03/28/22

#### How do I explain (in words) that basis B spans V, is linearly independent, and is a basis of V?

Let V be a vector space and basis B = {v1, . . . , vn} a subset of V . In complete sentences, explain what it means that(a) B spans V , if for every v ∈ V there are coefficients a1, . . . , an ∈ R,... more

03/13/22

#### The derivative of a function of f at x is given by

The derivative of a function of f at x is given byf′(x)=limh→0f(x+h)−f(x)hprovided the limit exists. Use the definition of the derivative to find the derivative of f(x)=7x2+3x+4. Enter the fully... more

02/11/22

02/08/22

#### Discrete math and structures

Suppose you are managing 17 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same... more

02/07/22

#### Prove that mn^k is even if k > 0

Let n, m, k be integers where n is even and m is odd. Prove that mn^k is even if k > 0.I know intuitively that n^k can just be expressed as an even number, because n is even. But is that a valid... more

02/06/22

#### Discreete mathematics proof

Let n and m be integers and assume that n is even. Prove that nm is even and that n + m has the same parity as m.

12/02/21

#### altitude and triangle

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the... more

11/25/21

#### Solve the differential equation using power series

If the series y(x) = Σn=0 to infinity (Cn x^n) is a solution of the differential equation 3y''-3x^2y'+3y=0. A general solution of the same equation can be written as y(x) = C0y1(x) + C1y2(x),... more

11/20/21

#### i cannot solve this exerccise

Let M = {1, 2, 3, 4, 5, 6, 7, 8, 9}. As usual, denote ¨ P (M): = {A | A ⊆ M} is the power set of M. We consider the maps⊕: P (M) × P (M) → P (M) and *: F2 × P (M) → P (M),byA ⊕ B: = A triangle B... more

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