Answer:
Conjecture
Disjunction
Counterexample
Conjunction
Inductive reasoning
Conditional
Step-by-step explanation:
I used Quizlet and I knew most of them.
Answer:
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is

Step-by-step explanation:
Given equation is

This Euler Cauchy type differential equation.
So, we can let

Differentiate with respect to x

Again differentiate with respect to x

Putting the value of y, y' and y'' in the differential equation



⇒m²-10m +24=0
⇒m²-6m -4m+24=0
⇒m(m-6)-4(m-6)=0
⇒(m-6)(m-4)=0
⇒m = 6,4
Therefore the auxiliary equation has two distinct and unequal root.
The general solution of this equation is

and

First we compute the Wronskian


=x⁴×6x⁵- x⁶×4x³
=6x⁹-4x⁹
=2x⁹
≠0
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is

3 sin ( 2 x ) = 3 cos x
3 · 2 sin x cos x - 3 cos x = 0
6 sin x cos x - 3 cos x = 0 /: 3
2 sin x cos x - cos x = 0
cos x ( 2 sin x - 1 )
cos x = 0,
x 1 = π/2, x 2 = 3π/2;
2 sin x - 1 = 0
2 sin x = 1
sin x = 1/2
x 3 = π/6, x 4 = 5π/6.
Answer:
Required volume is
unit.
Step-by-step explanation:
Given equations of curves,
,
substitute second in first we will get,

When
and
. Thus both curves intersect at the points (4,16),(-4,16). And thus
.
Considering width of the representative rectangle as
which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

Now,
Length of generating box=Length of
from line x=4(axis of revolution)=circumference of the shell=(4-x)
Width of box=
Hence,


![=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}](https://tex.z-dn.net/?f=%3D2%5Cpi%5C%7B144%5Cbig%5Bx%5Cbig%5D_%7B-4%7D%5E%7B4%7D-18%5Cbig%5Bx%5E2%5Cbig%5D_%7B-4%7D%5E%7B4%7D-%5Cfrac%7B8%7D%7B3%7D%5Cbig%5Bx%5E3%5Cbig%5D_%7B-4%7D%5E%7B4%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cbig%5Bx%5E4%5Cbig%5D_%7B-4%7D%5E%7B4%7D%5C%7D)

which is required volume of generating area.
Answer:
4/3
Step-by-step explanation:
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<em>Z-</em><em>7</em><em>/</em><em>9</em><em>=</em><em>5</em><em>/</em><em>9</em>
<em>Z</em><em>=</em><em>5</em><em>/</em><em>9</em><em>+</em><em>7</em><em>/</em><em>9</em><em> </em>
<em>Z</em><em>=</em><em>4</em><em>/</em><em>3</em><em> </em><em>not</em><em> </em><em>sure</em><em> </em><em />