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3 years ago

How to solve by the square root property

Mathematics

1 answer:

nata0808 [166]3 years ago

4 0

First, you want to divide both sides by 3 to isolate your variable. You get x^2 = 9. The square root of x^2 and 9 equals x = 3.

x = 3 is your answer.

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If 3x+2y=18 find x and y for which the product xy takes its maximum value

grin007 [14]

Answer:

(x, y) = (3, 4.5)

Step-by-step explanation:

You want to find x and y such that xy is a maximum subject to the constraint that 3x+2y=18.

<h3>Objective function</h3>

The objective function f(x, y) = xy is most easily maximized if it can be written in terms of one variable only. Solving the constraint equation for y, we have ...

3x +2y = 18

2y = 18 -3x

y = 1/2(18 -3x) = (3/2)(6 -x)

Then the objective function is ...

f(x) = x(3/2)(6 -x)

<h3>Maximum</h3>

We recognize this as the equation of a parabola that opens downward, and has zeros at x=0 and x=6. Its line of symmetry is halfway between those, at x = 3. That is the location of the maximum of the objective function.

The corresponding y-value is ...

y = (3/2)(6 -3) = 9/2 = 4.5

The values of x and y that maximize their product are (x, y) = (3, 4.5).

<em>Additional comment</em>

In the attached graph, the larger the product, the farther away the curve is from the origin. The product is maximized subject to the constraint when the curves are tangent to each other. That point of tangency is (x, y) = (3, 4.5).

5 0

1 year ago

The binary operation* is defined on the set R of real numbers by X*Y = 3x + 3y - xy for all X , y E R. determine on the terms of

torisob [31]

Answer:

This is the Answer

Step-by-step explanation:

Pls mark as brainliest

3 0

1 year ago

Factor completely x3y6 – 64

alexandr402 [8]

Answer:

x 3 y 6 − 64

is the difference of two cubes and can be factored in the following pattern.

a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 )

a 3

factors to a

b 3

factors to b

The pattern of the signs follows the acronym SOAP

S = same sign as the cubes

O = opposite sins of the cubes

AP = always positive

x 3 y 3

factors to xy

factors to 4

x 3 y 3 − 64 = ( x y − 4 ) ( x 2 y 2 + 4 x y + 16 )

Step-by-step explanation:

4 0

3 years ago

If x+y=12 and xy=15,find the value of (x^2+y^2)

Mice21 [21]

Answer: $x^2+y^2=\dfrac{105\pm 18\sqrt6}{2}$

<u>Step-by-step explanation:</u>

EQ1: x + y = 12 --> x = 12 - y

EQ2: xy = 15

Substitute x = 12-y into EQ2 to solve for y:

(12 - y)y = 15

12y - y² = 15

0 = y² - 12y + 15

↓ ↓ ↓

a=1 b= -12 c=15

$.\ y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\.\quad =\dfrac{-(-12)\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}\\\\\\.\quad =\dfrac{12\pm \sqrt{144-120}}{2}\\\\\\.\quad =\dfrac{12\pm \sqrt{24}}{2}\\\\\\.\quad =\dfrac{12\pm 2\sqrt{6}}{2}\\\\\\.\quad =6\pm \sqrt{6}$

Now, let's solve for x:

$xy=15\\\\x(6\pm\sqrt6)=15\\\\x=\dfrac{15}{6\pm\sqrt6}\\\\\\x=\dfrac{15}{6\pm\sqrt6}\bigg(\dfrac{6\pm\sqrt6}{6\pm\sqrt6}\bigg)=\dfrac{6\pm \sqrt6}{2}$

Lastly, find x² + y² :

$y^2=(6\pm \sqrt6)^2\quad \rightarrow \quad y^2=36\pm 12\sqrt6 +6\quad \rightarrow \quad y^2=42\pm 12\sqrt6$

$x^2=\bigg(\dfrac{6\pm \sqrt6}{2}\bigg)^2\quad \rightarrow \quad x^2=\dfrac{42\pm 12\sqrt6}{4}\quad \rightarrow \quad x^2=\dfrac{21\pm 6\sqrt6}{2}$

$x^2+y^2=\dfrac{21\pm 6\sqrt6}{2}+42\pm 12\sqrt6\\\\\\.\qquad \quad = \dfrac{21\pm 6\sqrt6}{2}+\dfrac{84\pm 24\sqrt6}{2}\\\\\\. \qquad \quad = \dfrac{105\pm 18\sqrt6}{2}$

5 0

3 years ago

The sum of three consecutive integers is -51 what is the value of the smallest number

zubka84 [21]

Answer: Let's say the first number is x, the next one is x+1, and so on

Step-by-step explanation:

x + (x + 1) + (x + 2) = -51

x + x + 1 + x + 2 = -51

3x + 3 = -51

3x = -54

x = -18

8 0

3 years ago