Algebra

Quadratic equations Solutions

Let f A → B be a function. Show that (a) If X ⊆ A, then X ⊆ f⁻¹(ƒ(X)). (b) If Y ⊆ B, then f⁻¹(B-Y) = A - f⁻¹(Y).

Geometry

Coordinate system Solutions

Draw an image of the following mapping and name the type of mapping. (x,y) - >(x-6,y+4) (x,y) → (x-6, y+4) Type of mapping: _______

Math - Others

Functions Solutions

Use the algorithm for Euler's method to determine approximations to the solution to the initial value problem y' = 3x²(y + 2),0≤x≤ 1,y(0) = 1 h = 0.2 And compare these with the exact values given by y(x) = 3eˣ(³) - 2

Basic Math Solutions

Prove or disprove: There exists an integer m that will make the equation m² - 3 be divisible by x such that x is prime and x = 2²ⁿ +1, for some n ∈ N.

Matrices & Determinants Solutions

Let x, y € R" be given. (a) If ||x|| = ||y|| = 1 and x * y = 1, show that x = y. (b) If ||x|| ≤ 1 and ||y|| ≤ 1, prove that √(1 - ||x||²) √(1 - ||y||²) ≤ 1 − |x · y|.

Determine whether the relation represents y as a function of x. Domain,x Range, y -2. 5 -1 6 0 7 1 8 2 O Yes, the relation represents y as a function of x. O No, the relation does not represent y as a function of X

Determine whether the relation represents y as a function of x. Domain, x Range, y -2 0 -1 1 0 2 1 2

Find the eigenvalues of A³ for 1 6 2 5 a= 0 12 3 7 0 0 19 3 Enter the eigenvalues in increasing order. Eigenvalues of A³ are:

Physics

Basic Physics Solutions

A vertical, solid steel post 28 cm in diameter and 2.5 m long is required to support a load of 8056 kg. You can ignore the weight of the post. What is the strain in the post. Ysteel = 200 GPa Round your answer to 2 decimal places.

Calculus

Vector Calculus Solutions

Find the value of a for this series, 3+2+2\5 +4\3 +8\9 +16\27+

Limits & Continuity Solutions

Find the following. f(x) = x/(x + 4), g(x) = x³ (a) (f + g)(x) = ______ (b) (f - g)(x) = ______ (c) (fg)(x) = ______ (d) (f/g)(x) = ______ What is the domain of fig? ______

Suppose that $2,400 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $3,500 at a 3.25% interest rate The account will grow to $3,500 in about years. (Type an integer or decimal rounded to one decimal place as needed.)

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