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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What are solutions to the equation tan squared x minus three equals zero?
Solve for x, where tan² x - 3 = 0.
tan² x = 3; then,
sec² x = tan² x + 1 = 4,
sec x = ±2, and
cos x = 1 /sec x = ±½.
Now, we know that
sin 30° = ½; whence
cos 60° = ½.
Therefore, if 0 ≤ x < 2π, then
x = 60°, 120°, 240°, or 300°;
or, in radians,
x = ⅓π, ⅔π, 1⅓π, or 1⅔π.
What is the slope of the line 2x minus 5y equals 10?
Put in this form. Y = mX + c
2X - 5Y = 10
- 5Y = - 2X + 10
Y = (2/5)X - 2
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What happens if you change over too soon from star to delta?
The Star/Delta starter was probably the most commonly used reduced-voltage starter, but in a large number of applications, the performance achieved is less than ideal, and in some cases, the damage and interference is much worse than that caused by a Direct On Line starter.
Electronic motor-control systems, which offer soft-starts in DELTA configuration, are now replacing the use of manual or semi-automatic star-delta starters.
The Star/Delta starter requires a six terminal motor that is normally delta-connected direct to the 3-phase service lines. The Star Delta starter employs three contactors to initially start the motor in a star connection, then after a period of time, to reconnect the motor to the supply in a delta connection.
If there is insufficient torque available while connected in star, the motor can only accelerate to partial speed. When the timer operates (set normally from 5-10 seconds), the motor is disconnected from the supply and then reconnected in Delta resulting in full voltage start currents and torque.
The transition from star connection to delta connection requires that the current flow through the motor is interrupted. This is termed "Open Transition Switching" and with an induction motor operating at partial speed (or full load speed), there is a large current and torque transient produced at the point of reconnection. This transient is far worse than any produced by the DOL starter and can cause severe damage to equipment and the supply.
If there is insufficient torque produced by the motor in star, there is no way to accelerate the load to full speed without switching to delta and causing those severe current and torque transients. These must be allowed-for in the design of the motor and its starting system if they are to have an economic useful life.
Technical explanation
When the windings of a 3-phase motor are connected in STAR:
- the voltage applied to each winding is reduced to only (1 /.'/'3) [1 divided by root three] of the voltage applied to the winding when it is connected directly across two incoming power service line phases in DELTA.
- the current per winding is reduced to only (1 /.'/'3) [1 divided by root three] of the normal running current taken when it is connected in DELTA.
- so, because of the power law V [in volts] x I [in amps] = P [in watts],
the total output power when the motor is connected in STAR is:
PS = (1 /.'/'3 VL) x (1 /.'/'3 ID) = 1/3 [one third] PD
where VL is the phase line voltage
ID is the line current drawn in DELTA
PS is the total power the motor can produce when running in STAR
PD is the total power it can produce when running in DELTA.
- a further disadvantage when the motor is connected in STAR is that its total output torque is only 1/3 of the total torque it can produce when running in DELTA.
For more information please see the answers to the Related Questions shown below.
How do you prove that the derivative of sec x is equal to sec x tan x?
Show that sec'x = d/dx (sec x) = sec x tan x.
First, take note that
sec x = 1/cos x;
d sin x = cos x dx;
d cos x = -sin x dx; and
d log u = du/u.
From the last, we have du = u d log u.
Then, letting u = sec x, we have,
d sec x = sec x d log sec x; and
d log sec x = d log ( 1 / cos x )
= -d log cos x
= d ( -cos x ) / cos x
= sin x dx / cos x
= tan x dx.
Thence, d sec x = sec x tan x dx, and
sec' x = sec x tan x,
which is what we set out to show.
x2 + 2x + 5 = 0 is already in the form ax2 + bx + c = 0 so to find the discriminant, D, you use
D = b2 - 4ac
Then if D is greater than 0 the equation has 2 real roots; if D = 0 the equation has one real root and if D is less than 0 the equation has no real roots. So to check this we work out D but we need to know what a, b and c are. From the equation we can see that
a = 1
b = 2
c = 5
so putting these values in to find D:
D = (2)2 - 4(1)(5) = 4 - 20 = -16
so the equation x2 + 2x + 5 = 0 has no real roots.
1st equation: 5x +7y +29 = 0 or 5x +7y = -29
2nd equation: 11x -3y -65 = 0 or 11x -3y = 65
Times all terms in the 1st equation by 11: 55x +77y = -319
Times all terms in 2nd equation by 5: 55x -15y = 325
Subtract the 2nd equation from the 1st equation: 92y = -644 or y = -7
By means of substitution point of intersection is made at: (4, -7)
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What is the solution of x2-x-4 equals 0?
have to put it was 2x and not x2
--back to the problem--
2x-x-4=0
x=4
* * * * *
True, but the question, in all likelihood WAS x2 - x - 4 = 0
and the solutions to that equation are -1.561553 and 2.561553
Which point is part of the solution of the inequality y-x 4 1?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "less than", "less than or equal to" etc.
What is the value of y when x equals 4?
Anything you like. x = -4 imposes no restrictions on the value that y can take.
2x + 2y isn't an equation and doesn't ask any question, so there's nothing to solve,
and nothing that needs an answer.
If (2x + 2y) were equal to something, and there was another equation to go along with
that one, then it would be possible to figure out what 'x' and 'y' must be.
What is the product of 15 and x the letter x?
x is a variable and can be any number
so if x=1 the product is 15
if x=2 the productis 30
x=3, product is 45 etc
How do you complete the square x squared plus 12x equals 5?
x^2 + 12x = 5
x^2 + 12x + __ = 5 + __
x^2 + 12x + 36 = 5 + 36 (The 36 I got from taking half of 12 and then squaring that number (which is 6).)
(x + 6)^2 = 41
x + 6 = (the square root of 41)
x = (the square root of 41) - 6.
Hope that helped :)
By unit of length and distance and conversion ,we can say thatm.
1 m =100 c
The word 'Guru' comes from the sanskrit roots 'gu', ''darkness'' and 'ru', ''that which dispels''.
This aptly describes the true function of a Guru which is to dispel the darkness of ignorance, which denotes a teacher. In ancient India the word guru was used to described a Spiritual Teacher.
A true Spiritual Teacher is one who has attained God-contact through Meditation.
In the west this word is often misused to apply to a 'teacher, instructor,expert, authority figure, or prominent leader who has a large or elite following.'
The true guru is uniquely qualified to help the student on his or her path to God-Wisdom.
Calculate linear dimension in inches?
height + width + depth = linear
Previous answer:
45 linear inches
2x=6
you need to get x by itself
since x is multiplied by 2, you must divide it by two so you get x=...
however, to keep it with the 2:6 ratio, you need to divide BOTH sides by 2
x=3
