If the perpendicular components
and
of a vector
are known, then
can also be found analytically. To find the magnitude
and direction
of a vector from its perpendicular components
and
, we use the following relationships:
Note that the equation
is just the Pythagorean theorem relating the legs of a right triangle to the length of the hypotenuse. For example, if
and
are 9 and 5 blocks, respectively, then
blocks, again consistent with the example of the person walking in a city. Finally, the direction is
, as before.
Determining vectors and vector components with analytical methods
Equations
and
are used to find the perpendicular components of a vector—that is, to go from
and
to
and
. Equations
and
are used to find a vector from its perpendicular components—that is, to go from
and
to
and
. Both processes are crucial to analytical methods of vector addition and subtraction.
Adding vectors using analytical methods
To see how to add vectors using perpendicular components, consider
[link] , in which the vectors
and
are added to produce the resultant
.
If
and
represent two legs of a walk (two displacements), then
is the total displacement. The person taking the walk ends up at the tip of
There are many ways to arrive at the same point. In particular, the person could have walked first in the
x -direction and then in the
y -direction. Those paths are the
x - and
y -components of the resultant,
and
. If we know
and
, we can find
and
using the equations
and
. When you use the analytical method of vector addition, you can determine the components or the magnitude and direction of a vector.
Step 1.Identify the x- and y-axes that will be used in the problem. Then, find the components of each vector to be added along the chosen perpendicular axes . Use the equations
and
to find the components. In
[link] , these components are
,
,
, and
. The angles that vectors
and
make with the
x -axis are
and
, respectively.
Step 2.Find the components of the resultant along each axis by adding the components of the individual vectors along that axis . That is, as shown in
[link] ,
and
Questions & Answers
differentiate between demand and supply
giving examples
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 .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
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Source:
OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
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