NewStats: 3,262,808 , 8,178,220 topics. Date: Tuesday, 03 June 2025 at 04:26 PM 4ozf

uwc buddy , keep practicing,,,happy solving

dprinz99:

tanks bro,datx a grt job.ah reali appreciate.
going tru dis problm,ah c DAT we sum pple r witch in mathz,(u inclusiv)
I solved to a certain point but didn't knw wen to apply d quad formula.

The height h in feet of a model rocket above the ground t seconds after lift-off is given by
h(t) = −5t² + 100t, if 0 ≤ t ≤ 20

And 0, if t > 20


1. Find and interpret h(10) and h(60).


2. Solve h(t) = 375 and interpret your answers.

Mathecian:
The height h in feet of a model rocket above the ground t seconds after lift-off is given by
h(t) = −5t² + 100t, if 0 ≤ t ≤ 20

And 0, if t > 20


1. Find and interpret h(10) and h(60).


2. Solve h(t) = 375 and interpret your answers.

1)
h(10)=-5(10)²+100(10)
=-5(100)+1000
=500
implies that at t=10(tenth seconds), the rocket is 500feet in the air.
h(60)=0
because wen we insert dat into d equation we get a negative result.
and its not posible for a height to neative. dat implies dat at t=60 the rocket is already back to the ground and its at rest hence height is zero(0)

2)h(t)=375
implies
375=-5(t)²+100(t)
dividing tru by 5 givs
75=-t²+20t
making t² positive by taking all values from the RHS to the LHS, we have
t²-20t+75=0
by factorization we av
t²-5t-15t+75=0
t(t-5)-15(t-5)=0
(t-5)(t-15)=0
thus t=5 or t=15
implies that
at the 5th seconds(t=5) the rocket was taking off(moving upward)
while at the 15th seconds(t=15) the rocket was already on its way back to the ground.
(not good at physics(always d C candidate) so pardon my poor interpretation)

ladokuntlad:

1)
h(10)=-5(10)²+100(10)
=-5(100)+1000
=500
implies that at t=10(tenth seconds), the rocket is 500feet in the air.
h(60)=0
because wen we insert dat into d equation we get a negative result.
and its not posible for a height to neative. dat implies dat at t=60 the rocket is already back to the ground and its at rest hence height is zero(0)

2)h(t)=375
implies
375=-5(t)²+100(t)
dividing tru by 5 givs
75=-t²+20t
making t² positive by taking all values from the RHS to the LHS, we have
t²-20t+75=0
by factorization we av
t²-5t-15t+75=0
t(t-5)-15(t-5)=0
(t-5)(t-15)=0
thus t=5 or t=15
implies that
at the 5th seconds(t=5) the rocket was taking off(moving upward)
while at the 15th seconds(t=15) the rocket was already on its way back to the ground.
(not good at physics(always d C candidate) so pardon my poor interpretation)

It's not really physics, but Exponential Modelling in Mathematics.


Good job though.

Find and simplify the diference quotients for the following functions

1. f(x) = x² − x − 2

2. g(x) = 3/( 2x + 1)

ladokuntlad:

1)
h(10)=-5(10)²+100(10)
=-5(100)+1000
=500
implies that at t=10(tenth seconds), the rocket is 500feet in the air.
h(60)=0
because wen we insert dat into d equation we get a negative result.
and its not posible for a height to neative. dat implies dat at t=60 the rocket is already back to the ground and its at rest hence height is zero(0)

2)h(t)=375
implies
375=-5(t)²+100(t)
dividing tru by 5 givs
75=-t²+20t
making t² positive by taking all values from the RHS to the LHS, we have
t²-20t+75=0
by factorization we av
t²-5t-15t+75=0
t(t-5)-15(t-5)=0
(t-5)(t-15)=0
thus t=5 or t=15
implies that
at the 5th seconds(t=5) the rocket was taking off(moving upward)
while at the 15th seconds(t=15) the rocket was already on its way back to the ground.
(not good at physics(always d C candidate) so pardon my poor interpretation)

Good job though but I don't totally agree with the h (60) interpretation because at t =60 the height is negative doesn't necessarily means the rocket is back to ground level it might as well means the time function is not valid for state or height of rocket at t=60

stlaibrowne:

Good job though but I don't totally agree with the h (60) interpretation because at t =60 the height is negative doesn't necessarily means the rocket is back to ground level it might as well means the time function is not valid for state or height of rocket at t=60

am 10000000000000000% sure the rocket is back to d ground
dats y h=0 at that point

ladokuntlad:


am 10000000000000000% sure the rocket is back to d ground
dats y h=0 at that point

I am 100000000000000% sure you need to read the question again. Because actually at t=60 h is not zero but h=-12000 and that's not zero. Get my point ?

stlaibrowne:


I am 100000000000000% sure you need to read the question again. Because actually at t=60 h is not zero but h=-12000 and that's not zero. Get my point ?

well in pure mathematics and some other mathematical methods question
we have something called boundary value problems(BVP) wich involves aving some constraints/conditions on a question.
Well i wont go further dan dat.

