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3 years ago

X^3+3x^2y+3xy^2+y^3 ———————————— X^3+y^3

1 answer:

7 0

To factor this fraction, you have be be aware of two special factoring formula:
a^3 + b^3 = (a + b)(a^2 – ab + b^2)

(a+b)³ = a³ + 3a²b + 3ab² + b³

You can see the top part in this case is (x+y)^3, and the bottom (denominator) can be factor into (x+y)(x^2-xy+y^2)
we can cancel (x+y), so what we have left is (x+y)^2/(x^2-xy+y^2)
or (x^2+2xy+y^2)/(x^2-xy+y^2)

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A pool measuring 12 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the poo

Hatshy [7]

Answer:

900 meters

Step-by-step explanation:

12*20=240

1140-240=900

hope this helps :P

4 0

4 years ago

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

Hence, the base and height of the solid is 5.5cm

7 0

3 years ago

There are 6 blue marbles, 4 red marbles, 7 green marbles, and 3 yellow marbles in a bag. Find the probability of choosing a blue

Ludmilka [50]

Answer:

70%

Step-by-step explanation:

If you add the marbles together you will have 20 marbles.

The probability of choosing a marble that not blue is 14/20

If you converted that into a percent it would be 70%

Hope this is helpful

- Please mark brainliest :)

3 0

3 years ago

Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the

Kobotan [32]

Answer:

.87

Step-by-step explanation:

She gets 13 off so 100-13 =87

She will pay 87%

Multiply by .87

3 0

3 years ago

Read 2 more answers

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

elena55 [62]

6x2 -5x –3 = 0
a = 6 b=-5 and c=-3

x = [-b +-sq root (b² -4ac)] / 2a
x = [--5 +-sq root (25 -4*6*-3)] / 2*6
x = [5 +- sq root (25 +72)] / 12
x = [5 +- sq root (97)] / 12

x1 = [5 + 9.8488578018 ] / 12
x1 = 14.8488578018 / 12
x1 = 1.2374048168 

x2 = [5 - 9.8488578018 ] / 12
x2 = -4.8488578018 / 12
x2 = -0.4040714835

5 0

4 years ago