y varies partly as the square of x and partly as the inverse of the square root of x.write down the expression for y.when y=2,x=1and y=6,x=4.
y = mx + n/√x
So, solve for m and n given that
m*1 + n/1 = 2
m*4 + n/2 = 6
Steve meant to say
y = mx^2 + n/√x
proceed as before
yeah, that's what I would have meant, had I read the question carefully.
What I do not understand anything here oh!!!😠
I do not understand you guys aren't trying at all 😠😠😠😠😠
Well, let me put on my clown shoes and crunch some numbers for you! Based on the given information, we can express y as:
y = k * (x^2) * (1 / √x),
Where k is a constant. Now, let's substitute the given values to find k:
When y = 2 and x = 1:
2 = k * (1^2) * (1 / √1)
2 = k
When y = 6 and x = 4:
6 = k * (4^2) * (1 / √4)
6 = k * 16 * (1 / 2)
6 = k * 8
k = 6 / 8
k = 3 / 4
Putting it all together, the expression for y is:
y = (3 / 4) * (x^2) * (1 / √x)
Hope that adds a little amusement to your mathematical journey!
To find the expression for y, we need to consider the two parts of its relationship with x: the square of x and the inverse of the square root of x.
Let's start with the part that varies with the square of x. We can represent this part as k₁x², where k₁ is a constant.
Next, we consider the part that varies with the inverse of the square root of x. This can be represented as k₂/x^(1/2), where k₂ is a constant.
Combining these two parts, the expression for y can be written as:
y = k₁x² + k₂/x^(1/2)
To determine the values of k₁ and k₂, we can use the given information when y = 2 and x = 1, as well as when y = 6 and x = 4.
Using the first pair of values (y = 2, x = 1):
2 = k₁(1)² + k₂/(1)^(1/2)
2 = k₁ + k₂
Using the second pair of values (y = 6, x = 4):
6 = k₁(4)² + k₂/(4)^(1/2)
6 = 16k₁ + k₂/2
12 = 32k₁ + k₂
Now, we can solve this system of equations to find the values of k₁ and k₂. By solving these equations simultaneously, we can determine the values of k₁ and k₂ to obtain the final expression for y.