There exist some a ,b, A, B such that it is not in B.
a+b is (x1^2+x2^2+y1^2+y2^2)<=1, which is not always true.
ca is not in B because
a=(.5,.5) and c=10
100(.5^2+.5^2) is greater then 1 so ca is not in B.
I think i am starting to understand it more.
A(x1^2+x2^2)+B(y1^2+y2^2)<=1 where A and B are scalers
a+b is not in B
ca is not in B either since c can be a scaler that makes a not a subspace in B
so B is not a subspace of R^2
If you have vectors a = (x1, y1) and b = (x2, y2) that are in B, will a + b also be in B?
a=x1^2+y1^2<=1
0^2+0^2<=1
b=x2^2+y2^2=1
0^2+0^2<=1
a+b<=1
If you have a vector a = (x1, y1) that is in B, will any scalar multiple of it also be in B?
a^2(x^2+y^2)<=1
if x and y are equal to 0 or a=0, then...
Homework Statement
is B in subspace R^2
B=[x] :x^2+y^2<=1
[y]
Homework Equations
1.0∈B
2.if u,v∈B u+v∈B
3.if u∈A a∈B then au∈B
The Attempt at a Solution
The <= is confusing me. I am not sure if i am suppose to treat it like an equal sign, or is it automatically not in the...
1. Homework Statement
Integrate h(x,y)=yi - xj over the triangle with vertices (-2,0), (2,0), (0,2) tranversed counterclockwise
2. Homework Equations
(1-t)a+tb
3. The Attempt at a Solution
(1-t)(-2,0)+t(2,0)=(-2+4t,0)
(1-t)(2,0)+t(0,2)=(2-2t,2t)
(1-t)(0,2)+t(-2,0)=(-2t,2-2t)
integral y-x...
1. Homework Statement
An 11 kg bowling ball at 0 degrees C is dropped into a tub containing a mixture of ice and water. A short time later, when a new equilibrium has been established, there are 5.0 g less ice.
From what height was the ball dropped? Assume that no water or ice splashes out...
[SOLVED] Converting Mol
1. A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20 degrees celsius.
How many moles of oxygen are in the cylinder?
so 1 mol = 6.022*10^23
oxygen atomic mass=16g/mol
50g/16(g/mol) = 3.125 mol
I don't know why it is wrong...
1. Integrate f(x,y)=x+y
1<=x^2+y^2<=4, x>=0, y>=0
3. ∬x+y dxdy x=rcos(o) y=rsin(o)
∬r(rcos(o)+rsin(o))drdo
r is from 1 to 4, o is from 0 to pi/2
I get the wrong answer and don't know why
1. ∬(4-y^2 )dxdy
bounded region between y^2=2x and y^2=8-2x
I took the integral 4-y^2 dx and got 4x-xy^2 from 0-4 = 16-4y^2
then I took the integral 16-4y^2 dy from -2-2 = 128/3
It is wrong and I don't know what to do.
1.A petrochemical company is designing a cylindrical tank with hemispherical ends to be used in transporting its products. If the volume of the tank is to be 10,000 cubic meters what dimensions should be used to minimize the amount of metal required?
2. V=pi*r^2 + 4/3*pi*r^3
SA=...