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3 years ago

What is the axis of symmetry for f(x)=- 3x^ 2 +18x-7? X=-3 X=3 X=-6 X=6

2 answers:

7 0

This is a quadratic equation with a squared "x" variable, and therefore a vertical parabolic graph, and thus, the axis of symmetry will be from the vertex's x-coordinate, hmmmm what is its vertex coordiinate anyway?

$\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
f(x)=\stackrel{\stackrel{a}{\downarrow }}{-3}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{-7}
\qquad \qquad 
\left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{18}{2(-3)}~~,~~\qquad \right)\implies \left( +\cfrac{18}{6}~~,~~\qquad \right)\implies (3~,\quad )
\\\\\\
\stackrel{\textit{axis of symmetry}}{x=3}$

Step2247 [10]3 years ago

6 0

The axis of symmetry is a vertical line through the vertex.

The vertex is at

$x=-b/2a=-18/(2(-3))=3$

Second choice.

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segment BC is an are of a circle with radius 30.0 cm, and point P is at the center of curvature of the arc Segment DA is an arc

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The magnetic field is $B = 3.87 *10^{-6} \ T$

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Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that

The radius of BC is $r_{BC} = 30 \ cm = 0.30 \ m$

The radius of DA is $r _{DA} = 20 \ cm = 0.20 \ m$

The length of CD is $r_{CD} = 10 cm = 0.1 \ m$

The length of AB is $r_{AB} = 10 cm = 0.1 \ m$

The current is $I = 11.4A$

The magnetic field is mathematically represented as

$B = B_{BC} + B_{DA} + B_{CD} + B_{AB}$

$B = \frac{\mu_o I}{4 \pi } [ \frac{\theta_{DA}}{r_{DA}} + \frac{\theta_{BC}}{r_{BC}}+ \frac{\theta_{CD}}{r_{CD}}+\frac{\theta_{AB}}{r_{AB}}]$

Where

$\theta_{BC} = \theta_{DA} = \frac{2\pi}{3}$

Where $\frac{2 \pi}{3} = 120^o$

$\theta_{CD} = \theta_{AB} = 0^o$

$B = \frac{\mu_o I}{4 \pi } [ \frac{\frac{2\pi}{3} }{0.20} - \frac{\frac{2\pi}{3}}{0.30}}+ \frac{0}{0.10}+\frac{0}{0.10}]$

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This is because according to Fleming's Left Hand Rule the direction of current is perpendicular to the direction of magnetic field so since current in arc BC and DA are moving in opposite direction their magnetic field will also be moving in opposite direction

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