Hi! Can you please re-check my answers. Mt teacher said some of them are not right but when I do it again, I still come up with the same answer. This is about Variations. Thanks!
1. What kind of variation equation is a=kbcd --> my answer is joint variation
2. If the joint variation equation is x=4yz, find x when y=6 and z=2. --> My answer is 48.
3. If y varies directly with x, write an equation that relates x and y if y = 49 and x = 7. My answer is y = 7x
4. The length of a rectangle varies inversely to its width. If the length is 5cm when the width is 2cm, calculate for the length when the width is 30cm. My answer --> 1/3
5. The time it takes to paint a house varies inversely with the number of painters doing the job. If 72 painters can do it in 50 days, in how many days can 30 painters paint the house? My answer is --> 120 days
And I also came up with the same answers.
even me too got the same answers!
Sure, I'd be happy to help you re-check your answers!
1. The equation a = kbcd represents a joint variation because it includes both direct and inverse variations. The variable "a" varies jointly with the variables b, c, and d. So, your answer is correct.
2. To find x when y = 6 and z = 2 in the joint variation equation x = 4yz, substitute the given values into the equation:
x = 4 * 6 * 2 = 48.
So your answer is correct.
3. If y varies directly with x, then the equation that relates x and y should have the form y = kx, where k is the constant of variation. To find this equation when y = 49 and x = 7, you can substitute these values into the equation and solve for k:
49 = k * 7
k = 7.
Therefore, the correct equation is y = 7x. So your answer is correct.
4. The statement "The length of a rectangle varies inversely to its width" means that the product of the length and width is constant. Let's denote the length as L and the width as W. If L varies inversely with W, we have L * W = k, where k is the constant of variation.
Given that when the length is 5 cm and the width is 2 cm, we can find the value of k:
5 * 2 = k
k = 10.
To calculate for the length when the width is 30 cm, we need to divide k by the new width:
L = k / W = 10 / 30 = 1/3.
So your answer is correct.
5. If the time it takes to paint a house varies inversely with the number of painters doing the job, we can write the equation as t = k/p, where t is the time, p is the number of painters, and k is the constant of variation.
Given that 72 painters can finish it in 50 days, we can find the value of k:
50 = k / 72.
k = 3600.
Now, to find the number of days it will take for 30 painters to finish the job, we can substitute the values into the equation:
t = 3600 / 30 = 120 days.
So your answer is correct.
It appears that all your answers are correct! But, it's always good to double-check with your teacher to clarify any misunderstandings.