Find the centroid of the region bounded by the given curves. give your answers correct to two decimal places. y = x^3, x + y = 10, y = 0

The centroid is the point ()=(4.32,2.62)

Step-by-step explanation:

We graph the functions given in the attached picture. As you can see the region R is surrounded by the functions:

y=x³

y=10-x

y=0

This region can be divided by 2, where the first is delimited by y=x³ (0≤x≤2) and the second is y=10-x (2≤x≤10).

The centroid of region is given by:

First, we have to find the value of

=

=(16/4-0)+(100-50-20+2)=4+32=36

Now we find :

=

=

Then, we find :

=

=

Hence,

The centroid is the point ()=(4.32,2.62)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

step-by-step explanation: the answer is 27. first multiply .32 by 25 which equals 8. then add 8 to 25 which gives you 33. then you subtract that from 6 since she gave 6 to her brother.

,, add !