Node.js

show that px^2 -4x + p = 2px - 3x^2 -1 has real root(s) for all real values of p

when i find the discriminant it is equal to 4 i think im doing somthing wrong because im sure you are suppose to get an expression for p so that u can indeed show that the roots are real for all real values of p

plzzzzzzzzzz help me, any help is appreciated :) thank u

Express the following in the form lnx = ax + b and find a and b

1) xe^-x = 3.46 ans a=1 and b=0.9

2) (xe^x)^2 = 30e^-x ans a=-1.5 and b =1.7

thank u allot i really appreciate it coz i seriously cant solve this

solve the simultaneous equation

ln(3x-y) = 2ln6 - ln9 and e^2x/e^y = e

thank you :)

By using the appropriate substitutions, solve(s) for x

2e^x = 7√e^x - 3 ans 1.39 and 2.20

thank u so much

find x to three significant figures

4(3^2x) = e^x ans =-1.16

solve the equation to 4 significant figures

2log[3](x) = log[4](x) + 1 ans 2.484

A cylinder of base radius r cm and height h cm is inscribed in a sphere of radius 6 cm, centre 0

Show that h^2 + 4r^2 =144

thank u in advance :)

A metal sheet of area 100 cm^2 is used to manufacture a closed cylinder can. Find to two significant figures , the largest possible volume of the can.

thank u :)

implicit differentiation :

for the implicit function obtain dy/dx in terms of x and y.hence find the gradient at p (1, 2)

a) 1/x - 1/y = 4 (method 1 )

x^-1 - y^-1 = 4

-1x^-2 +1y^-2dy/dx =0

1/y^2dydx =1/x^2

dy/dx= y^2/x^2 (correct answer)

at p (1, 2) dy/dx= 4/1

= 4

b) 1/x -1/y = 4 (method 2)

y - x = 4xy (multiplying by xy)

dy/dx -1 = 4x dy/dx + 4y

(4x-1)dy/dx=-1-4y

dy/dx=(-1-4y)/(4x-1) (suppose to be correct)

at p(1 , 2) dy/dx=-9/3

=-3

my question is why is the derivative of method 1 not equal to method 2 plzzzzz provide me with an answer as to why it is wrong or the correct answer if i made an error

thank you in advance :)

implicit differentiation :

for the implicit function obtain dy/dx in terms of x and y.

1/x - 1/y = 4

( ANSWER = y^2 / x^2 ) when i set the equation as x^-1 - y^-1 = 4 (which is correct)

(ANSWER= 1 - y/ 4x+1 when i multiply the equation by xy the remove the fraction

my question is why is the second answer wrong? if u set values for x an y u will see that it is plzzzzz provide me with an answer as to why it is wrong or the correct answer if i made an error

thank you in advance :)

Calculate the gradient(s) of the curve at the point(s) where it crosses the given line

y = (x+2) / x , y = x(the given line)

answer is -2 and -1/2

how do u arrive at the answer ?? thank u in advance btw :)

Estoy buscando mi gato - I am looking for my cat.

¿Qué gato? - WHAT cat? (i.e. you have a cat?)

Estoy buscando mi gato - I am looking for my cat.

¿Cuál gato? - WHICH cat? (i.e. of the several cats you have, which one are you looking for?)

Qué is used with nouns not Cuál. can anyone plzzz tell me why Cuál was used as in ¿Cuál gato? is it wright?? or is it wrong?? an plzz suggest other ways of asking the question if it is thxxx

i can conjugate verbs in different tenses an stuff, but what i had always had troubles with is how do i say dance,play, cry etc... (as in the sentence stated below) instead of i cry or he cries etc..

example:

ella me hace "what" - she makes me cry (is this the use of commands im not familiar with those so i don't know)

in an unrelated question

i normally say ¿Cómo estás ? - how are you

but i have seen ¿Cómo estás tú? - how are you

i know sometimes tú is omitted but y is it placed after estás??? plzzzz help me

i learn to use it like this :

De quién es esta bolsa? - when were are talking about singular nouns

De quién son los zapatos? - when we are talking about a plural nouns

but i have seen it used like this :

De quiénes son estos zapatos? - when talking about plural nouns as well

¿Quienes son ellas?

my question is why is (quiénes) used instead of (quién son ) or together (quiénes son) plzzz help im so confused :(