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o-na [289]
3 years ago
14

Find the centroid of the region bounded by y = 3x^2, y = 0, x = 4

Mathematics
1 answer:
ANTONII [103]3 years ago
7 0
To determine the centroid, we use the equations:

x⁻ = 1/A (∫ (x dA)) 
y⁻ = 1/A (∫ (y dA)) 

First, we evaluate the value of A and dA as follows:

A = ∫dA
A = ∫ydx
A = ∫3x^2 dx
A = 3x^3 / 3 from 0 to 4
A = x^3  from 0 to 4
A = 64

We use the equations for the centroid,
x⁻ = 1/A (∫ (x dA)) 
x⁻ =  1/64 (∫ (x (3x^2 dx))) 
x⁻ =  1/64 (∫ (3x^3 dx)
x⁻ =  1/64 (3 x^4 / 4) from 0 to 4
x⁻ =  1/64 (192) = 3

y⁻ = 1/A (∫ (y dA)) 
y⁻ = 1/64 (∫ (3x^2 (3x^2 dx))) 
y⁻ = 1/64 (∫ (9x^4 dx) 
y⁻ = 1/64 (9x^5 / 5) from 0 to 4
y⁻ = 1/64 (9216/5) = 144/5

The centroid of the curve is found at (3, 144/5).
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I don’t know how to do this
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Answer:

Option 1

Step-by-step explanation:

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3 0
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Round 76.3 to the nearest whole number
cestrela7 [59]
76.3 rounded to the nearest whole number is 76
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3 years ago
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Which of the following values would complete the ordered pair if the point is on the graph of f (x) = -3x + 2 ?
Scrat [10]

Answer: the y-coordinate that completes the point is 5.


Explanation:


An ordered pair (x, y) indicates the x-and-y coordinates of a general point, where x is the input value of a function and y is the output value.


The output value is y = f(x) and must be found applying the rule (function) to the given input value.


In this case the rulte is f(x) = - 3x + 2, and the input value, x,  is - 1 (the first value of the ordered pair).


This is the mathematical procedure:

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5 0
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A line passes through the points (-1, -6) and (-4, 3). What is the equation of this line in slope-intercept form?
g100num [7]

Since we have two ordered pairs, we can find the slope by plugging them into (y2-y1)/(x2-x1) which translates to (3-(-6))/(-4-(-1))=9/-3=-3

Since the slope is -3, we have the equation y=-3x+b, but we don't know b. So we plug in values for x and y and solve for b.

-6=-3(-1)+b

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So the y-intercept is -9 and the full equation is y=-3x-9 which means A is the only correct answer.

Hope this helped!

4 0
4 years ago
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