This question is incomplete, the complete question is;
A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel consumed at rate r, and the exhaust gases are ejected with constant velocity v(sub e) [relative to the rocket]. A model for the velocity of the rocket at time t is given by the equation:
v(t) = -gt - v(sub e) ln [(m-rt)/m]
where g is the acceleration due to gravity, and t is not too large. If g = 9.8 m/s^2, m = 30,000 kg, r = 160 kg/s, and v(sub e)= 3000 m/s, find the height of the rocket one minute after liftoff.
Answer:
the height of the rocket one minute after liftoff is 14.8441 km
Step-by-step explanation:
Given the data in the question;
Velocity of the rocket at time t is;
v(t) = -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex])
[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = ₀∫⁶⁰( -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex]) )dt
= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex] - [tex]V_{e\\}[/tex] ₀∫⁶⁰In( [tex]\frac{m-rt}{m}[/tex]) dt
= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex] - [tex]V_{e\\}[/tex] [ t In( [tex]\frac{m-rt}{m}[/tex]) + [tex]\frac{m}{r}[/tex] - t - mr[tex]\frac{1}{r^{2} }[/tex] In |m-rt| [tex]]^{60}_0[/tex]
= -g([tex][\frac{60^{2} }{2}][/tex] - [tex]V_{e\\}[/tex] [ 60 (In(1 - [tex]\frac{60r}{m}[/tex])-1) + [tex]\frac{m(In(m^{2})-In((m-60r)^2))) }{2r}[/tex] ]
we input our given values; g=9.8 m/s², m=30000 kg, Ve = 3000 m/s, r = 160 kg)
= -9.8([tex][\frac{60^{2} }{2}][/tex] - 3000 [ 60 (In(1 - [tex]\frac{60(160)}{m}[/tex])-1) + [tex]\frac{30,000(In(30,000^{2})-In((30,000-60(160))^2))) }{2(160)}[/tex] ]
[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = 14844.10 m
we convert to kilometer
[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = 14844.10 ÷ 1000
[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = 14.8441 km
Therefore, the height of the rocket one minute after liftoff is 14.8441 km
pls help the question is in the picture
Question 2 1 pts Asplaner has three sections colored green, purple, and pink. If the spinner is spun three times, how many possible outcomes are there!
Answer:
27
Step-by-step explanation:
The Counting Principle states that the number of possible outcomes is equal to the product of the number of outcomes for each event. In this case, (M)(N)(O).
There are 27 possible outcome if the spinner is spun three times.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A spinner has three sections colored green, purple, and pink.
From the general formula of probability:
Probability = (desired outcomes)/(Total outcomes)
In our case,
the three possible outcomes of this event occurring are Green, Purple, and Purple, Green.
The desired outcomes = 3
The total outcomes = 3 x 3 x 3 = 27
Learn more about probability here:
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Determine the graph that represents a function.
HELP ME PLS ASAP PLS PLZ
Answer:
11.5x 4.5-8 wayy easier all you do is add and multiply
pls solve this i cannot do it find x y z in the above
Answer:
x = 115
z= 40
y = 140
Step-by-step explanation:
x = 180 - (40 +25) = 115
z = 180 - (115+25) = 40
y = 180 - (40) = 140
Answer:
This is your answer!!!
Step-by-step explanation:
I attached a pic.
Hope it helps!!!
The coordinates of the vertexes of a triangle are A(3,3) B(6,6) C(9,3). What will be the new coordinates after a dilation
with a scale factor of 3 if you use the origin as the center of dilation?
0)
A)
A (9,9) B'(18,18) C'(27,9)
B)
A'(0,0) B'(3,3) C (6,0)
A'(1,1) B'(2.2) C'(3,1)
D)
A'(6,6) B'(9.9) C'(12,6)
Answer:
A
Step-by-step explanation:
Dilation by 3 from origin causes each point to be multiplied by 3.
(3,3) * 3 = (9, 9)
(6, 6) * 3 = (18, 18)
(9, 3) * 3 = (27, 9)
which is A
1. (-78) + (-98) =
2. (+45) + (+23) =
3. (+67) + (-56) =
4. (98) + (-73) =
5. (-971) + (+237) =
Answer:
1.-179
2.68
3. 11
4. 25
5. -734
What is 4 copies of 1/5
Answer:
1/5 + 1/5 + 1/5 + 1/5 = 4/5
Step-by-step explanation:
The 4 copies of the fraction 1/5 will be 4/5.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
As per the given,
4 copies of 1/5
The first copy of /5 = 1/5
Second one = 1/5
Third = 1/5
And fourth = 1/5
Collective all copies are 1/5 + 1/5 + 1/5 + 1/5
Take LCM as 5,
(1 + 1 + 1 + 1)/5 = 4/5
Hence "The 4 copies of the fraction 1/5 will be 4/5".
To learn more about the arithmetic operators,
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Translate the expression: Four-fifths of the sum of 4 and y (pls hurry it's timed)
[tex]\frac{4}{5}(4+y)[/tex]
55% of what number is 1100? Which of the following proportions could be used to
solve this problem?
Answer:
1100
55100=1100 x 55100
=1100x
Step-by-step explanation:
Hope it is helpful...
The required value of unknown number a would be 2000.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
WE need to determine 55% of what number is 1100.
Let the unknown number is a. then we get;
55% of a = 1100
55/100 of a = 1100
55/100 x a = 1100
Cross mulitiplication, we get;
55a = 1100 x 100
55a = 110000
Divide by 55, we have;
a = 110000/ 55
a = 10000/ 5
a = 2000
Therefore, the required value of unknown number a would be 2000.
More can be learned about proportions at;
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t-$5.60=$1.04
what does t =?
Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex] x = \frac{2*\sqrt{3}}{3} [/tex]
Step-by-step explanation:
Reference angle = 30°
Opposite side = x
Adjacent side = 2
Apply the tan trigonometric function, thus:
[tex] tan (30) = \frac{opp}{adj} [/tex]
[tex] tan (30) = \frac{x}{2} [/tex]
[tex] 2 * tan (30) = x [/tex]
[tex] 2 * \frac{1}{sqrt{3}} = x [/tex] (tan 30 = 1/√3)
[tex] \frac{2}{sqrt{3}} = x [/tex]
Rationalize
[tex] \frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x [/tex]
[tex] \frac{2*\sqrt{3}}{3} = x [/tex]
How many fourths are in 3 fourths?
Answer:
12 one fourths
Step-by-step explanation:
Answer:
12 one fourths
Step-by-step explanation:
There 3 × 1 1/4 = 3 × 4 = 12 one fourths in 3
what is x + 3 1/2 = 9
Answer:
Step-by-step explanation:
x+3 1/2=9
x=9-7/2
x=(18-7)/2=11/2
x=5 1/2
Answer:
3 1/2 + 5 1/2= 9.
Step-by-step explanation:
Hope this helps? im sorry if it doesn't :)
There are 35 boxes with 48 base balls in each box how many baseballs are there altogether
Answer:
35x48=1680
Step-by-step explanation:
1680
Can only like terms be combined?
Answer:
yes
Step-by-step explanation:
only like terms can be combined
Answer:
yes. If it's variables, then only like variables can be combined. If it's fractions, then they must be converted to a common denominator before combining.
Step-by-step explanation:
Please solve this problem tnx....
Answer:
27.50
Step-by-step explanation:
Since it is 16.50 each and they bought 5 packets total an easy way to solve this problem would be that you multiply 16.50 × 5 which will give you how much the total cost of the candy would be:
16.50 × 5 = 82.50
Since that is the total amount you would then divide 82.50 by 3 since Mary and her friends all split the cost three ways (since there are three of them):
82.50 ÷ 3 = 27.50
Which will give you your answer.
Please answer and explain I’ll mark brainliest!!!!!
Answer:
See below
Step-by-step explanation:
Problem 1
If n is the smallest of the consecutive integers, the next integer would be n+1.
Problem 2
The equation is terms of n is going to be
s = n + n + 1 + n + 2 + n+3
Problem 3
Collect like terms on the right
s = 4n + 6
Problem 4
4n + 6 = s Subtract 6 from both sides
4n = s - 6 Divide by 4
n = (s - 6)/4
Problem 5
Solve for n when s = 2174
n = (2174 - 6)/4
n = 2168 / 4
n = 542
check
n = 542
n + 1 = 543
n + 2 = 544
n + 3 = 545
Total 2174 Just as it should
This circle graph shows how a college student breaks down her study time
in typical week. If the student spends 40 hours per week studying, how
much time is spent studying Math and French.
French, 23%
English, 11%
Art, 14%
Math, 21%
History, 31%
what is 10 2/3 in inproper numbers
Answer:
[tex]\frac{32}{3}[/tex]
Step-by-step explanation:
you simply multiply the bottom number times the whole number:
10*3 =30
then add the top number:
30+2=32
and finally, you put the 32/3
Jake bought four peaches. The first two peaches weigh 2/6 of a pound, what could the third and fourth peach weigh in 1/6 of a pound?
Help please. 4. Solve for x.
please help i will mark brainliest if you are right
Answer:
56
Step-by-step explanation:
Range is difference between greatest and least. This is 97 - 41 = 56
A radius is a segment that connects any pount on the circle to the center of that circle
Answer:
This is true.
Step-by-step explanation:
No matter where you put the dot on the circumference, the radius will connect to the center, and be the same distance.
For what value of the constant c is the function f continuous on
(−∞,∞) where
f(b) = { cb + 9 if b ≤ 3
c(b)² − 9 if b > 3
9514 1404 393
Answer:
c = 3
Step-by-step explanation:
In order for the function to be continuous at b=3, the left and right limits must be the same. In short, we must have ...
c(3) +9 = c(3²) -9
18 = 6c . . . . . . . . add 9-3c to both sides
3 = c . . . . . . . . . . divide by 6
Function f is continuous when c=3.
Please help me you don't have to show your work just pls tell me the answer
Answer:
K should be the answer mark me Brainest :)
Step-by-step explanation:
Please help ASAP if you know how. Thanks so much
Answer:
A.6.21
Step-by-step explanation:
A=2, b=-10, c=-5
Which equation represents the line that has a slope of 4 and passes through the points (2,7)
Answer:
The answer is y = 4x - 1.
Step-by-step explanation:
The answer is y = 4x - 1.
Step-by-step explanation:
☆The equation we'll be using: y = mx + b
☆Since we already have the slope. we have to find the y-intercept.
☆\begin{gathered}y = mx + b \\ \\ 7 = 4(2) + b \\ 7 = 8 + b \\ \frac{ - 8 = - 8 \: \: \: \: \: \: \: \: \: \: \: }{ - 1 = b \: \: \: \: \: \: \: \: \: \: } \end{gathered}
y=mx+b
7=4(2)+b
7=8+b
−1=b
−8=−8
HALPPPPP!!
The equation of direct proportion y=kx is given by the table. Find the coefficient k, copy the table and fill it in
Answer:
20,2,0,-4,-.0625
Step-by-step explanation
3*-4=-12
depending on which side its on you can multiply or divide by -4
K= -4
A store donated cases of crayons to a day care center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many crayons did the center receive?
Answer:
They recieved 192 crayons?
Answer:
The Answer Is 192
Step-by-step explanation:
