Alan

"Suppose that the average of the six values,(3,-2,x,x-2,-1,2) , is equal to 2. Find the value of x"

(3 - 2 + x + x-2 - 1 + 2)/6 = 2

2x = 2*6

x = 6

If f(x) = 0.41*ln(x+1)+28 then

(i) f(0) = 0.41*ln(0+1)+28 → f(0) = 0.41*0 + 28 → 28      because ln(1) = 0

(ii) f(100) = 0.41*ln(100 + 1) + 28 → 0.41*ln(101) + 28    Use a calculator to evaluate this.

We have:

\(\frac{x}{y}=\frac{3}{7}\)

which means that \(y=\frac{7}{3}x\)

Use this in y - x = 56 to get \(\frac{7}{3}x-x=56 \rightarrow\frac{4}{3}x=56\rightarrow x=\frac{3\times56}{4}\rightarrow x=3\times14\rightarrow x=42\)

Use this in y - x = 56 to get  y - 42 = 56 or y = 98

Density = Mass/Volume, so just divide one by the other,   Using your values the result will have units of kg/m³

^.

False.

\((\frac{1}{64})^{5/6} \rightarrow(\frac{1}{64^{1/6}})^5\rightarrow(\frac{1}{2})^5\rightarrow \frac{1}{32}\)

Total:    25q + 5n = 525          where q = number of quarters, n = number of nickels

Also:    q = 0.1n                  number of quarters = 10% number of nickels    (10% = 0.1)

Replace q in the first equation by 0.1n:      

25*0.1*n + 5n = 525  or

2.5n + 5n = 525 or

7.5n = 525 so

n = 525/7.5  or 

n = 70

There are 70 nickels.

Need 10exp(-0.17x) to be interpreted as 10*e^(-0.17x) rather than 10^(-0.17x).

Here are graphs showing two solutions and the corresponding numerical values obtained using Newton-Raphson:

Heads:                humans + horses = 74

Legs:                   2*humans + 4*horses = 196

Multiply the Heads equation by 2:   2*humans + 2*horses = 148

Subtract this from the Legs equation term by term:     2*horses = 48   Hence horses = 24

Put this back into the original Heads equation:    humans + 24 = 74     Hence humans = 50

5x + 2y = 4        ...(1)

6x - 3y = -7       ...(2)

Multiply all terms in (1) by 3 and all terms in (2) by 2.  This will make the y terms the same in both equations.

15x + 6y = 12     ...(3)

12x - 6y = -14    ...(4)

Now add (3) and (4) term by term to get:

27x = -2

x = -2/27

Put this back into (1)

5*(-2/27) + 2y = 4

Multiply by 27

-10 + 54y = 108

54y = 118

y = 118/54  or y = 59/27