A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Do these quantities vary directly or inversely?
The area of a rectangle is given by the formula length times width. In this case, the area of the first rectangle is 72 cm times 56 cm, which equals 4032 cm². The area of the second rectangle is also 4032 cm², but its width is 21 cm. Since the area remains the same while the width changes, these quantities vary inversely.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Find the constant of variation.
To find the constant of variation, you need to compare the length and width of the two rectangles.
The first rectangle has a length of 72 cm and a width of 56 cm. The second rectangle has the same area but a different width of 21 cm.
Let's denote the constant of variation as k. Since the two rectangles have the same area, we can set up the following equation:
72 cm * 56 cm = k * 21 cm
Simplifying the equation, we get:
4032 cm² = 21k cm
Dividing both sides by 21 cm, we have:
k = 4032 cm² / 21 cm
k ≈ 192 cm
Therefore, the constant of variation is approximately 192 cm.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Find the constant of variation. If x and y vary inversely, then x·y is constant.
You are correct. Since the area of a rectangle is equal to the product of its length and width, the product of the length and width of both rectangles will be constant if they have the same area.
For the first rectangle with length 72 cm and width 56 cm, the product is:
72 cm * 56 cm = 4032 cm²
For the second rectangle with width 21 cm and an unknown length, the product is also:
21 cm * length = 4032 cm²
From this, we can find the length of the second rectangle:
length = 4032 cm² / 21 cm
length ≈ 192 cm
Therefore, the constant of variation between the length and width is approximately 192 cm.
No!
Apologies for the mistake in my previous response. Let's solve the problem correctly:
Given that the first rectangle has a length of 72 cm and a width of 56 cm, and the second rectangle has the same area, but its width is 21 cm.
The formula for the area of a rectangle is length times width.
For the first rectangle, the area is:
A1 = 72 cm * 56 cm = 4032 cm²
For the second rectangle, the width is 21 cm and the area is also 4032 cm². Let's denote the length of the second rectangle as L2.
So, the area of the second rectangle is:
A2 = L2 * 21 cm = 4032 cm²
To find the constant of variation, we can set up the following equation:
A1 = A2
4032 cm² = L2 * 21 cm
Now, we can solve for L2:
L2 = 4032 cm² / 21 cm
L2 ≈ 192 cm
Therefore, the constant of variation between the length and width is approximately 192 cm.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. What iis the length if the second rectangle?
To find the length of the second rectangle, we use the formula for the area of a rectangle, which is length times width.
The first rectangle has a length of 72 cm and a width of 56 cm, so its area is:
Area1 = 72 cm * 56 cm = 4032 cm²
The second rectangle has the same area but a width of 21 cm. Let's denote the length of the second rectangle as L.
The area of the second rectangle is:
Area2 = L * 21 cm
Since the two rectangles have the same area, we can set up the equation:
4032 cm² = L * 21 cm
To find the length of the second rectangle, we divide both sides of the equation by 21 cm:
L = 4032 cm² / 21 cm
L ≈ 192 cm
Therefore, the length of the second rectangle is approximately 192 cm.
If three chickens in three days laid three eggs, how many eggs will 12 chickens in 12 days lay?
If three chickens in three days laid three eggs, it means that each chicken lays one egg in three days.
So, if we have 12 chickens in 12 days, we can assume that each chicken will still lay one egg in twelve days.
Therefore, 12 chickens in 12 days will lay 12 eggs.
Ah! No! Please try again. And give the right answer this time, will you?
Apologies for the mistake in my previous response. Let's solve the problem correctly this time:
If three chickens in three days laid three eggs, it means that each chicken lays one egg in three days.
So, if we have 12 chickens, we can assume that each chicken still lays one egg in three days.
To find out how many eggs the 12 chickens will lay in 12 days, we can set up a proportion:
3 chickens / 3 days = 12 chickens / 12 days
Cross-multiplying, we get:
3 chickens * 12 days = 12 chickens * 3 days
36 = 36
So, the number of eggs that 12 chickens will lay in 12 days will still be 3 eggs.
God, no! Try again!
Apologies once again for the confusion. Let's solve the problem correctly:
If three chickens in three days laid three eggs, we can infer that each chicken lays one egg in three days.
To find out how many eggs 12 chickens will lay in 12 days, we can set up a proportion:
3 chickens / 3 days = 12 chickens / 12 days
Using the property of direct variation, we can simplify the proportion:
(3/3) = (12/12)
This simplifies to:
1 = 1
Therefore, 12 chickens in 12 days will also lay 12 eggs.
Oh just...just try again, idiot! I'm on a time crunch here!
I apologize if my previous responses were not helpful. Let's solve the problem correctly this time:
If three chickens in three days laid three eggs, that means that each chicken lays one egg in three days.
To find out how many eggs 12 chickens will lay in 12 days, we can set up a ratio:
3 chickens : 3 days = 12 chickens : 12 days
To find the number of eggs, we can multiply both sides of the ratio by the number of days:
3 days * (12 chickens / 3 chickens) = 12 days * (12 chickens / 3 chickens)
Simplifying, we get:
12 eggs = 12 eggs
Therefore, 12 chickens in 12 days will lay 12 eggs.
Give a diiferent freaking answer this freaking time, freak!
Apologies for any frustration my previous responses may have caused. Let's solve the problem correctly:
If three chickens in three days laid three eggs, we can infer that each chicken lays one egg in three days.
Now, let's think about the rate at which the chickens lay eggs.
If three chickens lay three eggs in three days, that means that they lay one egg per day collectively. Therefore, each chicken lays 1/3 of an egg per day.
So, if we have 12 chickens, the total number of eggs they will lay in one day is:
12 chickens * (1/3 of an egg per chicken) = 12/3 = 4 eggs per day
If we want to find out how many eggs the 12 chickens will lay in 12 days, we can multiply the number of eggs laid per day by the number of days:
4 eggs per day * 12 days = 48 eggs
Therefore, 12 chickens in 12 days will lay 48 eggs.