Let V, E, and F be the number of vertices, number of edges, and number of faces of a cube. Consider the following Pascal-like triangle, but we define each entry in the triangle, other than those on the boundary of the triangle, is obtained by the difference of two entries in the row above. For example, h² = E – h₁ and h² = h - 1. Find the value of h3. 1 1 1 1 h³ 1 h² h F E h² V h³ h³

Q: Evaluate each of the following for x = 4, 7, 9, 8 and 3. ∑x2 ∑x2 – 1 ∑(x2−1)

A: We have given that,  The data set :- x = 4, 7, 9, 8, 3

Q: Let     A= [ -2  3  -4           and      B= [ -3  2  4          3  -1  2…

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Q: If a and b are real numbers, the commutative property of addition states that a + b =

A: If a and b are real numbers, the commutative property of addition states that a+b =    Suppose two…

Q: Show by contraposition that : Vx ERX2-3x - 1020 → x25 or x< - 2

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Q: Provide an estimate for each very large or very small quantity.  Express your estimate as a single…

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Q: Step 1: Step 2: Step 3: Step 4: 50 40x + 9x - 7=0 50+ (-40x + 9x) - 7 = 0 50+ (-40 + 9)x - 7 = 0 50+…

A: Now, we adding the additive inverse of 43. So,                 -31x+43-43=0-43⇒-31x=-43⇒x=4331

Q: Define a * b = 3a + b, where a, b € R. Find the following: 1. 8 * 3 2. 3 * 8 1+2 3. 3+4

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Q: Let c- 0 2

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Q: V32 x V64

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Q: The letter a is a digit (i.e., 0; 1; ; 9). Find all choices of n so that 278n5 is divisible by

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Q: If a, b, and c are real numbers, the associative property of multiplication states that = a(bc).

A: Given a, b, c are real numbers.

Q: 13

A: Consider the integral

Q: Q1.write an 8086 program to perform this formula: x2 Y = E=1 (Using one subroutine) х!

A: We will use python programming to perform this formula. We will compute the finite series sum in the…

Q: an

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Q: Evaluate the combination. C(38,22)

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Q: 22) Create an expression that can be used to find Zg in terms of Zd.

A: There are so many ways to create expression for angle g but final expression will be same for all…

Q: Evaluate each of the following: 3. 1. xydxdy 0.

A: A double integral can be considered as an integral inside an integral. This can be mathematically…

Q: out Excel?

A: x y 0.5 0.541 1 0.398 1.5 0.232 2 0.106 2.5 0.052 f(x) = axebxf(x) = yy = axebx