Question

find the equation of the line with slope 4/3 and which passes through the mid -point of the line segment joining the points (3,-1) and ( 1,2). represent this line geometrically by taking at least three points on it​

Answer 1

Explanation:

Answer

Answered by

ApusApus

Answer:

1)

2)

3)

Step-by-step explanation:

Since we know that the segment joining the mid-points of two sides of a triangle is known as mid-segment of triangle. A triangle has three mid-segments.

1) Let us find midpoints of side ED and DF using midpoint formula.

Now let us find slope of line joining points (-1.5,2.5) and (-1,-0.5) using slope formula.

 

       

Now let us substitute our values in slope intercept form of the line to find y-intercept.

, where m= slope of the line, b= y-intercept.

 

 

Upon substituting m=-6 and b= -6.5 in slope intercept form of line, we will get,

Therefore, 1st equation that represents the mid-segment parallel to side EF of the given triangle will be .  

2) Let us find midpoint of segment EF.

Now let us find the slope of the line passing through points (1.5,1) and (-1,-0.5)

hope this helps ✌️❤️✌️

Answer 2

We develop a scaling model relating the friction forces between two polyelectrolyte brushes sliding over each other to the separation between grafted surfaces, number of monomers and charges per chain, grafting density of chains, and solvent quality. We demonstrate that the lateral force between brushes increases upon compression, but to a lesser extent than the normal force. The shear stress at larger separations is due to solvent slip layer friction. The thickness of this slip layer sharply decreases at distances on the order of undeformed brush thickness. The corresponding effective viscosity of the layer sharply increases from the solvent viscosity to a much higher value, but this increase is smaller than the jump of the normal force resulting in the drop of the friction coefficient. At stronger compression we predict the second sharp increase of the shear stress corresponding to interpenetration of the chains from the opposite brushes. In this regime the velocity-dependent friction coefficient between two partially interpenetrating polyelectrolyte brushes does not depend on the distance between substrates because both normal and shear forces are reciprocally proportional to the plate separation. Although lateral forces between polyelectrolyte brushes are larger than between bare surfaces, the enhancement of normal forces between opposing polyelectrolyte brushes with respect to normal forces between bare charged surfaces is much stronger resulting in lower friction coefficient. The model quantitatively demonstrates how polyelectrolyte brushes provide more effective lubrication than bare charged surfaces or neutral brushes.