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Mandarinka [93]
2 years ago
5

This is for 50 brainly points a brainliest for the best explained answer so here's the question.

Mathematics
1 answer:
Montano1993 [528]2 years ago
6 0
D) 37 degrees, 52 minutes
Step-by-step explanation:
3x-2y+1=0 y = 3/2 x + 1/2 ... slope₁ (m₁ = 3/2)
x-3y=0 3y =1/3 x ... slope₂ (m₂ = 1/3)
acute angle between two slopes: tan θ = (m₁-m₂) / (1+m₁*m₂)
tan θ = (3/2 - 1/3) / (1 + 3/2*1/3) = (7/6) / (3/2) = 7/9 = 0.77777777
θ = 37.875°
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Check the picture below.  So the parabola looks more or less like so.

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\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5

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