Find an equation for the line that passes through the point (-3,7) and is perpendicular to 3x-5y=80. give your answer in point-slope form. show as much work as possible to support your answer.

y-7=-(5/3)(x+3)

Step-by-step explanation:

step 1

Find the slope of the line that is perpendicular to 3x-5y=80

we have

3x-5y=80

5y=3x-80

y=(3/5)x-16

The slope of the given line is m1=3/5

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

m1*m2=-1

Find m2

(3/5)*m2=-1

m2=-5/3

step 2

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-5/3

point (-3,7)

substitute

y-7=-(5/3)(x+3) > equation of the line into point slope form

828 small spheres can be made from the metal.

Step-by-step explanation:

Side of the cube = 4.5cm

Volume = (a x a x a)

= (4.5 x 4.5 x 4.5)

= 91.125 cubic cm

Radius of the sphere = 3mm = 0.3 cm

Volume of 1 sphere = (4/3) π(r x r x r)

= (4/3) (3.14) (0.3 x 0.3 x 0.3)

= (4/3) (3.14) (0.027)

= 0.34/3

= 0.11 cubic cm

No. of spheres = 91.125/0.11

= 828.4

So, 828 small spheres can be made from the metal.