Alan

The answer to question 16 isn't, perhaps, as simple as the person who set the question might have thought.  Here are some links that discuss the problem; some like thermal conductivity, some like specific heat!!

$$$$\frac{3}{4}x+\frac{5}{8}=4x$$\\
Subtract $\frac{3}{4}x$ from both sides to get
$$ \frac{5}{8}=3\frac{1}{4}x$$\\
We can write $3\frac{1}{4}$ as the improper fraction: $\frac{13}{4}$ so
$$\frac{5}{8}=\frac{13}{4}x$$\\
Multiply both sides by $\frac{4}{13}$ to get $$\frac{5}{8}\times\frac{4}{13}= x$$ or $$x=\frac{5}{26}$$$$

if x is the basic price we must add 7% to this.  As a fraction 7% is 7/100.  As a decimal number this is 0.07, so the total to be paid is x + 0.07x (which can also be written as 1.07x).  This must equal $45, so 1.07x = 45; divide both sides by 1.07 to get x:

$${\mathtt{x}} = {\frac{{\mathtt{45}}}{{\mathtt{1.07}}}} \Rightarrow {\mathtt{x}} = {\mathtt{42.056\: \!074\: \!766\: \!355\: \!140\: \!2}}$$

or x = $42.06 to the nearest penny.

You can do this using the calculator here (I assume the 500 is 500°)

$${\mathtt{x}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{500}}^\circ\right)}\right)} \Rightarrow {\mathtt{x}} = -{\mathtt{50.000\: \!000\: \!000\: \!002^{\circ}}}$$

This is a fourth quadrant value.  Could also have a third quadrant value:

x = 180°+50° = 230°

Check:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left(-{\mathtt{50}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{230}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{500}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

(-50° can also be written as 310°)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{310}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

(w + 2)*(w + 5) = w² + 7w + 10, so if this equals zero, then there are two possible values of w, namely w = -2 and w = -5

Suppose the question was |N| = 3

Then N could be 3 because |3| is 3, or N could be -3 because |-3| is 3.

Now replace N by 7/5x - 12.

Good, thorough explanation ND!

-2x - 4 = 8x - 6

Add 6 to both sides  

-2x +2 = 8x

Add 2x to both sides

2 = 10x

Divide both sides by 10

2/10 = x

or x = 2/10

or x = 0.2

An error in the upper limit Aziz (you replaced the correct -4 with +8 in the last step!):

Q1001.  

The following image should help here:

Q will be 88*|e|.

Q2014.

Use the standard equation for force, F, (as in my first post above) with q1 = 4|e| and q2 = 8|e|. The distance, r, is √(3.3² + 6.9²) mm (You might want to change this into metres to make sure your units are consistent).

The angle of interest, θ, is tan^-1(3.3/6.9) (which I get to be 25.56°, not 27.4°), giving the component of force along the x-axis as F*cos(θ).

NB k ≈ 9E+9  not 9E-9.

The particles act on each other with the same magnitude force (opposite directions):- Newton's 3rd law of motion.