Evaluate (3)/(sqrt(0.0136)) − (3.72)² correct to 4 s.f.

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5. Evaluate $\frac{3}{\sqrt{0.0136}} - (3.72)^2$ correct to 4 s.f.

Note: As I do not have access to physical tables, I will perform the calculations directly and round the final answer to 4 significant figures.

Evaluate $\sqrt{0.0136}$ .
$\sqrt{0.0136} \approx 0.11662076$
Evaluate $\frac{3}{\sqrt{0.0136}}$ .
$\frac{3}{0.11662076} \approx 25.72457$
Evaluate $(3.72)^2$ .
$(3.72)^2 = 13.8384$
Perform the subtraction.
$25.72457 - 13.8384 = 11.88617$
Round the result to 4 significant figures.
$11.88617 \approx 11.89$
The value is $\boxed{11.89}$ .

6. Simplify as far as possible $\frac{3}{x-y} - \frac{1}{x+y}$
Find a common denominator, which is $(x-y)(x+y)$ .
Rewrite each fraction with the common denominator.
$\frac{3}{x-y} - \frac{1}{x+y} = \frac{3(x+y)}{(x-y)(x+y)} - \frac{1(x-y)}{(x+y)(x-y)}$
Combine the numerators over the common denominator.
$\frac{3(x+y) - 1(x-y)}{(x-y)(x+y)}$
Expand the numerator and the denominator.
Numerator: $3x + 3y - x + y = 2x + 4y$
Denominator: $(x-y)(x+y) = x^2 - y^2$
Write the simplified expression.
$\frac{2x+4y}{x^2-y^2}$
The simplified expression is $\boxed{\frac{2x+4y}{x^2-y^2}}$ .

7. Fifteen men working for eight hours a day can complete a certain job in exactly 24 days. For how many hours a day must sixteen men work in order to complete the same job in exactly 20 days.

This is an inverse proportion problem. The total work done is constant.
Let $M$ be the number of men, $H$ be the hours per day, and $D$ be the number of days.
The total work is proportional to $M \times H \times D$ .
Set up the equation based on the given information.
$M_1 \times H_1 \times D_1 = M_2 \times H_2 \times D_2$
Given:
$M_1 = 15$ men
$H_1 = 8$ hours/day
$D_1 = 24$ days

$M_2 = 16$ men
$H_2 = ?$ hours/day
$D_2 = 20$ days
Substitute the known values into the equation.
$15 \times 8 \times 24 = 16 \times H_2 \times 20$
Calculate the left side of the equation.
$15 \times 8 \times 24 = 120 \times 24 = 2880$
Simplify the equation and solve for $H_2$ .
$2880 = 320 \times H_2$ $H_2 = \frac{2880}{320}$ $H_2 = 9$
Sixteen men must work 9 hours a day.

The number of hours per day is $\boxed{9 \text{ hours}}$ .

Evaluate (3)/(sqrt(0.0136)) - (3.72)² correct to 4 s.f.

Step-by-step solution

Evaluate $\sqrt{0.0136}$ .

Evaluate $\frac{3}{\sqrt{0.0136}}$ .

Evaluate $(3.72)^2$ .

Perform the subtraction.

Round the result to 4 significant figures.

Find a common denominator, which is $(x-y)(x+y)$ .

Rewrite each fraction with the common denominator.

Combine the numerators over the common denominator.

Expand the numerator and the denominator.

Write the simplified expression.

Set up the equation based on the given information.

Substitute the known values into the equation.

Calculate the left side of the equation.

Simplify the equation and solve for $H_2$ .

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