Let
and
be the sides of a triangle, and
be the height.
So
.
We can further name the parts of the base in each triangle established by the height such that
Using the Pythagorean Theorem,
and
Since
then
Expanding, we find that
We can then add
to each side of the equation to get
Substitute this result into the equation
yields
Then replacing
with
gives
Solve for
to get
Since
we get an expression in terms of
and
Therefore,
And since
then
Properties of the Dot Product
Proof:
Proof:
Proof:
Standard Form of the Ellipse centered at the Origin
Derivation
An ellipse consists of all the points for which the sum of distances from two foci is constant:
Consider a vertex.
Then,
Consider a covertex.
Then
Let
Because
then
Standard Form of the Hyperbola
Derivation
A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances between two fixed points is constant.
Diagram 1: The difference of the distances from Point
P to the foci is constant:
Diagram 2: When the point is a vertex, the difference is
Define
as a positive number such that
Trigonometric identities
Pythagorean Identity
Even-Odd Identities
Cofunction Identities
Fundamental Identities
Sum and Difference Identities
Double-Angle Formulas
Half-Angle Formulas
Reduction Formulas
Product-to-Sum Formulas
Sum-to-Product Formulas
Law of Sines
Law of Cosines
Toolkit functions
Trigonometric functions
Unit Circle
Angle
Cosine
1
0
Sine
0
1
Tangent
0
1
Undefined
Secant
1
2
Undefined
Cosecant
Undefined
2
1
Cotangent
Undefined
1
0
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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