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3 years ago

Solves the inequality. Write your final answer in interval notation: -3(2x+1) > -2(x+6)

Mathematics

1 answer:

3241004551 [841]3 years ago

7 0

-3(2x+1) > -2(x+6)

-6x -3 > -2x - 12

-6x -3+6x > -2x - 12+6x

-3>4x-12

-3+12>4x-12+12

9 > 4x

4x<9

x<4/9

(-∞, 4/9)

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We have that
$y=- x^{2} +36$

we know that
Is the equation of a vertical parabola open down
so
the vertex is a maximum

step 1
convert the equation of the parabola in the vertex form
$y=- x^{2} +36 \\ y-36=- x^{2}$

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0
so
for y=0
$- x^{2} +36=0 \\ x^{2} =36 \\ x= (+/-) 6$

the points are (-6,0) and (6,0)

see the attached figure

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