Please help me

b minus 3/4 = 7/10

Answers

Answer 1

Answer: b - 3/4 = 7/10
b = 3/4 + 7/10
b = 15/20 + 14/20
b = 29/20
b = 1 and 9/20

Answer 2

Answer: b - 3/4 = 7/10
add 3/4 to both sides to isolate the b
b = 7/10 + 3/4
b = 28/40 + 30/40
b = 58/40
b = 1 18/40
b = 1 9/20

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Answers

Hello,

Answer 1277

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derive the equation of the parabola with a focus at (4,-7) and a directrix of y=-15. put the equatiom in standard form

Answers

Answer:

The equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

Step-by-step explanation:

we need to drive the equation of the parabola with a focus at ( 4, -7) and a directrix of y= -15

From the given focus ( 4, -7) and equation of directrix y = - 15 calculate p

$p=(1)/(2)(y_0-y)$

where $y_0$ is is ordinate of focus and y is equation of directrix.

$p=(1)/(2)(-7-(-15))$

$p=(1)/(2)(-7+15)$

$p=(1)/(2)(8)$

$p=4$

Calculate the vertex (h,k)

$h=4\; \text{and}\; k=(-7+(-15))/(2)=-11$

vertex (h,k) =(4,-11)

Since, vertex form is :

$(x-h)^(2)=4p(y-k)$ (positive 4p shows it open upward)

$(x-4)^(2)=4(4)(y-(-11))$

$(x-4)^(2)=16(y+11)$

$x^(2)+16-8x=16y+176$

subtract both the sides by 176,

$x^(2)-8x-160=16y$

Divide both the sides in above by 16,

$(x^(2))/(16)-(8x)/(16)-(160)/(16)=y$

$(x^(2))/(16)-(x)/(2)-10=y$

Hence, the equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

$\sqrt{(x_(0) - 4)^(2) + (y_(0) - (-7))^(2)} = |y_(0) - (-15)|$
$(\sqrt{(x_(0) - 4)^(2) + (y_(0) + 7)^(2))^(2)} = (y_(0) + 15)^(2)$
$(x_(0) - 4)^(2) + (y_(0) + 7)^(2) = (y_(0) + 15)^(2)$
$(x_(0)^(2) - 8x_(0) + 16) + (y_(0)^(2) + 14y_(0) + 49) = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 16 + 49 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 65 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) - 8x_(0) - 16y_(0) - 160 = 0$
$16y_(0) = x_(0)^(2) - 8x_(0) - 160$
$(16y_(0))/(16) = (x_(0)^(2) - 8x_(0) - 160)/(16)$
$y_(0) = (1)/(16)x_(0)^(2) - (1)/(2)x_(0) - 10$
$y = (1)/(16)x^(2) - (1)/(2)x - 10$

Describe the shape of the cross section