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2 years ago

A rectangle's length to width ratio is 9:4. If its length is 14 cm more than its width, what is its area?

Mathematics

1 answer:

sergiy2304 [10]2 years ago

6 0

The area of the rectangle should be 87.1cm^2

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A powdered drink mix calls for a ratio of powder to water of 1:8 if there are 32 cups of powder how many total of water are need

Citrus2011 [14]

If you do x- number of water cups 1 over 8 will equal 32 over x ,x=256 so 256
if this makes any sense if not ill try better to explain

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2 years ago

jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize i

FrozenT [24]

Answer:

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is 2(x +y) = 80

x + y =40

y = 40 -x

now the area of the rectangle A = length X width

A = x y

substitute 'y' value in above A = x (40 - x)

A = 40 x - x^2 .....(1)

Step :2

now differentiating equation (1) with respective to 'x'

$\frac{dA}{dx} = 40 -2x$ ........(2)

Find the dimensions

$\frac{dA}{dx} = 0$

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

Step 3:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

$\frac{d^2A}{dx^2} = -2$

Now the maximum area A = x y at x =20 and y=20

A = 20 X 20 = 400

Conclusion:-

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

verification:-

The perimeter = 2(x +y) =80

2(20 +20) =80

2(40) =80

80 =80

8 0

2 years ago

Which of the following notations correctly describe the end behavior of the polynomial graph below?

ipn [44]

The end behaviour of the polynomial graph is (b) x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝

<h3>How to determine the end behaviour of the polynomial graph?</h3>

The polynomial graph represents the given parameter

This polynomial graph is a quadratic function opened downwards

Polynomial function of this form have the following end behaviour:

As x increases, f(x) decreases
As x decreases, f(x) decreases

This is represented as

x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝

Hence, the end behaviour is (b)

A rectangle's length to width ratio is 9:4. If its length is 14 cm more than its width, what is its area?​

A rectangle's length to width ratio is 9:4. If its length is 14 cm more than its width, what is its area?