Please, help Me with this

The equation of a parabola is given by (x-2)²=32(y+1). Find
i. The vertex
ii. The focus
iii. The equation of the directrix
iv. The length of the Latus Rectum

tags: benbuks, doubleDx, Laplacian, dejt4u, tohero, efficiencie, all math generals and sergeants

jackpot:
Please, help Me with this

The equation of a parabola is given by (x-2)²=32(y+1). Find
i. The vertex
ii. The focus
iii. The equation of the directrix
iv. The length of the Latus Rectum

tags: benbuks, doubleDx, Laplacian, dejt4u, tohero, efficiencie, all math generals and sergeants

Comparing it to (x-h)²=4p(y-k)
So that
Vertex=(h,k)
Focus=(h,k+p)
Directrix is (y=k-p)
Lenght of lactus rectum=(4p)

The question is equivalent to
(x-2)²=4*8(y-(-1))

Hence,
Vertex=(2,-1)
Focus=(2,7)
Directrix is at y=-9
Lenght... =32

Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

sorbentcrooner:
Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

Are you sure u typed in all the values correctly? because the answer I have gotten is a decimal and I think I ought not to have decimals since the others are integers. Confirm please.

AlphaMaximus:

Are you sure u typed in all the values correctly? because the answer I have gotten is a decimal and I think I ought not to have decimals since the others are integers. Comfirm please.

Your solution might be right. It is not compulsory to have a whole no as an answer. Just convert your decimal part to terms of Minutes and Seconds

tohero:

Your solution might be right. It is not compulsory to have a whole no as an answer. Just convert your decimal part to terms of Minutes and Seconds

sorbentcrooner:
Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

alright,here it is:
let the fluid dissipation time of the first,second and third pipes be x,y and z respectively. from the info,when work is done(the filling of the tank) jointly by the first and second pipes the time taken is equivalent to the time taken by the third pipe working independently.
mathematically,the formula for the time taken to complete work when two entities work jointly is: xy/x+y.......in that case, we have that:
xy/x+y=z.......(1)
Again,it was stated that the second pipe is 5hrs faster than the first and 18hrs slower than the third, mathematically:
y=x-5, thus x=y+5.....(2)
And,
y=z+18, thus , z= y-18...(3)
substituting (2) and (3) into (1) and simplifying, we have:
y²-36y-90=0, and solving the quadratic equation ,we have that y=38.374.....recall that x=y+5, therefore,x=38.347+5=43.347hrs......thus the time required by the first pipe is 43.347hrs......for accuracy, it's 43.34698995hrs

AlphaMaximus:

let the fluid dissipation time of the first,second and third pipes be x,y and z respectively. from the info,when work is done(the filling of the tank) jointly by the first and second pipes the time taken is equivalent to the time taken by the third pipe working independently.
mathematically,the formula for the time taken to complete work when two entities work jointly is: xy/x+y.......in that case, we have that:
xy/x+y=z.......(1)

r u sure equation (i) is correct??

Drniyi4u:

r u sure equation (i) is correct??

yes,I'm sure.

AlphaMaximus:

Are you sure u typed in all the values correctly? because the answer I have gotten is a decimal and I think I ought not to have decimals since the others are integers. Confirm please.

I thought as much

AlphaMaximus:

alright,here it is:
let the fluid dissipation time of the first,second and third pipes be x,y and z respectively. from the info,when work is done(the filling of the tank) jointly by the first and second pipes the time taken is equivalent to the time taken by the third pipe working independently.
mathematically,the formula for the time taken to complete work when two entities work jointly is: xy/x+y.......in that case, we have that:
xy/x+y=z.......(1)
Again,it was stated that the second pipe is 5hrs faster than the first and 18hrs slower than the third, mathematically:
y=x-5, thus x=y+5.....(2)
And,
y=z+18, thus , z= y-18...(3)
substituting (2) and (3) into (1) and simplifying, we have:
y²-36y-90=0, and solving the quadratic equation ,we have that y=38.374.....recall that x=y+5, therefore,x=38.347+5=43.347hrs......thus the time required by the first pipe is 43.347hrs......for accuracy, it's 43.34698995hrs

V/T₁ + V/T₂ = V/T₃ .............(i)

Where V/T is the rate of flow

T₂ = T₁ - 5 = T₃ + 18
T₂ = T₁ - 5
T₃ + 18 = T₁ - 5
T₃ = T₁ - 23

Substituting into (i)

V/T₁ + V/(T₁ - 5) = V/(T₁ - 23)
1/T₁ + 1/(T₁ - 5) = 1/(T₁ - 23)
(2T₁ - 5)/(T₁² - 5T₁) = 1/(T₁ - 23)

T₁² - 46T₁ + 115 = 0

T₁ = 43.347 hrs or 2.653 hrs

Hailings Sir @AlphaMaximus
I got the latest Oxford Advanced Learners Dictionary for your comments

@ PatEinstEin ( m ), AlphaMaximus

this's. benbuks. speaking ...

greet thee. men & brethren..

happy solving...

