A. Packaging is one important feature in producing quality products. designer needs to produce a package for a product in the shape of a pyramid with a square base having a total volume of 200 cubic inches. The height of the package must be 4 inches less than the length of the base. Find the dimensions of the product. Solution: 1. Let = area of the base 2. Let height of the pyramid %3D 3. If the volume of the pyramid is V = 1/3 (area of the base)(height), then the equation that will lead to the solution is 200 = 4. Using synthetic division, the roots are Note: After getting the first root, apply quadratic formula to find the other two roots. 5. Therefore, the length of the base of the package is 6. and its height is

Q: Q.2. Proof that V= u8--

A:

Q: Q.1 2 - A- 4 B= 5 Findd the following (chease 5 Only) A+ B 2.

A:

Q: PROBLEM A. PARTICIPANT X Y A 1 4 3 4 2 E

A: Since you have posted multiple questions , we will solve first question  for you. To get the…

Q: 12 1 If R = and S= 31 0 that R² = 2R+cS. (5 pts) 0 1 find a number c such

A:

Q: Prove the following statement: (Vx € Z) (3y = Z) (x + y = 0)

A:

Q: 4. Define = {1,2,3,4,5,6} and A₁ = {i} for i = 1,2, ...,6, B = {1,4}, C = {2,3,4}, D = {1,2,3} and E…

A: here given,   Ω={1,2,3,4,5,6,} Ai={i} , i=1,2,3,4,5,6 B={1,4} C={2,3,4} D={1,2,3}…

Q: e. 3(v+ w)

A:

Q: and B =

A: (2/5,1/5,1/2)

Q: 9. Which of the following is equivalent to E-1(3i + 2)? [5(6)] 의 + 2(5) c. 3|2의 + 2(4) а. 3 b. 3°|+…

A: (a) option is the correct answer.

Q: 4. Statements Reasons x+y=d +y = c(d) %3D x+y= cd x+y-y= cd-y x = cd- y

A: Write the statement as done in the left side.

Q: Given that v = and w =. Find

A:

Q: 8. Find all values of h, if any exist, such that b a linear combination of vị an h (а) Vi V2 = b =…

A:

Q: Suppose a, b e (0, ) and a b- a.

A: I hope that this solution will help you .Thankyou. Best regards.

Q: What is the least accumulative cost from cell course (0) to cell X? a b 1 3 4 d e f 4 7 3 9 10 |3 h…

A: the number of rows = 4 and columns = 4   1 2 3 4   A 1 3 6 4   B 4 6 7 3   C 8 9 10 3   D…

Q: -1 1 2 A 3 3 4 det A 0 0 -2 0 0 2 4 B = -5 6. 1 5 3 3 det B: -1 0 0 0 3 0 0 C = 2 0 0 4 0 0 0 0 -2…

A:

Q: If v = -2 4 and w = 4 11 3 " compute proj(w) and proj(w).

A: (.) Given vectors are,      (.)  If  are two vectors then,         (.) Vector  is an orthogonal…

Q: a la and |A2 4

A:

Q: 1) G T. 2) YSXA CAA AZA2 F K R E R

A:

Q: 18

A:

Q: If P(A) = 3/4 and P(B) = 5/6, then P(A and B) = а. %3D

A:

Q: ex iR Py, z)-0 fined diz H and x=2-4

A: We have to find partial derivative.

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

A:

Q: If price P is bigger than AVC, the decision for the firm is to continue production even at a loss. O…

A:

Q: Find x, y, z, and w. X II y II Z = W = y (x 5) (2x - -1 [** (*+5] - [(²9) + -] = z 8 8y (9 y) -8…

A:

Q: Suppose A = (a, 0, 2) and B= (6, –2, b), for some a > 0 and b> 0. (a) If projĄB = 12 24 =,0,), find…

A: Suppose A=a, 0, 2 and B=6, -2, b, for some a>0 and b>0.If projAB=125, 0, 245, then to find the…

Q: show that if A occurs in a larger proportion of the cases where B is than wgere B is not, then B…

A:

Q: Prove the following statement: (VxR) (x 0 ⇒ (y R) (xy = 1))

A:

Q: 2. 2. 2. 2. is it Linear tsenstormetion? Li L (U+v). LLu) +L(V). LkU). k L (U).

A:

Q: 2.11) Write as 1 y- linear combination of X₁² -2 2 F 2 -1

A:

Q: 13. Evaluate. ,zE (-x,0] 24 h(z) = zE (0, 8] (2– 1)(z+3) , z€ (8, x) h(-3) = [ %3D A. 27 B. 20 C.…

A:

Q: If X= { a, b, c, d } and Y = { f, b, d, g},      find. (i) X – Y           (ii) Y – X          (iii)…

A: The given sets are

Q: 国~ Let aj = a2 -24 and b: For what value(s) of h is b a linear combination of aj and a2?

A: Explained below

Q: Find Lt Vx (Vx+c- Vx)

A: We have to solve the following limits, limx→∞xx+c-x

Q: true. Show that (a v bc)(a Abc); but the converse is not

A: Solution: