1. Homework Statement
I have lim of n > infinity (1+1/n)^n
2. Homework Equations
3. The Attempt at a Solution
I know that I must use l'hospital rule and setting ln y = n ln (1+1/n)
And after lim n ln (1+1/n) as n approaches infinity.
After what do I do ?
1. Homework Statement
I have the following complex numbers : -3,18 +4,19i
I must put it in polar form.
2. Homework Equations
r=(a^2+b^2)^(1/2)
cos x = a/r
sin x = b/r
3. The Attempt at a Solution
I was able to find with cos x = a/r that the x = 127,20
But when I do it with sin x = b/r I...
1. Homework Statement
A stone is thrown into still water, forming ripples which travel from the center of disturbance in the form of circles. If the circumference of the circle which bounds the disturbed area is 10 ft and the circumference is increasing at the rate of 3 ft. per second, how fast...
1. Homework Statement
So I have the following hyperbola
x^2/4 - y^2/4 = -1
I need to find the focus points of this hyperbola. What is some analytical way to do this ?
Thank yoU!
2. Homework Equations
I don't know...
3. The Attempt at a Solution
I need some analytical way to be able to...
1. Homework Statement
I have : (x)^2+(2xy)+y^2+2(2)^(1/2)x−2(2)^(1/2)y+4=0
Now when I use the rotation formulas I get : y'=(x'^2)/2 + 1
But I don't know if this makes sense....
2. Homework Equations
tan2β=B/(A−C)
x=x'cos β - y'sin β
y=x'cos β + y'sin β
3. The Attempt at a Solution
We...
1. Homework Statement
When the train has passed at the point C, the radii of curvature is 20 m and the apparent weight is 2 2 times bigger than the real weight. At the moment when the picture was taken, the train was at the point s, located 8 m higher than the hollow C. At s, the radii of...
1. Homework Statement
z^6+(2i-1)z^3-1-i=0
2. Homework Equations
3. The Attempt at a Solution
I know that I must put k=z^3 and solve the quadratic. But I'm not able to simplify the quadratic. I get the square root of (-8i+1)
What am I supposed to do ?
1. Homework Statement
A bloc of 0,2 kg is attached on a horizontal spring without any friction on the floor. The other side of the sprin gis attached to a wall. He does a movement of back and forth . Between the two extremities of the back and forth movement, the bloc has a displacement of 40...
1. Homework Statement
I have two complex numbers that are non real, k and z. K and z are going to be complex conjugates if and only if the product (x-k)(x-z) is a polynomial with real coefficients.
Here is my answer :
k=a+bi
z=c+di
(x-k)(x-z) = x^2 -(k+z)x+kz
2. Homework Equations
3...
1. Homework Statement
A bloc of 0,2 kg is attached to a spring on a horizontal surface with no friction. (The other side of the spring is attached to a wall, so it doesn't move) The spring constant is 5 N/m. If we pull on the spring, we move it by 0,12 m from its natural position and we let it...
1. Homework Statement
What must be the period of rotation of a spatial station so that artificial gravity in a cabin that is 45 m of radius from the axis of ration corresponds to gravitational field at the surface of Earth ?
2. Homework Equations
T=(2(pi)r)/v
Sum of forces r prime = (mv^2)/r...
1. Homework Statement
Two blocs with the same mass have the same rope which links them. The friction coefficients are the same whatever the surface. The blocs are initialy stationary and we let them move. What is the module of the acceleration of the blocs if static coefficient of friction...
1. Homework Statement
On a surface without friction, we have 3 blocs with mass A=0,4 kg B=0,1 Kg C=0,3 Kg which are placed one beside the other, with A being first, B second and C third.. If we push on the bloc A with a horizontal force of 2,4 N, determine what is the acceleration and what are...
1. Homework Statement
I need to explain why I can't lift myself by pulling my shoes' laces.
