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sineoko [7]
3 years ago
12

Help pls!! Find the marc GFD

Mathematics
1 answer:
Serhud [2]3 years ago
8 0
I believe it would be D 275!
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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
Solve the system of equations. 4y + 11x – 67 = 0 2y + 5x - 19 = 0 x= y=​
katen-ka-za [31]

Answer:

x = 29, y = -63

Step-by-step explanation:

Solve the following system:

{4 y + 11 x - 67 = 0 | (equation 1)

{2 y + 5 x - 19 = 0 | (equation 2)

Express the system in standard form:

{11 x + 4 y = 67 | (equation 1)

v5 x + 2 y = 19 | (equation 2)

Subtract 5/11 × (equation 1) from equation 2:

{11 x + 4 y = 67 | (equation 1)

{0 x+(2 y)/11 = -126/11 | (equation 2)

Multiply equation 2 by 11/2:

{11 x + 4 y = 67 | (equation 1)

{0 x+y = -63 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{11 x+0 y = 319 | (equation 1)

{0 x+y = -63 | (equation 2)

Divide equation 1 by 11:

{x+0 y = 29 | (equation 1)

{0 x+y = -63 | (equation 2)

Collect results:

Answer: {x = 29, y = -63

3 0
2 years ago
Read 2 more answers
The population of Clairette
masha68 [24]
The estimated amount of people in Clairette, Texas is roughly 55-65 people 
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3 years ago
How would you interpret the number of sars deaths as an area under a curve?
anyanavicka [17]
Check the attached file for the answer.

4 0
3 years ago
Henry can write 5 pages of his novel in 3 hours. At this rate, how many pages can Henry write in 8 hours
Ludmilka [50]

Answer:

13 novels

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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