32i=143-24

How many 1/6 cup servings of. Rice are in 2/3 cup of rice

Answers

9514 1404 393

Answer:

  4

Step-by-step explanation:

2/3 = 4/6

There are four 1/6-cup servings of rice in 4/6 cups of rice.

: (570)=2 م Let m 1 = (342) and m .16 = m1= =OFE هم (​

Answers

Answer:

x = 6

m<1 = 20°

m<CFE = 140°

Step-by-step explanation:

m<1 = (3x + 2)°

m<2 = (5x - 10)°

✔️Given that FB bisects AFC, therefore,

m<1 = m<2

Substitute

3x + 2 = 5x - 10

Collect like terms and solve for x

3x - 5x = -2 - 10

-2x = -12

-2x/-2 = -12/-2

x = 6

✔️m<1 = 3x + 2

Plug in the value of x

m<1 = 3(6) + 2

m<1 = 18 + 2

m<1 = 20°

✔️m<CFE = 180° - m<AFC (angles on a straight line)

m<CFE = 180° - (m<1 + m<2)

m<CFE = 180° - (20 + 20)

m<CFE = 180° - 40°

m<CFE = 140°

Soda is sold in aluminum cans that measure 7 inches in height and 2.8 inches in diameter. How many cubic inches of soda are contained in a full can?

Answers

9514 1404 393

Answer:

  43.1 in³

Step-by-step explanation:

The volume can be computed using the formula ...

  V = (π/4)d²h . . . . where d is the diameter and h is the height

For your dimensions, the volume is ...

  V = (π/4)(2.8 in)²(7 in) ≈ 43.103 in³

A full can contains a volume of about 43.1 cubic inches.

⚠️⚠️HELP DUE IN 3 HOURS⚠️⚠️

If f(1)=10 and f(n)=-2f(n-1) then find the value of f(5)

Answers

9514 1404 393

Answer:

  f(5) = 160

Step-by-step explanation:

The first several terms of the sequence are ...

  10, -20, 40, -80, 160, -320, 640, ...

Each term is -2 times the previous term.

  f(5) = 160

Hi :), im really struggling with this. Just wanted to know if anyone can explain step by step for me please. Id really appreciate it.

Answers

Answer:

222

Step-by-step explanation:

What I did was calculate the area of each sides of the triangular prism.

For the two triangles:

1/2(6x5)=15 (for 1 triangle, notice there are 2 so -> 30)

For the 2 rectangles:

5x12=60 x2 = 120

For the base:

6x12=72

Add all them together we get 222

Which of the following equations has the solution set {0}?

-14m - 7m + 1 = -7m + 1
-14m + 7m + 1 = -7m + 2
14m - 7m - 1 = -7m + 1

Answers

Answer:

the first one

-14m - 7m + 1 = - 7m + 1

If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish

Answers

Answer:

87.5%

Step-by-step explanation:

Complete question  -

75% of the people who eat at Doug's Diner order fish and 90% of the people who order fish also order fries. Given that 80% of all people who eat at Doug's order fries, what is the probability that a randomly chosen customer orders fries without fish?

Solution

Given

People who order fish at the Doug's Diner  = 75%

Out of this 75%, 90% also order  fries which means that nearly 67.5% ordered fries with the fish.

Given that, 80% of people dining at Doug's Diner order fries

Then percentage or people who ordered only fires and no fish = 80% - 67.5% = 12.5%

The probability of customers who ordered fish = 100 - 12.5% = 87.5%

A box contains 15 green marbles and 16 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble

Answers

Answer:  8/31

===================================================

Explanation:

16/31 represents the probability of picking a white marble

This is because there are 16 white out of 15+16 = 31 total.

---------

After we make a first selection, we have 16-1 = 15 white marbles left out of 31-1 = 30 marbles overall. The probability of selecting another white marble is 15/30 = 1/2.

Multiply those two fractions:

(16/31)*(1/2) = (16*1)/(31*2) = (2*8)/(31*2) = 8/31

which represents the probability of selecting two white marbles in a row, such that we don't put the first one back (and there's no replacement).

Phil's average is 0.250. This is about 5/6 as much as Joe's average. What is Joe's average? (Write answer is decimal form - do not round).

Answers

Let Joes average = x

Phil’s average is 0.250 and is 5/6X ( 5/6 of Joe’s)

5/6x = 0.250

Solve for x by dividing both sides by 5/6. When dividing by a fraction, flip the fraction over and multiply;

X = 0.250 x 6/5 = (0.250 x 6)/5 = 1.5/5 = 0.30

Joes average is 0.3

Need help solving for x, look at image above

Answers

Answer:

x = 1.2

Step-by-step explanation:

We can use a ratio to solve since they are similar triangles

6        (6+4)

----- = ---------

x             2

Using cross products

6*2 = (6+4)*x

12 = 10x

Divide by 10

12/10 = x

1.2 =x

Hope this help!!!

Have a nice day!!!

5. If the lines 2x + 3ay – 1 = 0 and 3x + 4y + 1 = 9 are mutually perpendicular, then the value of a is (1 Point) O a. O b.3 O-1/2​

Answers

because the multiplication Slope of 2 perpendicular is -1

Please show work for BRAINLIEST

Answers

Answer:

the anser is 54 cm square (30+15+9)

Answer:

it area is 54 cm square

Step-by-step explanation:

first point it's divide in three part . it's first is up side 3 by 3 . it's second part is middle side 3 by 5. it's third part is down side 10 by 3.then a

You buy a used car for $9,000. The car depreciates 9% per year. Find the value of the
car after 10 years.

Answers

Answer:

$19,000.

Step-by-step explanation:

#hopeithelpsbrainliest me.

In ABC, c=66,m∠A=3230', and m∠C=11140'. Find the length of side a to the nearest tenth.

Answers

y
=

2
x
+
5
y
=
-
2
x
+
5
Use the slope-intercept form to find the slope and y-intercept.
Tap for more steps...
Slope:

2
-
2
y-intercept:
(
0
,
5
)
(
0
,
5
)
Any line can be graphed using two points. Select two
x
x
values, and plug them into the equation to find the corresponding
y
y
values.
Tap for more steps...
x
y
0
5
5
2
0

A school cafeteria wants to survey a random sample of 50 students about the quality of food. During one lunch period, every 5th student who walks through the cafeteria door is surveyed until 50 students are selected. Which of the following statements is true about this sample?

Answers

Answer:

B

Step-by-step explanation:

Answer:

B EDGE

Step-by-step explanation:

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