let the referees in the house come and second ur opinion or mine

@ Ladokuntlad, it is possible for height to be negative in physics particularly when an object is going up or down. If you get a negative height, it means the object is going against gavity( I.e moving up).

naturalwaves:
@ Ladokuntlad, it is possible for height to be negative in physics particularly when an object is going up or down. If you get a negative height, it means the object is going against gavity( I.e moving up).

i strongly disagree as pertaining to this particular question above.
Why?
since some certain condition as been given so its already under a constraint, which cant make us say its going against gravity (-g) even at -g(going against gravity) we don't get our distance to b negative.
I stand to b corrected though.
Bt for dis particular question above.
d reason i gave is still very legit until someone comes here and give His/Her own clear reason

ladokuntlad:

i strongly disagree as pertaining to this particular question above.
Why?
since some certain condition as been given so its already under a constraint, which cant make us say its going against gravity (-g) even at -g(going against gravity) we don't get our distance to b negative.
I stand to b corrected though.
Bt for dis particular question above.
d reason i gave is still very legit until someone comes here and give His/Her own clear reason

Well, I am yet to check out the question itself, just saw where you wrote it can't be negative. Will check out the question tomorrow.

ladokuntlad:

well in pure mathematics and some other mathematical methods question
we have something called boundary value problems(BVP) wich involves aving some constraints/conditions on a question.
Well i wont go further dan dat.

let the referees in the house come and second ur opinion or mine

I understand boundary value as also we do set up elementary volume for some mathematical method. But in the case rocket is going up against gravity. And the operation is defined with a time function. Definitely it is possible the time function fail to work

Mathecian:

Find and simplify the diference quotients for the following functions

1. f(x) = x² − x − 2

2. g(x) = 3/( 2x + 1)

Difference quotients is given by

f(x)=(f(x+h)-f(x))/h

1)f(x)= x² − x − 2
let us solve in bits for simplification
f(x+h)= (x+h)² − (x+h) − 2
= (x²+2xh+h²)-x-h-2
Now lets put all dis into the difference quotients calling it a function k(x)
thus
k(x)=((x²+2xh+h²)-x-h-2-(x² − x − 2))/h
=(2xh+h²-h)/h
=2x+h-1

2)
g(x) = 3/( 2x + 1)
K(x)=(3(2(x+h)+1)^-1-3(2x+1)^-1)/h
=(3/(2(x+h)+1)-3/(2x+1))/h
=((3(2x+1)-3(2(x+h)+1))/(2(x+h)+1)(2x+1)h)
=((6x+3-6x-6h-3)/(2(x+h)+1)(2x+1)h)
=-6h/(2(x+h)+1)(2x+1)h
=-6/(2(x+1)+1)(2x+1)

stlaibrowne:

Good job though but I don't totally agree with the h (60) interpretation because at t =60 the height is negative doesn't necessarily means the rocket is back to ground level it might as well means the time function is not valid for state or height of rocket at t=60

Not that I don't understand you but you should read what ladokuntlad wrote above succinctly, they ar constraints in exponential modelling.
H(60) is zero because of the strict inequality in the problem above.

stlaibrowne:


I am 100000000000000% sure you need to read the question again. Because actually at t=60 h is not zero but h=-12000 and that's not zero. Get my point ?

I think you should be the one to read the question. Ladokuntlad is very correct. The height function is a parabola. It was also stated in the question that h(t)=0 when t>20. my question to you is, is 60 greater than 20? if yes please apologize to Ladokuntlad (lol). It is worth adding that at t=0 and 20 the height is zero.(this implies it goes up reaches its maximum at t=10 before coming down) the function is also symmetric. Pls try to read questions and understand the interpretation before solving. Cheers

masperano:


I think you should be the one to read the question. Ladokuntlad is very correct. The height function is a parabola. It was also stated in the question that h(t)=0 when t>20. my question to you is, is 60 greater than 20? if yes please apologize to Ladokuntlad (lol). It is worth adding that at t=0 and 20 the height is zero.(this implies it goes up reaches its maximum at t=10 before coming down) the function is also symmetric. Pls try to read questions and understand the interpretation before solving. Cheers

Yeah sure I just read the question again at t>20 h will always be zero.

