4b - 10 = 2 (2b - 5)
4b - 10 = 4b - 10
4b - 4b = -10 + 10
b = 0
Hence, b has only one answer so,
we can say that this equation has only one solution.
Answer: 2x + 5y = -5
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope.
The equation of the line given :
2x + 5y = 10
To find the slope , we will write it in the form y = mx + c , where m is the slope and c is the y - intercept.
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10/5
y = -2/5x + 2
This means that the slope is -2/5 ,the line that is parallel to this line will also have a slope of -2/5.
using the formula:
= m ( ) to find the equation of the line , we have
y - 1 = -2/5(x -{-5})
y - 1 = -2/5 ( x + 5 )
5y - 5 = -2 ( x + 5 )
5y - 5 = -2x - 10
5y + 2x = -10 + 5
therefore :
2x + 5y = -5 is the equation of the line that is parallel to 2x + 5y = 10
Answer:
y = -5x + 12
Step-by-step explanation:
10x + 2y = −2
-10x - 10x
_______________
2y = -10x - 2
__ ________
2 2
y = -5x - 1, [0, 12] ∥↷
12 = -5[0] + b
0
12 = b
y = -5x + 12
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Answer:
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Step-by-step explanation:
(x+8)(y+3)
The coordinates of the centroid are the average values of the - and -coordinates of the points that belong to the region. Let denote the bounded region. These averages are given by the integral expressions
The denominator is just the area of , given by
where we rewrite the integrand using the identities
Now, if
with , then
Find where this simpler sine curve crosses the -axis.
In the interval [0, 8], this happens a total of 5 times at
See the attached plots, which demonstrates the area between the two curves is the same as the area between the simpler sine wave and the -axis.
By symmetry, the areas of the middle four regions (the completely filled "lobes") are the same, so the area integral reduces to
The signs of each integral are decided by whether lies above or below axis over each interval. These integrals are totally doable, but rather tedious. You should end up with
Similarly, we compute the slightly more complicated -integral to be
and the even more complicated -integral to be
Then the centroid of is