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insens350 [35]
3 years ago
8

3x^2 + 2x-4 = 0 help

Mathematics
2 answers:
igomit [66]3 years ago
5 0

Answer:

I dont know

Step-by-step explanation:

how to answer that

Gnesinka [82]3 years ago
3 0

Answer:

{ \rm{3 {x}^{2} + 2x - 4 = 0 }}

• let's use the quadratic formular to solve the quadratic equation given.

• Considering general quadratic equation; ax² + bx + c = 0

• therefore;

{ \tt{x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\

  • a is 3
  • b is 2
  • c is -4

• substitute following the mathematical operation rules:

{ \rm{x =  \frac{ - 2 \pm \sqrt{ {2}^{2} - (4 \times 3 \times  - 4) } }{(2 \times 3)} }} \\  \\ { \rm{x =  \frac{ - 2 \pm52}{6} }} \\

• split the values:

{ \rm{either \:  \{x =  \frac{ - 2 +  \sqrt{52} }{6} \} \:  \: or \:  \:  \{x =  \frac{ - 2 -  \sqrt{52} }{6}  \} }} \\  \\ { \rm{either \:  \{x = 0.87 \} \:  \: or \:  \:  \{x =  - 1.54 \}}}

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(i) Velocity is the rate of change of position, so if

<em>r</em><em>(t)</em> = <em>b</em> cos(<em>ω t </em>) <em>i</em> + <em>b</em> sin(<em>ω t </em>) <em>j</em> + <em>v</em> <em>t</em> <em>k</em>

then

<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em>

<em>v</em><em>(t)</em> = -<em>b</em> <em>ω </em>sin(<em>ω t</em> ) <em>i</em> + <em>b</em> <em>ω</em> cos(<em>ω</em> <em>t</em> ) <em>j</em> + <em>v</em> <em>k</em>

The speed of the particle is the magnitude of the velocity, given by

|| <em>v</em><em>(t)</em> || = √[(-<em>b</em> <em>ω </em>sin(<em>ω t</em> ))² + (<em>b</em> <em>ω</em> cos(<em>ω</em> <em>t</em> ))² + <em>v</em> ²]

… = √[<em>b </em>²<em>ω </em>² + <em>v</em> ²]

(ii) The path is a helix. Suppose you zero out the <em>k</em> component. Then the path is a circle of radius <em>b</em>, and the value of <em>ω</em> determines how quickly a particle on the path traverses the circle. Now if you reintroduce the <em>k</em> component, the value of <em>v</em> will determine how far from the plane <em>z</em> = 0 the particle moves in a helical path as <em>t</em> varies.

(iii) Acceleration is the rate of change of velocity, so

<em>a</em><em>(t)</em> = d<em>v</em>/d<em>t</em>

<em>a</em><em>(t)</em> = -<em>b</em> <em>ω </em>²<em> </em>cos(<em>ω t</em> ) <em>i</em> - <em>b</em> <em>ω</em> ² sin(<em>ω</em> <em>t</em> ) <em>j</em>

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3 years ago
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