1. find the value of P in the ratio below

Question

P:5=48:40
2. find the multiplication inverse of 0.8
3. A ladder 6m long leans against a wall and makes an angle of 50 degree with the wall. find the distance between the wail and the foot of the ladder, correct to two decimal places.

Answer 1

1. To find the value of P in the ratio, we can set up the proportion:

P/5 = 48/40

Then, cross-multiply and solve for P:

40P = 240

P = 240 / 40
P = 6

2. The multiplication inverse, or reciprocal, of 0.8 is the number that, when multiplied by 0.8, gives a product of 1. To find the reciprocal, divide 1 by the number:

1 / 0.8 = 1.25

So, the multiplication inverse of 0.8 is 1.25.

3. We'll use the trigonometric function of cosine to find the distance between the wall and the foot of the ladder:

cos(angle) = adjacent side (distance between the wall and the foot of the ladder) / hypotenuse (ladder length)

We can rearrange the equation to solve for the adjacent side:

Adjacent = Hypotenuse * cos(angle)

Adjacent = 6m * cos(50)

Using a calculator:

Adjacent ≈ 6m * 0.6427876

Adjacent ≈ 3.86m

So, the distance between the wall and the foot of the ladder is approximately 3.86 meters, correct to two decimal places.