2a) if 1 ft³ weighs 150 lb==>the TOTAL VOLUME =5,000/150 =33.334 ft³
2b) 1 ft³ 1,728 in³. So the TOTAL volume in in³ =33.334 x 1728 = 57,600 in³
c) Volume =(1/3)(πR²).H but R = H then V= (1/3)(πR³).plug V (=57600)
57,600 = 1/3 (πR³) ==> R³ = (3 x 57600) / π ==> R = 38 in
d) Area x thickness = Volume ==> Area x 2 in = 57600 in then:
Are =57600/2 & Area =28,800 in²
Answer:
1. There are 609 more fiction books than non-fiction books in the library
2. Cheryl had $900 initially
Answer:
The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.
Step-by-step explanation:
By definition of rectangular prism, we get the respective formulas for the volumes of the community swimming pool and the wadling pool, respectively:
Community swimming pool

Wading pool

Where:
l – Length of the swimming pool, measured in feet.
h – Depth of the swimming pool, measured in feet.
w – Width of the swimming pool, measured in feet.
– Volume of the community swimming pool, measured in cubic feet.
– Volume of the wading swimming pool, measured in cubic feet.
The ratio of the volume of the community swimming pool to the volume of the wadling pool is:



The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then
.
C) Consider
. This set is orthogonal because
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in
. Then the columns of A form an orthonormal set. We have that
. To see this, note than the component
of the product
is the dot product of the i-th row of
and the jth row of
. But the i-th row of
is equal to the i-th column of
. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set
and suppose that there are coefficients a_i such that
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then
then
.