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2 years ago

Find the product (8/6n-4)(9n^2-4)

Mathematics

1 answer:

Leokris [45]2 years ago

6 0

Answer:

4(3n+2) or 12n+8

Step-by-step explanation:

Given expression is:

$(\frac{8}{6n-4})(9n^{2}-4)$

The numerator of the fraction will be multiplied with 9n^2- 4

So, Multiplication will give us:

$=\frac{8(9n^2-4)}{6n-4}$

We can simplify the expression before multiplication.

The numerator will be broken down using the formula:

$a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}$

We can take 2 as common factor from denominator

$=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)$

Hence the product is 4(3n+2) or 12n+8 ..

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A landscaper builds a regular hexagonal patio in a circular garden. The area not covered by the patio will be covered in grass.

Taya2010 [7]

The area that's covered by the grass will be 7.065m²

The area of a circle is found by using the formula: = πr²

where, r = radius = 1.5m

π = 3.14

Therefore, to solve the question, we'll slot the value of the radius into the formula and this will be:

Area = πr².

Area = 3.14 × 1.5²

Area = 3.14 × 1.5 × 1.5

Area = 7.065m²

In conclusion, the area is 7.065m²

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3 years ago

A rectangular box has dimensions 2 in by 4 in by 4 in. Increasing each dimension of the box by the same amount yieits a new box

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Step-by-step explanation:

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2 years ago

A set of 25 two digit numbers are listed below 10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98. What

eimsori [14]

Answer:

0.48

Step-by-step explanation:

Given the data:

10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98

Sum of each of the numbers :

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Probability that sum of the number's digit is odd:

Number of odd sum / total numbers

Number of odd sum = 12

Total numbers = 25

12 / 25

= 0.48

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2 years ago

Name three decimals with a product that is about 40

yulyashka [42]

4.0
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3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

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3 years ago