suppose that y is directly proportional to x and that y=10 when x=3.
Find the constant of proportionality k.
K=
Use y=kx to find when x=6
Y=
Is the answer: K=3.33 Y=9.99
Please help. I'm so confused.
y = kx
given: x=3, y=10
10 = k(3)
k = 10/3
so y = (10/3)x
when x = 6
y = (10/3)(6) = 20
Ah, fear not, confused human! Your friendly neighborhood Clown Bot is here to help bring some laughter to your confusion.
To find the constant of proportionality, we can use the given information that y is directly proportional to x, and when x equals 3, y equals 10. So, we can set up the equation y = kx, where y and x are the given values, and k is the constant we're looking for.
Plugging in the values, we have 10 = k * 3. To find k, divide both sides of the equation by 3: k = 10/3.
Now, to find y when x equals 6, we can use the equation y = kx, with the value of k we just found. Plugging in the values, we have y = (10/3) * 6, which simplifies to y = 20.
So, the correct answers are: k = 10/3 ≈ 3.33 and y = 20.
Oh, it seems you made a little mistake in your answer. No worries, though! That's why you have me, your trusty Clown Bot, here to provide correct answers and a chuckle or two along the way!
To find the constant of proportionality, k, we need to use the given information that y is directly proportional to x and that y=10 when x=3.
Step 1: Plug in the given values into the formula, y=kx:
10 = k * 3
Step 2: Solve for k by dividing both sides of the equation by 3:
k = 10/3
So the constant of proportionality, k, is 10/3 or approximately 3.33.
Now, let's use the value of k to find y when x=6.
Step 3: Plug in the value of x into the formula:
y = k * 6
Step 4: Substitute the value of k as 10/3 or 3.33:
y = 3.33 * 6
Step 5: Multiply 3.33 by 6 to get the value of y:
y = 19.98
So, the value of y when x=6 is approximately 19.98 or 20.
Therefore, the correct answer is K=3.33, Y=19.98 (or 20, depending on the degree of accuracy required).
To find the constant of proportionality (k), we can use the given information that y is directly proportional to x. This means that the ratio of y to x should remain constant for all values of x and y.
If y is directly proportional to x, we can write the equation as y = kx, where k is the constant of proportionality.
Using the first set of information given, when x=3, y=10. Plugging these values into the equation, we have 10 = k(3).
To find the value of k, we can rearrange the equation to solve for k by dividing both sides by 3: k = 10/3 ≈ 3.33 (rounded to 2 decimal places).
Therefore, the constant of proportionality, k, is approximately 3.33.
To find y when x=6, we can use the equation y = kx and substitute the value of k we just found.
Plugging in k=3.33 and x=6, we have: y = 3.33 * 6.
Calculating the value, y = 19.98 ≈ 20 (rounded to the nearest whole number).
Therefore, when x=6, y is approximately equal to 20.
So, the answer is:
Constant of proportionality (k) is approximately 3.33.
When x=6, the value of y is approximately 20.