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3 years ago

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A rope 18 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a funct

ion representing the area of both square and circle as a function of the length of one side of the square.

1 answer:

Svetach [21]3 years ago

3 0

Please give me a brainliest for this, it was so much work. The answer is

f(x)=x^2 + (4x^2 -18x +81)/pi

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An open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the

natka813 [3]

Please find the attachment.

Let x represent the side length of the squares.

We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.

The side of box will be $8-x-x=8-2x$ and $10-x-x=10-2x$ .

The height of the box will be $x$ .

The volume of box will be area of base times height.

$\text{Volume of box}=(8-2x)(10-2x)\cdot x$

Now we will use FOIL to simplify our expression.

$\text{Volume of box}=(80-16x-20x+4x^2)\cdot x$

$\text{Volume of box}=(80-36x+4x^2)\cdot x$

Now we will distribute x.

$\text{Volume of box}=80x-36x^2+4x^3$

$V(x)=80x-36x^2+4x^3$

Therefore, the volume of the box would be $V(x)=80x-36x^2+4x^3$ .

6 0

3 years ago

3. Increase £60 by 10%

Serggg [28]

£66 because 60/10=6 60+6= £66

5 0

3 years ago

How to reduce the fraction 12/15

FinnZ [79.3K]

4/5 because 12/3=4 and 15/3=5

6 0

3 years ago

Read 2 more answers

Solve the equation. StartFraction dy Over dx EndFraction equals5 x Superscript 4 Baseline (1 plus y squared )Superscript three h

dangina [55]

Answer:

Step-by-step explanation:

To solve the differential equation

dy/dx = 5x^4(1 + y²)^(3/2)

First, separate the variables

dy/(1 + y²)^(3/2) = 5x^4 dx

Now, integrate both sides

To integrate dy/(1 + y²)^(3/2), use the substitution y = tan(u)

dy = (1/cos²u)du

So,

dy/(1 + y²)^(3/2) = [(1/cos²u)/(1 + tan²u)^(3/2)]du

= (1/cos²u)/(1 + (sin²u/cos²u))^(3/2)

Because cos²u + sin²u = 1 (Trigonometric identity),

The equation becomes

[1/(1/cos²u)^(3/2) × 1/cos²u] du

= cos³u/cos²u

= cosu

Integral of cosu = sinu

But y = tanu

Therefore u = arctany

We then have

cos(arctany) = y/√(1 + y²)

Now, the integral of the equation

dy/(1 + y²)^(3/2) = 5x^4 dx

Is

y/√(1 + y²) = x^5 + C

So

y - (x^5 + C)√(1 + y²) = 0

is the required implicit solution

5 0

3 years ago

Please help!!!<br><br> i need help with this

goblinko [34]

Answer:

Step-by-step explanation:

Combine like terms. Like terms have same variable with same power

a) (2xy + 4x) + (15xy - 5x) = <u>2xy + 15xy</u> +<u> 4x - 5x</u>

= 17xy - x

b) (6a + 4b² - 3) + (3b² - 5) = 6a + <u>4b² + 3b²</u> <u>- 3 - 5 </u>

= 6a + 7b² - 8

c) (4x³ - 3x² +4x) + (8x² - 5x ) = 4x³ <u>- 3x² + 8x²</u> <u>+ 4x - 5x</u>

= 4x³ + 5x² - x

d) (7b - 6a + 9y) - (12b + 5a - 2y) =

In subtraction, add the additive inverse of (12b + 5a - 2y)

additive inverse = - 12b - 5a + 2y

(7b - 6a + 9y) - (12b + 5a - 2y) = 7b - 6a + 9y -12b -5a + 2y

= 7b - 12b -6a - 5a + 9y + 2y

= -5b - 11a + 11y

e) (2x² + 7x - 2 + 9y) - (13x + 4x² + 5 - 6y)

Additive inverse of 13x + 4x² + 5 - 6y = -13x + 4x² - 5 + 6y

(2x² + 7x - 2 + 9y) - (13x + 4x² + 5 - 6y)= 2x² + 7x - 2 + 9y -13x - 4x² -5 +6y

= 2x² - 4x² + 7x -13x -2 - 5 + 9y + 6y

= -2x² - 6x - 7 + 15y

5 0

3 years ago