Explanation

To find the perimeter of a semi-circle, we need to consider two parts:

1. The half of the circumference of the circle, which is $frac{1}{2} times 2pi r = pi r$.
2. The diameter of the circle, which is $2r$.

• The radius $r = 700$ meters.

1. Calculate the curved part (half of the circumference):

   $$text{Curved part} = pi times r = pi times 700 approx 3.1416 times 700 approx 2199.12 , text{m}$$

2. Add the diameter:

   $$text{Diameter} = 2 times r = 2 times 700 = 1400 , text{m}$$

3. Total perimeter:

   $$text{Perimeter} = text{Curved part} + text{Diameter} = 2199.12 , text{m} + 1400 , text{m} = 3599.12 , text{m}$$

4. Convert the result to kilometers:

   $$3599.12 , text{m} = 3.6 , text{km}$$

Explanation

Let the number of sweets Roni gives to Tony be x.

After giving x sweets: Roni will have 2 25−x sweets.

Tony will have 55+x sweets.

We want Tony to have four times as many sweets as Roni, so: 55 + x = 4 ( 25 − x )

1. Expand the equation:

   $$55 + x = 100 - 4x$$
   

2. Add $4x$ to both sides to combine the $x$-terms:

   $$55 + 5x = 100$$
   

3. Subtract 5 from both sides:

   $$\mathrm{<font\; color="\#0000ff">5</font>}\mathrm{<font\; color="\#0000ff">x</font>}<font\; color="\#0000ff">=</font>\mathrm{<font\; color="\#0000ff">45</font>}$$5x = 45
   

4. Solve for $x$:

   $$$$x=45/5=9x 
   

Explanation

The temperature in Murree at noon was 16.6°C, and at midnight, it was 20.4°C lower.

To find the temperature at midnight, subtract 20.4°C from the noon temperature:

$$16.6°C - 20.4°C = -3.8°C$$

Explanation

We know that:

1. x + y = 45
2. 4x = 5y - 9

From the first equation, we can express y in terms of x:

y = 45 - x

Substitute this into the second equation:

4x = 5(45 - x) - 9

Expand and simplify:

4x = 225 - 5x - 9

9x = 216

x = 24

Now, substitute x = 24 into the first equation:

24 + y = 45

y = 21

Therefore, the two parts are 24 and 21.

Explanation

• The son's current age be $x$
  
• The man's current age is 5 times the son's age, so the man's age is $5x$.

• Four years ago, the product of their age was 52.

Four years ago:

• The son's age was $x - 4$.
• The man's age was $5x-4$.

According to the problem, the product of their ages 4 years ago is 52:

$$(x-4)(5x-4)=52$$

1. Expand the left side:

   
   

Explanation

Let's define the ages of the three people:

• Let David's age be $D$.
• John's age is 4 years more than David's, so John's age is $D+4$.
• Joe's age is 2 years less than David's, so Joe's age is$D-2$.

The sum of their ages is given as 41:

$$(D)+(D+4)+(D-2)=41$$

1. Simplify the equation:

   $$D + D + 4 + D - 2 = 41$$ $$3D + 2 = 41$$

2. Subtract 2 from both sides:

   $$3D = 39$$

3. Divide both sides by 3:

   $$D = 13$$

So, David is 13 years old.

• John's age is $D + 4 = 13 + 4 = 17$ years.
• In 8 years, John's age will be: $$17 + 8 = 25 text{ years}$$

Explanation

Explanation

Explanation

Let's denote the total scholarship grant as "x".

The student spends:

• 15% on food: 0.15x
• 45% on tuition: 0.45x

So, after these expenses, he has:

x - 0.15x - 0.45x = 0.4x remaining.

He then spends 50% of this remaining amount on hostel fees:

0.5 * 0.4x = 0.2x

After this, he is left with Rs 8,000. So, we can set up the equation:

0.4x - 0.2x = 8000

Simplifying the equation:

0.2x = 8000

Dividing both sides by 0.2:

x = 40000

Therefore, the student's scholarship grant is Rs 40,000.

Explanation

1. 
   

2. $$a^2 + b^2 = 25 - 12 = 13.$$