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2 years ago

Write an equation of the line that passes through (1,-2) and (-5,4)

Mathematics

1 answer:

denis23 [38]2 years ago

7 0

Answer: x+y+1=0

Step-by-step explanation:

m=y2-y1/x2-x1

= 4-(-2) /-5-1

=6/-6

=-1

equation of line

y-y1=m(x-x1)

y-(-2) =-1(x-1)

y+2=-x+1

x-1+y+2=0

x+y+11=0

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3 years ago

A lines passes through the points (-4, 7) and (5, -8). What is the slope of the line?

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Answer:

Step-by-step explanation:

The formula to find the slope of a line is:

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We can substitute the points (-4, 7) and (5, -8) to find the slope:

(-8 - 7) / (5 - (-4))

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which is option C

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A cylindrical container that has a capacity of 4000 cubic centimeters is to be produced. The top and bottom of the container are

Aleks04 [339]

Answer:

the optimal size of the cylinder to minimise cost is

radius= R = 7.985 cm ≈ 8 cm

height =h = 19.969 cm ≈ 20 cm

Step-by-step explanation:

Since the cost function is

C= 2*π*R²*c₁+ 2*π*R*h*c₂

where R = cylinder radius , h = height ,c₁= cost of the top material ,c₂ = cost f the side material

The volume of the cylinder is:

V=π*h*R² → h= V/(π* R²)

then

C= 2*π*R²*c₁ + 2*π*R* V/(π* R²) *c₂

C= 2*π*R²*c₁ + 2*π*c₂* V/(π* R) *c₂

the value of h that minimises the cost can be found through dC/dR=0 . Thus

dC/dR= 4*π*R*c₁ - 2*π*c₂* V/(π* R²) = 0

2*R*c₁ - c₂* V/(π* R²) = 0

2*R³*c₁ = c₂* V/π

R = ∛[(c₂/c₁)* (V/(2*π)]

replacing values

R = ∛[(c₂/c₁)* (V/(2*π)] = ∛ [($0.40/$0.50)*4000 cm³/(2*π)] = 7.985 cm

R = 7.985 cm

and the height would be

h= V/(π* R²) = 4000 cm³/[π*(7.985 cm)²]] = 19.969 cm

h= 19.969 cm

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