1. Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. x2 + y2 = 16, z = 2 Choose the correct description. A. The circle with center (0, 0, 2) and radius 4, parallel to the xy-plane. B. The line through (4, 4, 2), parallel to the z-axis. C. The line that passes through the points (4, 0, 2) and (0, 4, 2).D. The circle with center (4, 4, 0) and radius 2, parallel to the xy-plane.2. For the points P1(-5, 3, 1) and P2(5, l, 0), find the direction of P1P2rightarrow and the midpoint of line segment P1P2. 3. Find the following for the vectors u = -5i + 4j + root7 k and v = 5i - 4 j - root7 k. a. v·u, |v|, and |u| b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vector projvu v·u 4. Find a vector of magnitude 3 in the direction of v = 12i - 9 k.

10 * 563.67 = 5636.7

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3