1. find the value of P in the ratio below
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.
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.