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Liula [17]
3 years ago
7

In quadrilateral abcd the measures of the angles are represented by measure angle a=6x-2, measure angle b=6x+5, measure angle c=

8x+2, and measure angle d=3x+10. Find the measure angle c
Mathematics
2 answers:
OleMash [197]3 years ago
8 0

\bf \textit{sum of all interior angles in a polygon}\\\\ S = 180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n = \stackrel{quadrilateral}{4} \end{cases} \\\\\\ \stackrel{\measuredangle a}{(6x-2)}~~+~~\stackrel{\measuredangle b}{(6x+5)}~~+~~\stackrel{\measuredangle c}{(8x+2)}~~+~~\stackrel{\measuredangle d}{(3x+10)}~~=~~180(4-2)

\bf 23x+15=180(2)\implies 23x+15=360\implies 23x=345 \\\\\\ x = \cfrac{345}{23}\implies \boxed{x = 15} \\\\\\ \stackrel{\measuredangle c}{8x+2}\implies 8(15)+2\implies 122

balandron [24]3 years ago
7 0

Answer:

c = 122 degrees

Step-by-step explanation:

A quadrilateral is a shape bounded by four sides. It has four angles too. The sum of the angles in the quadrilateral is 360 degrees. From the information given above, the four angles of the quadrilateral are angle a, angle b, angle c and angle d.

The sizes of the angles are

angle a = 6x-2 degrees

angle b = 6x+5 degrees

angle c= 8x+2 degrees

angle d = 3x+10 degrees

Sum of the angles = 360. Therefore,

6x-2+6x+5 +8x+2 +3x+10 = 360

= 6x + 6x + 8x + 3x = 360 -5-10

23x = 345

x = 350/23 = 15

Angle c = 8x+2 = 8×15 +2 = 122 degrees

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Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5
lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer:  v = 5v + 4u + 1.5sin(3t),

  • 0
  • 1
  •  4
  • 5
  • 0
  • 1.5sin(3t)
  • 1
  •  2.5

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t)        where u'(1) = 2.5   u(1) = 1

v represents the "velocity function"   i.e   v = u'(t)

As v = u'(t)

<em>u' = v</em>

since <em>u' = v </em>

v' = u"

v'  = 5u' + 4u + 1.5sin(3t)   ( given that u" - 5u' - 4u = 1.5sin(3t) )

    = 5v + 4u + 1.5sin(3t)  ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt \left[\begin{array}{ccc}u&\\v&\\\end{array}\right]= \left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]  \left[\begin{array}{ccc}u&\\v&\\\end{array}\right] + \left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]  = \left[\begin{array}{ccc}1\\2.5\\\end{array}\right]

7 0
3 years ago
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