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)

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: