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nevsk [136]
3 years ago
7

Can anyone please help me solve this problem about a graph? Please help immediately!!! :(

Mathematics
1 answer:
slavikrds [6]3 years ago
7 0

Answer:

Step-by-step explanation:

I think the first part of that is asking for the equation for the line of symmetry, although I do not have access to your drop down menu to know for sure!  The axis of symmetry is the equation that splits the parabola into 2 parts that are mirror images of each other.  In this type of parabola, it will be an "x = " equation.  The line that splits the parabola in half is the line x = -2.  The function is increasing where the y values are going up.  This happens in the interval  (-∞, -2].

The function is decreasing where the y values are going down.  This happens in the interval [-2, ∞)

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Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
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Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

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thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

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