Find the values of e, a, b, and c for r = 24/(4 + 2sin theta)

Step-by-step explanation:

r=24/(4+2sin θ)

4r+2r sin θ=24

divide by 2

2r+r sin θ=12

2√(x²+y²)+y=12

2√(x²+y²)=12-y

squaring

4(x²+y²)=144-24y+y²

4x²+3y²+24y=144

4x²+3(y²+8y+16-16)=144

4x²+3(y+4)²-48=144

4x²+3(y+4)²=144+48

4x²+3(y+4)²=192

divide by 192

which is an ellipse with centre(0,-4) major axis on y-axis.

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204