PatEinstEin:

I thought as much

V/T₁ + V/T₂ = V/T₃ .............(i)

Where V/T is the rate of flow

T₂ = T₁ - 5 = T₃ + 18
T₂ = T₁ - 5
T₃ + 18 = T₁ - 5
T₃ = T₁ - 23

Substituting into (i)

V/T₁ + V/(T₁ - 5) = V/(T₁ - 23)
1/T₁ + 1/(T₁ - 5) = 1/(T₁ - 23)
(2T₁ - 5)/(T₁² - 5T₁) = 1/(T₁ - 23)

T₁² - 46T₁ + 115 = 0

T₁ = 43.347 hrs or 2.653 hrs

hmmmm....a welcome approach...looks more technical than mine...

PatEinstEin:
Hailings Sir @AlphaMaximus
I got the latest Oxford Advanced Learners Dictionary for your comments

agentofchange1:
@ PatEinstEin ( m ), AlphaMaximus

this's. benbuks. speaking ...

greet thee. men & brethren..

happy solving...

I hail you Sir Ben....

AlphaMaximus:

hmmmm....a welcome approach...looks more technical than mine...

i prefer urs tho,i seems to understand it easily

wow! It has really been long....years i surpose.........nice work all .........*still following from the sidelines*..........#busytimes

f**k!...I just hate maths...can the world end already?!

sorbentcrooner:
Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

sorbentcrooner:
Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

sorbentcrooner:
Hello house , kindly help out with ds. Thanks in anticipation:
A tank is filled by three pipes with uniform flow. The
first two pipes operating simultaneously fill the tank
in the same time during which the tank is filled by
the third pipe alone. The second pipe fills the tank 5
hours faster than the first pipe and 18 hours slower
than the third pipe. The time required by the first is?

question long like this

AlphaMaximus:
I hail you Sir Ben....

yes. boss ....nice job..

how far you na ?

[color=#990000][/color]which math text book does it best in term of thorough explanation which math text book does it best in term of thorough explanation

yusuflaw07:
[color=#990000][/color]which math text book does it best in term of thorough explanation which math text book does it best in term of thorough explanation

Comprehensive mathematics

Kentnickole:


Comprehensive mathematics

u know anything about engineering mathematics by k a stroud

yusuflaw07:
u know anything about engineering mathematics by k a stroud

Yea! Thats also very good for engineering students.

Kentnickole:


Yea! Thats also very good for engineering students.

Kentnickole:


Yea! Thats also very good for engineering students.

yea.. m an engineering student

yusuflaw07:
yea.. m an engineering student

For your mind now oooo!

tohero:


Comparing it to (x-h)²=4p(y-k)
So that
Vertex=(h,k)
Focus=(h,k+p)
Directrix is (y=k-p)
Lenght of lactus rectum=(4p)

The question is equivalent to
(x-2)²=4*8(y-(-1))

Hence,
Vertex=(2,-1)
Focus=(2,7)
Directrix is at y=-9
Lenght... =32

confam!

Please, help Me with this


Does the differential equation y"+sin(y')=0 has a degree?

If Yes, what is the degree?

If No, explain why.


tags: benbuks, agentofchange1, tohero, doubleDx, Laplacian, dejt4u,
tohero, efficiencie, all math generals and
sergeants.

jackpot:
Please, help Me with this


Does the differential equation y"+sin(y')=0 has a degree?

If Yes, what is the degree?

If No, explain why.


tags: benbuks=, agentofchange1, tohero, doubleDx, Laplacian, dejt4u,
tohero, efficiencie, all math generals and
sergeants.

hay. my angel its me ben. I've deactivated the benbuks account ...

its a second order. non-linear D.E .... with degree 1

jackpot:
Please, help Me with this


Does the differential equation y"+sin(y')=0 has a degree?

If Yes, what is the degree?

If No, explain why.

YES! All differential equations has a degree! Some might not be seen easily until you rationalise them.

In your case, the degree is one. Because one (1) is the power of the highest order(y'') in your differential equation.

So I would define a DEGREE as the power of the highest order of a differential equation after it has been rationalised.

tohero:

YES! All differential equations has a degree! Some might not be seen easily until you rationalise them.
In your case, the degree is one. Because one (1) is the power of the highest order(y'') in your differential equation.
So I would define a DEGREE as the power of the highest order of a differential equation after it has been rationalised.

What is the degree of the differential equation
sin(y'')+y'=0.?

Tags: agentofchange1, doubledx, tohero

jackpot:
What is the degree of the differential equation
sin(y'')+y'=0.?

Tags: agentofchange1, doubledx, tohero

One of the not easily seen degrees! Do some little combos using the sin-squares and u may get a result.

Mind you, differential equations are usually models of a real life situation, you can't just form them. I wonder what kind of physical change will have such!



Anyways, its a new year. So happy new year.

jackpot:
What is the degree of the differential equation
sin(y'')+y'=0.?

Tags: agentofchange1, doubledx, tohero

It's a 2nd order nonlinear ODE with degree 1 . Happy new year to y'all!

doubleDx:


It's a 2nd order nonlinear ODE with 1 degree. Happy new year to y'all!

why is it nonlinear? because of the "sin" ?