(1 point) find three positive real numbers whose sum is 37 and whose product is a maximum.

Numbers less than 20 which have exacly 3 factors pls!

Lana71 [14]

Answer:

9,40 is the answer of your question

3 0

2 years ago

Read 2 more answers

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

• Determine the coordinates of the vertices of the rectangle to compute the area of the rectangle using the distance formula (ro

sukhopar [10]

Answer:

the correct answer is d

Step-by-step explanation:

4 0

2 years ago

Sketch the graph of each line

adoni [48]

Answer:

(0,5) (1,0)

Step-by-step explanation:

Place your first dot on the 5 (0,5) of the y-axis (The one that is vertical) from there count down the line one value at a time until you have counted DOWN 5 times. Go to the right once and place another point there (1,0). Then draw a straight line that connects those two points.

6 0

2 years ago

The solution to the system is (6,2) Select all the equations that could be the other equation in the system. PLZ HELPPPPPP there

Dovator [93]

9514 1404 393

Answer:

A, C

Step-by-step explanation:

The attached graph shows which lines go through the given point. They are ...

y = 1/2x -1 . . . . 1st selection

y = -1/6x +3 . . . 3rd selection

__

The equations can be found algebraically by substituting the given point in the equation and seeing if the result is a true statement.

a) 2 = (1/2)(6) -1 = 3 -1 . . . true

b) 2 = -3(6) . . . . false

c) 2 = -1/6(6) +3 = -1 +3 . . . true

d) 2 = 2/3(6) -1 = 4 -1 . . . . false

e) 2 = 4(6) -2 = 24 -2 . . . . false

f) 2 = -3/2(6) +6 = -9 +6 . . . . false

6 0

2 years ago