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vredina [299]
3 years ago
9

Line A: y = 1/2x+2

Mathematics
1 answer:
hammer [34]3 years ago
7 0

Lines B and C are perpendicular ⇒ answer C

Step-by-step explanation:

The product of the slopes of the perpendicular line is -1

The slopes of the parallel lines are equal

The slopes of two lines are m_{1} and m_{2}

1. If m_{1} × m_{2} = -1, then the two lines are perpendicular

2. If m_{1} = m_{2} , the the two lines are parallel

The equation of a line in slope-intercept form is y = m x + c, where m is

the slope of the line

Line A: y = \frac{1}{2} x + 2

The slope of the line is m_{A} = \frac{1}{2}

Line B: y = -\frac{1}{2} x + 7

The slope of the line is m_{B} = -\frac{1}{2}

Line C: y = 2 x + 4

The slope of the line is m_{C} = 2

Line D: \frac{1}{2} x + \frac{5}{4}

The slope of the line is m_{D} = \frac{1}{2}

∵ m_{B} = -\frac{1}{2}

∵ m_{C} = 2

∵ -\frac{1}{2} × 2 = -1

∴ Line B and Line C are perpendicular because the product of their

   slopes is -1

Lines B and C are perpendicular

Learn more:

You can learn more about slope in brainly.com/question/4152194

#LearnwithBrainly

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Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is
Mamont248 [21]

Answer:

1)The rocket hit the ground at     x = \frac{5}{4}

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation  

                y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

             \frac{dy}{dx} = -2( 2x) +5(1) =  -4x +5

Equating zero

            \frac{dy}{dx} = 0

⇒      -4 x +5 =0

⇒      -4 x = -5

⇒          x = \frac{5}{4}

<em> The rocket hit the ground at     </em>x = \frac{5}{4}<em></em>

<u><em>Step(ii):</em></u>-

    \frac{dy}{dx}  =  -4x +5  ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

 \frac{d^{2} y}{dx^{2} }  = - 4(1)

The maximum height at x = \frac{-5}{4}

  y = -2 x² + 5 x + 7

 y = -2 (\frac{5}{4})^{2}  + 5 (\frac{5}{4} )  + 7

y = \frac{-2(25)+ 25 (16)+7(64)}{64}

y = \frac{798}{64} = 12.468 feet

<em>The maximum height of the rocket = 12.468 feet</em>

       

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2 years ago
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