Answer: 2 + n less-than 14
Or 2 + n < 14
Step-by-step explanation:
Let n = number
Two more than a number is less than 14
n + 2 < 14
Or 2 + n < 14 which is the same as
2 + n less-than 14
Answer:
The correct option is
The origin is included in the shaded region and the shaded area is below the line.
Step-by-step explanation:
Y>3/2x + 2
Put x=0
Y= 2
(0,2)
Put y=0
X= -4/3
(-4/3,0)
See attached picture for the sketch
Answer:
x»-2
Step-by-step explanation:
![6x - 2 \geqslant 4x - 6 \\ 2x \geqslant - 4 \\ x \geqslant - 2](https://tex.z-dn.net/?f=6x%20-%202%20%5Cgeqslant%204x%20-%206%20%5C%5C%202x%20%5Cgeqslant%20%20-%204%20%5C%5C%20x%20%5Cgeqslant%20%20-%202)
Let the width = x
=>length = 2x-1
91= x(2x-1)=2x^2-x
2x^2-x-91=0
=(2x+13)(x-7)
=> x=-13/2=> no
=>x= 7 cm
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
![\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E5%20%285-x%29%28x%5E2%2B2%29%5C%2C%5Cmathrm%20dx%3D2%5Cpi%5Cint_0%5E5%20%2810-2x%2B5x%5E2-x%5E3%29%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B%5Cfrac%7B925%5Cpi%7D6%7D)