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olga nikolaevna [1]
3 years ago
14

Sqrtx^2+6x+9 if x≥3 please help quick idk how to do this at all

Mathematics
1 answer:
katrin [286]3 years ago
7 0

Answer:

x+3

Step-by-step explanation:

sqrt(x^2+6x+9)

factor

We know this is a perfect square trinomial

sqrt(( x+3)^2)

Taking the square root of a square

x+3

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find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0
11 months ago
Please help me with this
Illusion [34]

Answer:

2x for the first term

The whole thing is 2x+3

Step-by-step explanation:

Think of it like normal division

What will get the closest answer to 2x^2+x?

2x*x-1=2x^2-2x

Now the expression is 3x-3 so if you but 3 than it becomes 3x-3 which would be a remainder of 0

5 0
3 years ago
paul was given 2760$ to buy toys for a group of children.A)what would be the greatest number of toys paul could buy if each toy
Radda [10]

Answer:

2760 ÷ 9 = x

x = 306

306(9) = 2754

2760 - 2754 = 6

Have a good day! :)

7 0
2 years ago
Question 3
Katyanochek1 [597]

Answer:

oooooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

5 0
2 years ago
Hank bought 5 CDs for $64.75. If each CD cost the same price, how much did each cost?
dem82 [27]
64.75/5= $12.96

you simply divide 64.75 by 5 
6 0
2 years ago
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