Mathecian:



Not that I don't understand you but you should read what ladokuntlad wrote above succinctly, they ar constraints in exponential modelling.
H(60) is zero because of the strict inequality in the problem above.

masperano:

I think you should be the one to read the question. Ladokuntlad is very correct. The height function is a parabola. It was also stated in the question that h(t)=0 when t>20. my question to you is, is 60 greater than 20? if yes please apologize to Ladokuntlad (lol). It is worth adding that at t=0 and 20 the height is zero.(this implies it goes up reaches its maximum at t=10 before coming down) the function is also symmetric. Pls try to read questions and understand the interpretation before solving. Cheers

Tank u my brodas oo.
Even if i no sabi physics or word problem.
I really tried in dis case

ladokuntlad:

1)
h(10)=-5(10)²+100(10)
=-5(100)+1000
=500
implies that at t=10(tenth seconds), the rocket is 500feet in the air.
h(60)=0
because wen we insert dat into d equation we get a negative result.
and its not posible for a height to neative. dat implies dat at t=60 the rocket is already back to the ground and its at rest hence height is zero(0)
[/b]

actually h(60)=0 ONLY because of the stated boundary condition, not for ANY of the reasons u stated...have a nice day&kudos

stlaibrowne:

Good job though but I don't totally agree with the h (60) interpretation because at t =60 the height is negative doesn't necessarily means the rocket is back to ground level it might as well means the time function is not valid for state or height of rocket at t=60

ur interpretation is right sir...nice criticism!!!

Setting the record straight. Weldone Laplacian for the mopping up.

it might as well means the time function is not valid for state or height of rocket at t=60

Laplacian:

ur interpretation is right sir...nice criticism!!!

I vehemently disagree with this, the interpretation is wrong. Even if we assume there is no boundary condition (i.e h(t)#0 when t>20). h(60) being negative can be interpreted. (It simply means you are on the cliff when you shoot the rocket, and by time 20 units the rocket reaches the height of the cliff before descending (i.e it is 12000 units below the cliff at time 60 units).

So I have a joke great mathematicians(told by my pde lecturer(he is Russian)).

A team of Engineers from England visited and they saw a black goat. They came back and said "all goats are black in "

Next a team of Physicist visited and they saw a black goat.They came back and said "there is one black goat in ".

Finally a team of Mathematicians visited and saw a black goat. They came back and said. "There exist at least one black goat in which is black".

Moral of the story always check the rightness of your statement as a scientist.

Cheers my people

K

masperano:
So I have a joke great mathematicians(told by my pde lecturer(he is Russian)).

A team of Engineers from England visited and they saw a black goat. They came back and said "all goats are black in "

Next a team of Physicist visited and they saw a black goat.They came back and said "there is one black goat in ".

Finally a team of Mathematicians visited and saw a black goat. They came back and said. "There exist at least one black goat in which is black".

Moral of the story always check the rightness of your statement as a scientist.

Cheers my people

Only a mathematician can tell such joke, cos it's all in favour of mathematicians. Funny, clever joke


Today I was thinking something. The ratio of the circumference of a circle to its diameter is a number that doesn't occur in nature any other way, besides as a ratio of circumference to diameter. Isn't that just spectacular? Or am I wrong? Does it have other occurences?

Y=10cos(at)exp(-mt) .
use newton raphson method to determine the time when the displacement fall to 4.5
m=0.7, a=4.5
initial guess ti=0.1

thanks all

MathsChic:

Only a mathematician can tell such joke, cos it's all in favour of mathematicians. Funny, clever joke


Today I was thinking something. The ratio of the circumference of a circle to its diameter is a number that doesn't occur in nature any other way, besides as a ratio of circumference to diameter. Isn't that just spectacular? Or am I wrong? Does it have other occurences?

Yea good question, this month i randomly bumped into a paper that stated how some Rochester University physicists by serendipity discovered the number Pi(i had thought it was always associated with geometric figures) in quantum mechanics while calculating the energy state of hydrogen atom.

You may want to take a look at this website: http://www.gizmodo.com.au/2015/11/theres-a-hidden-connection-between-pi-and-quantum-mechanics/ or better still the article from here: http://scitation.aip.org/docserver/fulltext/aip/journal/jmp/56/11/1.4930800.pdf?expires=1448498047&id=id&accname=guest&checksum=F3D4695391CC583C50ECDCDA779B6C74

The size of the article is beyond the allowable size on Nairaland else i would have attached it.

iameugene:
our jamb whatsapp group num: 07019747550

Since I've been studying Mathematics, I just realised there is cramming in Mathematics in my 3rd year. It suck!

LordPherule:
Since I've been studying Mathematics, I just realised there is cramming in Mathematics in my 3rd year. It suck!

Oh, words are not enough to describe how much I hate cramming. Especially when it comes to definitions.

Gurus help me solve dis set question
1)A company employs 100 people,65 of whom are men. 60 people,including all the women,are paid weekly.How many of the men are paid weekly?
2)In a village all the people speak hausa or English or both.97% speak hausa and 64% speak English,what percentage speak both languages?
3)In a survey of villagers,it is found that 20% of the people have visited kano and 25%have visited portharcourt. If 5% have been to both cities,what percentage have visited neither place?

saipn:
Gurus help me solve dis set question
1)A company employs 100 people,65 of whom are men. 60 people,including all the women,are paid weekly.How many of the men are paid weekly?
2)In a village all the people speak hausa or English or both.97% speak hausa and 64% speak English,what percentage speak both languages?
3)In a survey of villagers,it is found that 20% of the people have visited kano and 25%have visited portharcourt. If 5% have been to both cities,what percentage have visited neither place?

1. 25.
2. 61%.
3. 60%