Peter walked 10m from X to Y on bearing 020° and then he turned and walked 20m to Z with bearing 140° of Z from Y. Find the distance between X and Z. Find the bearing of Z from X.

17.32m ; 110°

Step-by-step explanation:

Distance between X and Z

To calculate the distance between X and Z

y^2 = x^2 + z^2 - (2xz)*cosY

x = 20, Z = 10

y^2 = 20^2 + 10^2 - (2*20*10)* cos60°

y^2 = 400 + 100 - (400)* 0.5

y^2 = 500 - 200

y^2 = 300

y = sqrt(300)

y = 17.32m

Bearing of Z from X:

Using cosine rule :

Cos X = (y^2 + z^2 - x^2) / 2yz

Cos X = (300 + 100 - 400) / (2 * 20 '*10)

Cos X = 0 / 400

Cos X = 0

X = cos^-1 (0)

X = 90°

Bearing of Z from X

= 20° + X

= 20° + 90°

= 110°

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.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have