Answer:
X= -12 +6√10
X= 6.973
Step-by-step explanation:
Volume of the box= (36-2x)(24-2x)x
Volume of the box
=( 864 -96x -4x²)x
But 864 -96x -4x²
=216 - 24x-x²
Solving for x quadratically
X= (24+12√10)/-2
X= -12 -6√10
X= -30.97
Or
X= (24-12√10)/-2
X= -12 +6√10
X= 6.973
X will definitely be a positive number
So X= -12 +6√10
X= 6.973
Answer:
Final cost = £779
Step-by-step explanation:
It is given that:
Cost of summer holiday = £650
Amount increased by 11%
Increased cost = 11% of 650
Increased cost = ![\frac{11}{100}*650](https://tex.z-dn.net/?f=%5Cfrac%7B11%7D%7B100%7D%2A650)
Increased cost = 0.11 * 650 = £71.50
Amount after increment = 650 + 71.50 = £721.50
Further increase = 8%
Amount = 0.08 * 721.50 = £57.72
Final cost = 721.50 + 57.72 = £779.22
Thus,
Final cost = £779
So, to factor out the equation x²+12x+35, first multiply the first and last numbers.
1×35=35
So, you need to find the multiples of 35 that add up to 12.
So, you find 7 and 5. These two numbers are the magic numbers that will be used as the correct factored form of x²+12x+35, because:
>7×5=35
>7+5=12
So, using these two numbers, you get your factored form as:
(x+5)(x+7)
Answer:
The question asks arc length:
![\frac{ \frac{ \frac{2\pi}{3} }{2\pi} }{1} = \frac{1}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cfrac%7B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%7D%7B2%5Cpi%7D%20%7D%7B1%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20)
Dividing by
![2\pi](https://tex.z-dn.net/?f=2%5Cpi)
Because 360°(by formula)
Therefore:
![\frac{1}{3} \times \frac{2\pi \times 8}{1} = \frac{16\pi}{3 } = 5 \ \frac{\pi}{3} \\ so \: arc \: length \: = \frac{16\pi}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B2%5Cpi%20%5Ctimes%208%7D%7B1%7D%20%20%3D%20%20%5Cfrac%7B16%5Cpi%7D%7B3%20%7D%20%20%3D%205%20%5C%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%20%5C%5C%20so%20%5C%3A%20arc%20%5C%3A%20length%20%5C%3A%20%3D%20%20%5Cfrac%7B16%5Cpi%7D%7B3%7D%20)
Good luck!
Intelligent Muslim,
From Uzbekistan.