The scale on the map is stated as 1 : 2. a main road connects two towns which are 28 kilometres apart. how far will it be on the map, in centimetres, between the two towns along the main road

The distance on the map between the two towns=14 cm

Step-by-step explanation:

Step 1

Express the scale as;

1:200,000 this means that 1 cm on the map represents 200,000 cm on the road, 1 cm:200,000 cm

Step 2

Convert 28 kilometers to m

1 meter=1,000 kilometers

28 kilometers=28×1,000=28,000 meters

Convert 28,000 meters to centimeters

1 meter=100 centimeters

28,000 meters=28,000×100=2,800,000 centimeters

Step 3

Using the scale factor of 1:200,000 convert 2,800,000 cm on the road can be converted to map measurements as follows;

Distance on the map=scale factor×distance on the road

where;

scale factor=1/200,000

distance on the road=2,800,000 cm

replacing;

Distance on the map=(1/200,000)×2,800,000

Distance on the map=14 cm

The distance on the map between the two towns=14 cm

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.