2. Homework Equations
Newton's third law
3. The Attempt at a Solution
My explanation is that by pulling on your laces, there is always going to be a force that goes against your force, so this is...
1. Homework Statement
There is a bloc B that is on a surface S. A bloc A is on on the bloc B. We pull the rope towards the right. There is friction between all surfaces and the blocs stay stationary (They don't move). Identify all the forces which are applied on the bloc B...
1. Homework Statement
A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the lenght of the spring is 50 cm, the block has a force of 5 N on the right; When the lenght of the spring is 80 cm, the block has a...
1. Homework Statement
Calculating the roots of a quadratic with complex coefficients
2. Homework Equations
x^2 - (5i+14)x+2(5i+12)=0
3. The Attempt at a Solution
I tried the quadratic solution but it gives too complicated solutions. I have no idea on how to do this...
I was wondering, why is the set of complex numbers needed to solve problems that the set of reals doesn't permit to ? I mean, in relation to the fundamental theorem of algebra, that is.
1. Homework Statement
I must prove that the mean of one number and its absolute value is superior or equal to 0 but inferior or equal to the absolute value of the number
2. Homework Equations
I must prove this by the method of case.
3. The Attempt at a Solution
I know that the first case...
1. Homework Statement
An octagon is on a table with no friction. There are two equal forces which are put on two faces of the octagon, one in direction of the north, the other in direction of the south-east. These forces are all 0,5 N. If the module of the acceleration is 0,3 m/s^2, what is the...
1. Homework Statement
Someone runs on a circle in the direction of a clock. He goes at constant speed. The circle is put in a xy plane that is centered at the origin. The radius is 10 m. At a certain moment he has a speed of (3i + 3j) m/s. Determine the position at this moment. (in vectorial...
1. Homework Statement
A fountain projects water horizontaly at a height of 12 m. The water goes on the floor after having travelled 15 m horizontally. Calculate the angle the water does with the floor.
2. Homework Equations
I know that the accelerate is constant, so its one of the cinematic...
1. Homework Statement
John move 8m 20 degrees north of the west. After, he moves another time 6 m 80 degrees south of the east. Calculate the difference between the two vector of his movement in cartesian form.
2. Homework Equations
Vector =ai +bj
3. The Attempt at a Solution
By using...
1. Homework Statement
A train is at 0 m/s at the begining. It accelerates on a distance of 60 m, after it goes on a constant speed on the next 120 m and it finally decelerates on the next on 30 m and stops. The whole traject is 25 sec. Find the constant speed.
2. Homework Equations
x final =...
1. Homework Statement
At what speed must I throw vertically an object so that it will lose 25 % of its speed during the first second.
2. Homework Equations
V final = v initial + a * t
3. The Attempt at a Solution
v final * 0.75 = v initial + -9.8 m/s^2 * 1 second
That's pretty much what I...
1. Homework Statement
A train is going towards a stationary car at a speed of 50 km/h. There is a distance of 250 m between the train and the car. What must be the acceleration (which is constant) of the train so that the train wont collide with the car ?
Initial position of train = 0
final...
Albert goes upstair on a moving floor. When he lets the moving floor make him go upstairs, it takes him 30 seconds. When he walks while being on the moving floor, it takes him 10 seconds. How much time would it take him to go upstair if the moving floor didn't work anymore (So, you can only...
1. Homework Statement
There is one car which got stolen which goes from the point 30 in the negative sense of the "x" axe towards the point 0 and has a constant speed of 160 km/h. Another person notices the stealing 3 minutes later and takes another car to catch the stealer. What must be the...
http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV7.html
I was just wondering something . We know that if a line touches a circle at one point, then this means that this line is forming a right angle with the diameter of the circle. (“From this it is clear that the straight line drawn...
So, according to this figure :http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII23.html We cannot have similar segments of circles and unequal ones be built on the same side of the same straight line.
My question is : Can we build similar segments of circles but unequal ones ? (It...