1.The speed of a stey diver t seconds afer jumping is given by VCt) = 80(1-e) ft.lsec. After how many seconds is the speed equal to 7oft.lsec.?

Q: 1 · [3 2], ¤ - [ -2 -²3], ² - [2 ?]. E Let: D= find: a) the dot product between the eigenvectors of…

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Q: Find the matrix corresponding to the linear map T: R³ R³ which is defined as T(x, y, z) (x+2y, x+y,…

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Q: 2. Construct a 2x2 matrix and obtain the Hill cipher for a message built using seven distinct…

A: To construct a 2 X 2 matrix for Hill Cipher, we need to choose four integers a, b, c, and d such…

Q: Which of the series α) x − x³ + x6 − x¹0 + x¹5 b) X x² x3 xs .... are power series?

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Q: 2. (a) Write a Riemann sum approximating the area of the region in Figure 8.14, using vertical…

A: (a) We have to write a Riemann sum approximating the area of the region in Figure 8.14 using…

Q: Calculus Question

A: Please see the white board. Also, Recall the famous rule of differentiation:d(xn) / dx =…

Q: Express the quadratic form (c₁x₁ + €2₂x2 + ... + Cnn)² in the matrix notation TA, where A is…

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Q: J 1 √4x-3-x² =dx, x= sint +2

A: Given that a integration and we solve this integration by using general property of integral.

Q: 10x + 2 | x3 – 5x2 +x-5 dx; use A x-5 + Bx + C x² +1

A: The given integral is (10x+2)/(x3+x-5)

Q: For any invertible matrix B E M nxn(K), define a function TB: Mnxn(K) → M nxn(K) by TB(A)=B-¹AB,…

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Q: Prove your answer the given pair of expressions are logically equivalent? \x(P(x) ▼ Q(x)) and…

A: Given: Here consider the given logic expressions, ∀xPx∨Qx and ∀xPx∨∀xQx To find: Prove the…

Q: Determine the truth value of each of these statements if the domain is R. Explain your answer. 3.…

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Q: The graph of a periodic function f(x) is given in Figure 3: f(x) 10 -11-9 -101 O 9 11 X Figure 3.…

A: The graph of periodic function f(x) is given below.We need to find the exponential Fourier series.We…

Q: 2. Consider the following augmented matrices. 1 2 3 001 000 (01 (A) 4] (C) (B) 1 2 3 0 0 0 10 0000 […

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Q: The figure shows the graph of r as a function of 8 in Cartesian coordinates. Use it to sketch the…

A: The graph of r as a function of  in cartesian coordinate is shown as

Q: Order the following functions according to their growth rates, from the least to greatest.. en nlnn…

A: Advance maths

Q: Suppose V is a vector space and T: V → V is a linear operator. A subspace UCV is said to be…

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Q: or space of all (2 × 2)-matrices. The trace tr( al elements, i.e. the base b tr (ad). =a+d. 0 ₂ -…

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Q: 3. M44 is a set of 4 x 4 matrices, whose trace equals 12. Construct two distinct vector spaces,…

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Q: Find the sums (exactly). a)r= "=1·2+2·3+3.4+4.5+...+1000-1001 100 b) u = ËS(K), k=1 U=Σƒ(k), where…

A: To find the sums.(a) (b) , where

Q: Let W₁ and W₂ be subspaces of an inner product space V. Prove the following. If W₁ ≤ W₂ then W₂t ≤…

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Q: Pn(x) = [(x² - 1)"](") Show that the Legendre polynomials T:R[X] → R[X], T(f)(x) = (x² - 1)ƒ"(x) +…

A: The Legendre polynomials P_{n}(x) = [(x² - 1)n]n are eigenvectors for the endomorphism T: R[X]…

Q: he two linear equations above can be used to express god (225, 50) as a linear combination of 225 as…

A: We have to find the value of linear combination 25=C.225+D.50

Q: find the first six terms of the recursively defined sequence. a) Sn = 2sn-1 +3 for n > 1 and s₁ = 1…

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Q: Let T: R² → R³ be the linear transformation defined by the formula T(x₁, x₂) = (x₁ + 3x2, I1 = I2,…

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Q: What is the Big O notation for following run time function? T(n) = 1000nlogn+ 10000n + 20000 O O(n…

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Q: 6. Sketch an even continuous function with all of the following features: ✓✓✓✓ Absolute maximum at 6…

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Q: Let F: R³ → R4 be the linear transformation that satisfies 2 2 ·0-09)··0-0-0-0) F 1 = 2 = <) 1 -2 1…

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Q: Q1: Solve the system of linear equation by Matrix method: x + z = 6, z-3y=7, 2x + y + 3z = 15…

A: given  x+z=6            z-3y=7            2x+y+3z=15re write the given equation in standard form…

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.