I really dk how to do them,only 2 questions pls anyone help thanks
17)The number of hours N required to dig a certain hole is inversely proportional too the number of men available X.When 6 men are digging, the hole takes 4 hours.Find the time taken when 8 men are available.If it takes 1/2 hour to dig a hole, how many men are there?
19)The force of attraction F between 2 magnets varies inversely as the square of the distance d between them. When the magnets are 2cm apart, the force of attraction is 18 newtons.How far apart are they if the attractive force is 2 newtons?
nx = k, a constant
So, you want to find x such that
8x = 6*4
Fd^2 = k
You want d such that
2d^2 = 18*2^2
Omg thank you so much Mr/Ms oobleck for the steps
Sure, I can help you solve these two questions.
For question 17, let's start by understanding the relationship between the number of hours required to dig a hole and the number of men available. The problem states that it is inversely proportional, which means that as one variable increases, the other decreases and vice versa.
Let's denote the number of hours needed to dig a hole as N and the number of men as X.
Given that when 6 men are digging, the hole takes 4 hours, we can write the following equation:
N = k/X, where k is a constant of proportionality.
To find the value of k, substitute the given values:
4 = k/6
Multiply both sides by 6:
24 = k
Now we have the equation N = 24/X to represent the relationship.
To find the time taken when 8 men are available, substitute X = 8 into the equation:
N = 24/8
N = 3 hours
Therefore, when 8 men are available, it would take 3 hours to dig the hole.
Next, let's solve question 19. We are given that the force of attraction F between two magnets varies inversely as the square of the distance d between them.
Let's denote the force of attraction as F and the distance between the magnets as d.
Using the inverse square law, we can write the following equation:
F = k/d^2, where k is a constant of proportionality.
Given that when the magnets are 2 cm apart, the force of attraction is 18 newtons, we can write the equation as:
18 = k/2^2
18 = k/4
Multiply both sides by 4:
72 = k
Now we have the equation F = 72/d^2 to represent the relationship.
To find how far apart the magnets are if the attractive force is 2 newtons, substitute F = 2 into the equation:
2 = 72/d^2
Multiply both sides by d^2:
2d^2 = 72
Divide both sides by 2:
d^2 = 36
Take the square root of both sides:
d = 6 cm
Therefore, the magnets are 6 cm apart if the attractive force is 2 newtons.
I hope this helps!