We want
, and we have
and
. If we could get the angle
, then we could use the cosine rule to determine
. This is possible, as
is a right-angled triangle. We know this from circle geometry, that any triangle circumscribed by a circle with one side going through the origin, is right-angled. As we have two angles of
, we know
and hence
. Using the cosine rule, we can get
.
Thus
Now the cosine rule gives
For the diagram on the right,
Find
in terms of
.
Find an expression for:
Using the above, show that
.
Now do the same for
and
.
is a diameter of circle
with radius
.
,
and
.
Show that
.
The figure below shows a cyclic quadrilateral with
.
Show that the area of the cyclic quadrilateral is
.
Find expressions for
and
in terms of the quadrilateral sides.
Show that
.
Suppose that
,
,
and
. Find
.
Find the angle
using your expression for
. Hence find the area of
.
Problems in 3 dimensions
is the top of a tower of height
. Its base is at
. The triangle
lies on the ground (a horizontal plane). If we have that
,
,
and
, show that
We have that the triangle
is right-angled. Thus we can relate the height
with the angle
and either the length
or
(using sines or cosines). But we have two angles and a length for
, and thus can work out all the remaining lengths and angles of this triangle. We can thus work out
.
We have that
Now we need
in terms of the given angles and length
. Considering the triangle
, we see that we can use the sine rule.
But
, and
So
The line
represents a tall tower, with
at its foot. Its angle of elevation from
is
. We are also given that
.
Find the height of the tower
in terms of
,
and
.
Find
if we are given that
,
and
.
Other geometries
Taxicab geometry
Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates.
Manhattan distance
The metric in taxi-cab geometry, is known as the
Manhattan distance , between two points in an Euclidean space with fixed Cartesian coordinate system as the sum of the lengths of the projections of the line segment between the points onto the coordinate axes.
For example, the Manhattan distance between the point
with coordinates
and the point
at
is
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .