To convert from rectangular coordinates (x,y) to polar coordinates (r, θ), the following equations should be used:
r = sqrt( x^2 + y^2)
<span>θ = tan^-1 (y/x)
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Substituting (-3,3) accordingly to the equations, we obtain r equal to 3*sqrt(2) and θ equal to -π/4. Thus, the polar coordinates equivalent to (-3,3) is (3*sqrt(2), -π/4).
Answer:
Points A, C, and D are coplanar, and Point B is noncollinear.
Step-by-step explanation:
Answer:
See explanation
Step-by-step explanation:
Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.
The store keeps an inventory of 80 shovels, then
x+y+z=80
The store always buy twice as many spade shovels as square, so
x=2z
The total cost of all shovels is
16x+9.60y+12.80z=1,072
a) The system of three equations is
b) In matrix form this is
c) The determinant is
d) Find three determinants:
So,
e) If the store doubled all prices and inventory, then the new matrix is
The normal vectors to the two planes are (3, 3, 2) and (2, -3, 2). The cross product of these will be the direction vector of the line of intersection, (12, -2, -15).
Using x=0, we can find a point on this line by solving the simultaneous equations that remain:
... 3y +2z = -2
... -3y +2z = 2
Adding these, we get
... 4z = 0
... z = 0
so the point we're looking for is (x, y, z) = (0, -2/3, 0). This gives rise to the parametric equations ...
- x = 12t
- y = -2/3 -2t
- z = -15t
By letting t=2/3, we can find a point on the line that has integer coefficients. That will be (x, y, z) = (8, -2, -10).
Then our parametric equations can be written as
- x = 8 +12t
- y = -2 -2t
- z = -10 -15t
Answer:
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Step-by-step explanation:
