For Exercises 29-48, use a variation model to solve for the unknown value. The area of a picture projected on a wall varies directly as the square of the distance from the projector to the wall. a. If a 15-ft distance produces a 36 ft 2 picture, what is the area of the picture when the projection unit is moved to a distance of 25 ft from the wall? b. If the projected image is 144 ft 2 , how far is the projector from the wall?
For Exercises 29-48, use a variation model to solve for the unknown value. The area of a picture projected on a wall varies directly as the square of the distance from the projector to the wall. a. If a 15-ft distance produces a 36 ft 2 picture, what is the area of the picture when the projection unit is moved to a distance of 25 ft from the wall? b. If the projected image is 144 ft 2 , how far is the projector from the wall?
For Exercises 29-48, use a variation model to solve for the unknown value.
The area of a picture projected on a wall varies directly as the square of the distance from the projector to the wall.
a. If a 15-ft distance produces a
36 ft
2
picture, what is the area of the picture when the projection unit is moved to a distance of 25 ft from the wall?
b. If the projected image is
144 ft
2
, how far is the projector from the wall?
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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