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tekilochka [14]

3 years ago

8

Why mathematicians use radicals instead of decimals?

1 answer:

zaharov [31]3 years ago

8 0

Mathematicians use radicals instead of decimals to provide a more accurate answer. For example, √14 would be a never ending decimal, but rounded it would be 3.74165738677. So do most imperfect squares such as √2 or √8. To get a more accurate number for an answer, it is better to use radicals as rounded numbers would not get the exact answer.

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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)

<u>Step :2</u>

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

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

<u>Find the dimensions</u>

<u></u> $\frac{dA}{dx} = 0$ <u></u>

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

<u>Step 3</u>:-

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

<u>Conclusion</u>:-

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

<u>verification</u>:-

The perimeter = 2(x +y) =80

2(20 +20) =80

2(40) =80

80 =80

8 0

3 years ago

Last time, one out of every 4 students in our class was absent. This time, after Jen came back, only one out of every 5 students

VMariaS [17]

Answer: There are 20 students and 4 students are not here today.

Step-by-step explanation:

If the number of students = 4

Let the number of students be 'x'.

Fraction of students absent = $\dfrac{x}{4}$

If the number of students = 5

Fraction of students absent = $\dfrac{x}{5}$

And Jen came back,

So, the fraction of student absent is also written as

$\dfrac{x}{4}-1$

According to question, it becomes,

$\dfrac{x}{5}=\dfrac{x}{4}-1\\\\\dfrac{x}{5}=\dfrac{x-4}{4}\\\\4x=5(x-4)\\\\4x=5x-20\\\\4x-5x=-20\\\\-x=-20\\\\x=20$

Hence, there are 20 students in our school.

And number of students are not here today is $\dfrac{20}{5}=4$

3 0

3 years ago

a cash register has $1.04 in coins. all the coins are pennies and dimes.there are 24 pennies in the cash register. Which represe

VladimirAG [237]

3-1 finds for she did to is to is to to fix l Fick

8 0

3 years ago

Which expression is equivalent to 4/5 divided by 8

notsponge [240]

4/5 divided by 8 is 0.1 other than that I don’t know that question is kind of vague

6 0

3 years ago

What property is illustrated in the identity shown below?<br> 2(3x+1)=6x+2

Paha777 [63]

It’s a infinite because do fist 2•3x= 6x then 2•1=2 then look 6x+2=6x+2

8 0

3 years ago

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