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Computer Science
Give asymptotic estimates, using the Θ-notation, for the following functions. Justify your answer, using asymptotic relations between common functions.
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- f(x)=x^2(x-4)(x+2)^2 Bounce(B) or Cross(C) (in ascending order of zeros): Incorrect (So type CBC or BBB or...)1. Write the code using vpasolve and find the x and y values. (1) ((log(x)/log(3))+3y=13, x^2-2y=1 2. Quadratic square matrix A=[2 3; 1 a], the sum of all elements of A^5 is 2474856. Find the value of the constant a. (a<=100, natural number)If S = { x | 0 ≤ x ≤ 10}, A = { x | 1 ≤ x ≤ 5}, B = { x | 1 ≤ x ≤ 6}, and C = { x | 2 ≤ x ≤ 7}(a) S ⋃ C(b) A ⋃ B(d) A’ ⋂ C(c) A’⋃ (B ⋂ C)(e) (A ⋂ B) ⋃ (B ⋂ C) ⋃ (C ⋂ A)
- eliminate arbitrary constant: a. y^2 = 4ax b. y = cx + c^2 + 1 c. y = A + Bx + Cx^2 - 2x^3An operation ∗ on the set of positive integers is defined by a ∗ b = (a + b) a−b . Evaluate 1024 ∗ (512 ∗ (256 ∗ (128 ∗ (64 ∗ (32 ∗ (16 ∗ (8 ∗ (4 ∗ (2 ∗ 1). a. 2028 b. 2048 c. 2047 d. 2027What is the smallest 32-bit floating point number f such that 128 + f > 128? and What is the smallest 32-bit floating point number g such that 1 + g > 1 ? solve this please
- def sind_approx(x: float) -> float: """ sind_approx(x) returns the Bhaskara I's sine approximation for sine in degrees. This approximation is only valid within the range [0, 180]. The sine approximation is given as: 4 * x * (180 - x) / (40500 - x * (180 - x)) example: sind_approx(90.0) -> 1.0 example: sind_approx(0.0) -> 0.0 example: sind_approx(180.0) -> 0.0 example: sind_approx(45.0) -> 0.7058823529... TODO: add param and return descriptions here """ pass # TODO: replace 'pass' with the function implementation7) Under computer integer arithmetic, the quotient J/K of two integers J and K is less than or equal to the usual quotient. True or false?C (n,k) = n! k!(n-k)! Using above formula calculate the following: C(15,14) C(20,7)
- Given the following definitions: U={a,b,c, d, e, f, g} A={a, c, e, g} B={a,b,c,d} find A n BGiven sphereRadius, compute the volume of a sphere and assign sphereVolume with the result. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division.Volume of sphere = (4.0 / 3.0) π r3 (Hint: r3 can be computed using *)For all positive numbers aaand bbwith a>ba>b, ln(a−b)=ln(a)/ln(b)ln(a−b)=ln(a)/ln(b) True or false