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vladimir1956 [14]
3 years ago
12

A function is created to represent the amount of texts sent each month. What restrictions would be made to the range?

Mathematics
1 answer:
Ksju [112]3 years ago
5 0

Answer:

frttt7

[T434444 it's a

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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
What is the answer to graphing this equation y= -4x
MAXImum [283]

Answer:

x=0

Step-by-step explanation:

7 0
2 years ago
Simplify 9i(2+3i)
viktelen [127]
Simplify 9i(2+3i):
9i×2=18i
9i×3i=27i

18i+27i
3 0
3 years ago
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(5.2x + 36.4x + 52)/ (2.6x +13)
g100num [7]
Combine like terms in the first set and get
41.6x +52/2.6x + 13

I got 16x + 4
4 0
3 years ago
Please please help please
Readme [11.4K]

Step-by-step explanation:

its .86 which is closer to .87

so choose the first one

7 0
2 years ago
Read 2 more answers
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