Help with chemistry and maths questions! (1 Viewer)

[x.Exhaust.x]

1. Describe the solubility of sucrose and cellulose.

The dissacharide sucrose is very soluble in water while the polysaccharide cellulose is insoluble in water. Sucrose is soluble due to the polar interactions between the molecules, with like dissolving like. Cellulose is insoluble in water due to its high molar mass and being very large molecules.

Is the above correct?

2. What are the differences between the solubility of NaCl and Sucrose?

I know that they're both soluble, but I'm not sure how to describe the main differences between both compounds in terms of solubility and bonding.

3. Find the locus of the point that is equidistant from the point (2,5) and the line y=-3.

4. Find the equation of the locus of point P(x,y) that moves so that is always equidistant from the point (-1,3) and the line y=-5

Please point any flaws in my working out:

A(-1,3)
Let point B be (0,-5) on the directrix. (I sense this part is wrong)
Let P(x,y) be a point on the locus.

PA=PB
PA^2=PB^2
(x+1)^2+(y-3)^2=x^2+(y+5)^2
x^2-2x+1+y^-6y+9=x^2+y^2+10y+25
2x-6y+10=10y+25
2x-16y-15=0

The answer has the x^2 in front of my equation, but isn't that cancelled?

5. Find the value of k in the quadratic equation x^2-3x+k+1=0 if the roots are consecutive numbers.

6. The cubic equation 2x^3+x^2-15x-18=0 has three roots, one of which is positive and equals the product of the other two roots. Find the roots of the equation.

And this is why I shouldn't be doing 4U lol . Thanks in advance.

 

[moshizzle]

1. Describe the solubility of sucrose and cellulose.

The dissacharide sucrose is very soluble in water while the polysaccharide cellulose is insoluble in water. Sucrose is soluble due to the polar interactions between the molecules, with like dissolving like. Cellulose is insoluble in water due to its high molar mass and being very large molecules.

Is the above correct?

yeppp

2. What are the differences between the solubility of NaCl and Sucrose?

I know that they're both soluble, but I'm not sure how to describe the main differences between both compounds in terms of solubility and bonding.

in terms of bonding, NaCl has ionic bonds, whereas sucrose has molecular bonds. the solubility of NaCl is due to the ion-dipole attraction of Na+ and Cl- ions with the water molecules (dissociation of its ions), but for sucrose, the solubility is due to the same bonds existing in both sucrose and water.

3. Find the locus of the point that is equidistant from the point (2,5) and the line y=-3.

4. Find the equation of the locus of point P(x,y) that moves so that is always equidistant from the point (-1,3) and the line y=-5

Please point any flaws in my working out:

A(-1,3)
Let point B be (0,-5) on the directrix. (I sense this part is wrong)
Let P(x,y) be a point on the locus.

PA=PB
PA^2=PB^2
(x+1)^2+(y-3)^2=x^2+(y+5)^2
x^2-2x+1+y^-6y+9=x^2+y^2+10y+25
2x-6y+10=10y+25
2x-16y-15=0

The answer has the x^2 in front of my equation, but isn't that cancelled?

5. Find the value of k in the quadratic equation x^2-3x+k+1=0 if the roots are consecutive numbers.

6. The cubic equation 2x^3+x^2-15x-18=0 has three roots, one of which is positive and equals the product of the other two roots. Find the roots of the equation.

And this is why I shouldn't be doing 4U lol . Thanks in advance.

not in the mood for maths. just had my exam today :angry:

 

[clintmyster]

for 3)

sqroot (5-y)^2 + (2-x)^2 = sqroot (-3-y)^2 + (x-x)^2
then square both sides
i got something like x^2 - 4x -16y +20 = 0

for 4)


the value for the x coordinate is just x because its an unknown so when you you are using the distance forumla it becomes (x-x) so then you get 0 and therefore a get a solution with x^2 in it. As for the y^2 they cancel because you got one on each side. Answer should be x^2 + 16y +2x -15 =0

for 5)

5. Find the value of k in the quadratic equation x^2-3x+k+1=0 if the roots are consecutive numbers.

if the roots are consecutive numbers then it would alpha and alpha + 1.

therefore sum of roots = alpha + alpha + 1 = 2alpha +1 =-b/a = 3
therefore alpha = 1 so the roots are just 1 and 2.

now product of roots = alpha x (alpha + 1) = 1 x 2 = 2 = c/a = (k+1)/1
therefore k = 1

for 6)

product of roots = 9
since alpha = beta x gamma, alpha^2 = 9, therefore alpha is 3 because its positive
sum of roots = -1/2.
sub in alpha being 3 and replace either beta or gamma with 3/gamma or beta.
Should get quadratic and have solutions of -3/2 and -2.

and im done xD

 

[ratcher0071]

5. Find the value of k in the quadratic equation x^2-3x+k+1=0 if the roots are consecutive numbers.

5) let roots be t and t+1
SUM OF ROOTS:
t+t+1=3
2t=2
t=1
therefore roots are 1 and 2
x^2-3x+(k+1)=0
(x-2)(x-1)=0
(k+1)=-1 x -2
k+1=2
k=1

3. Find the locus of the point that is equidistant from the point (2,5) and the line y=-3.

(x-2)^2 + (y-5)^2 = (y+3)^2
x^2 -4x+4 +y^2-10y+25 = y^2 +6y +9
x^2 -4x -16y+20=0

 

[x.Exhaust.x]

Thanks moshizzle, clintmyster and ratcher .

 

[ratcher0071]

Thanks moshizzle, clintmyster and ratcher .