Find the equation for the line is perpendicular to 9x+3y=15 (-3,3)

well, let's keep in mind that perpendicular lines have negative reciprocal slopes, so hmmm wait a second, what's the slope of the equation above anyway?

so then, we're really looking for the equation of a line whose slope is 1/3 and runs through (-3,3)

-x + 3y = 12.

Step-by-step explanation:

OK. First we need to find the slope of 9x + 3y = 15.

3y = -9x + 15

y = -3x + 5

So it's slope = -3.

Now the slope of the line perpendicular to it is  - 1 / -3 = 1/3.

Now we use the general form point-slope to find the required equation:

y - y1 = m(x - x1)

Here x1 = - 3,  y1 = 3 and m = 1/3:

y - 3 = 1/3(x - -3)

y - 3 =  1`/3(x + 3)

Multiply through by 3:

3y - 9 = x + 3

-x + 3y = 12.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.