The variable z varies jointly as the second power of x and the third power of y. When x equals 2 and y equals 2.4, z equals 31.5. Approximate the constant of variation to the nearest hundredth.

The constant of variation, k = 0.57

Step-by-step explanation:

We are given that z varies jointly as the second power of x (x²), and the third power of y (y³).

For a constant of variation, k, z can be written as

z = x²y³k.

We are also given

z = 31.5

x = 2

x = 2.4

31.5 = (2²)(2.4)³k

31.5 = 4×13.824k

31.5 = 55.296k

k = 31.5/55.296

= 0.57

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!