X is partly varies as y and as partly as the cube root of y. If x=2 where y=8 and x=3 and y=27.find x when y=81
x = ay+b∛y
So, using your two data points, you can find a and b by solving
8a+2b = 2
27a+3b = 3
That means that a=0, b=1 and
x = ∛y
Seems kind of strange, but if there are no typos, it is what it is.
x^3 = 81
X = 4.3267.
To find the value of x when y is equal to 81, we need to determine the relationship between x and y based on the given information.
The problem states that x partly varies as y and partly as the cube root of y. This means that x can be expressed as the product of these two parts.
Let's write the equation for this relationship:
x = (k * y) * (m * ∛y)
Here, k and m represent constants of proportionality.
Now, we can substitute the given values x = 2, y = 8 into the equation to find the value of k:
2 = (k * 8) * (m * ∛8)
2 = 8k * 2m
Dividing both sides by 16:
1/8 = k * m
Next, we substitute the second set of values x = 3, y = 27 into the equation to find the value of m:
3 = (k * 27) * (m * ∛27)
3 = 27k * 3m
Dividing both sides by 81:
1/27 = k * m
Since k * m is a constant, we can equate the two expressions for k * m:
1/8 = 1/27
To solve for k, we can multiply both sides of the equation by 8:
k = 8/27
Now that we know the value of k, we can find the constant m:
1/8 = (8/27) * m
1/8 * 27/8 = m
27/64 = m
Now that we have determined the values of k and m, we can find x when y = 81 using the equation:
x = (k * y) * (m * ∛y)
x = (8/27) * 81 * (27/64 * ∛81)
Simplifying further:
x = (8/27) * 81 * (27/64 * 3)
x = 8 * 3 * 3
x = 72
Therefore, when y is equal to 81, x is equal to 72.