Mathematics, 20.10.2020 19:01 ashtonfordham987

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Answer from: leo4687

9,15,19 is a triangle

Obtuse Scalene Triangle

Side a = 15
Side b = 9
Side c = 19
Angle ∠A = 50.617° = 50°37'1" = 0.88343 rad
Angle ∠B = 27.63° = 27°37'46" = 0.48223 rad
Angle ∠C = 101.754° = 101°45'13" = 1.77594 rad

Area = 66.0847
Perimeter p = 43
Semiperimeter s = 21.5

Height ha = 8.81129
Height hb = 14.68549
Height hc = 6.95628

Median ma = 12.8355
Median mb = 16.51514
Median mc = 7.92149

Inradius r = 3.07371
Circumradius R = 9.70346

Vertex coordinates: A[0, 0] B[19, 0] C[5.71053, 6.95628]
Centroid: [8.23684, 2.31876]
Inscribed Circle Center: [6.5, 3.07371]
Circumscribed Circle Center: [9.5, 1.97663]

14,16,4 is a triangle

Obtuse Scalene Triangle

Side a = 16
Side b = 14
Side c = 4
Angle ∠A = 113.132° = 113°7'57" = 1.97453 rad
Angle ∠B = 53.576° = 53°34'35" = 0.93509 rad
Angle ∠C = 13.291° = 13°17'28" = 0.23197 rad

Area = 25.74879
Perimeter p = 34
Semiperimeter s = 17

Height ha = 3.2186
Height hb = 3.6784
Height hc = 12.87439

Median ma = 6.48074
Median mb = 9.32738
Median mc = 14.89966

Inradius r = 1.51463
Circumradius R = 8.69944

Vertex coordinates: A[0, 0] B[4, 0] C[-5.5, 12.87439]
Centroid: [0.5, 4.29146]
Inscribed Circle Center: [1, 1.51463]
Circumscribed Circle Center: [2, 8.46642]

6,22,6 is not a triangle

The sum of two sides must be larger than the third

9.1,2.5,12.3 is not a triangle

The sum of two sides must be larger than the third

Answer from: Quest

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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