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why do we blink? Ans)Every time you blink, your eyelids spread a cocktail of oils and mucous secretions across the surface of the eye to keep your globes from drying out. Blinking also keeps eyes safe from potentially damaging stimuli, such as bright lights and foreign bodies like dust

A rectangular frame measures 195cm by 95cm does a 2.2m piece of wood fit diagonally and why ??

Hi, Are you familiar with the Mechanical Engineering mathematical principles of Impellers used in Compressors enough to assist me with a design problem involving the selection of Impeller styles?

I admit that my question are probably very academic, I still require help with the subject matter because I am trying to learn how to contemplate this type of engineering problem within the mathematical elements that govern their operations.

I have a few questions that I would like ask if maybe you are able to assist me in answering. I am a design student trying to work out the math behind how to redirect the flow of air out of the backside of the impeller wheel due to space restrictions.

Thinking about colour and the impact of colour on memory recall - what memory mechanisms are mediated by colour aids? How does colour stimuli increase recall of said stimuli, or what memory mechanisms could be argued to support this idea?

How do plants use anaerobic and aerobic respiration to survive?

Solve (D2-3D+2)y =x(x+4) and show that its general solution is given by y=Aex + Be2x +(x2/2) + (7x/2) + (19/4)

My work :

auxiliary eqn , m2 - 3m + 2= 0 m=1 , m=2

Reduced eqn : yn = Aex + Be2x

P.I. = 1/f(D)F(x) = (1/(D2-3D+2))(x(x+4))

P.I. = [(x2+4x) + ( (1/2)( 2- 3(2x) - 3(4) ) ) + (1/4)(92) )

P.I. = x2 + (4x/2) - (6x/4) - (5/2) + (18/4)

P.I. =(x2/2) + x + 8/4

General solution : y= Aex + Be2x + (x2/2) + x + 8/4

Could anyone point out my mistakes?

Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and z=0. Take boundary of the above triangular surface as the path of the line integral.

For the surface integral I got,

integrate [x=0 - 1] , [y=0 , 2-2x] ( (1/14)*(54 - 38x - 27y) dx dy )

I got the y limit setting z=0 in the plane equation , ==> (y/2) + x = 1==> 2x+y=2 ==> y=2x-2 (Am i correct???)

When working it the other way around using curl, i got Curl F = -i + 2k

N = unt normal vector to the surface =k

N.k = 2/7

(Curl F). N = -2/7

Fnally got the integrate [(-2/7) ÷ (2/7) dx dy] , limits : [x=0 - 1] , [y=0 , 2-2x]

Finally I got -1 as the answer here.

Could someone point out my mistakes please?

Many thanks!

write the required external CSS rules for the following :

Set the font size and font style , of the first bold word of all the paragraphs in a document into 14px and italic respectively.

Derive and draw the world relative supply curve for good 1, which relates the world relative supply of good 1 (q1/q2) to its relative price in world markets (p1/p2). Make sure to label your graph as comprehensively as possible.

Prove that (grad)2 f(r) = D2/dr2 + (2/r) Df/Dr

Where D2/dr2 refers to the second partial derivative of f , w.r.t. r and

Df/ Dr refers to partial derivative of f, w.r.t r

vector r = xi + yj + zk and f(r) is twice differentiable