find a linear equation whose graph is the straight line with the given properties through (0.5, -2.25) and (1,-5.25)

Q: 1.2 Y(s) = Y(s) = Find the inverse of the following Laplace transforms: (s+1) (s²+2s+5) (s+1)…

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Q: 7+ 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6- -7+ Slope = m = 1 2 3 4 5 6 7 Find the slope…

A: The graph of a line is shown.We need to find two points on the graph.From graph we get and

Q: Consider the following. f(x, y) = 6x - 5y (a) Find f(3, 1) and f(3.1, 1.05) and calculate Az. f(3,…

A: Given that, Now,

Q: Considering Φm(Φ) Show that: .2п * dom() =0 for all values of m #0 the following set of functions: 1…

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Q: B. A circle is tangent to the line 2x -y + 1 = 0 at the point P(2, 5), and the center is on the line…

A: The figure

Q: Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the…

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Q: The graph of a function f is given. (Enter your answers as comma-separated lists (a) At what numbers…

A: The condition of existence of limit at x=aThe condition of continuity of function at x=a

Q: (A) Estimate the area under the graph of f(x) = 56x² from x = -4 to x = 2 using three approximating…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The first function is,.The second function is,

Q: Does fx(x,y) when at (a,b), fy(x,y) has to be at (a,b) Explain why statement is true or explain why…

A: Let f(x, y) and its first and second derivatives are continuous at (a, b) and that, , then1) f has…

Q: The total U.S. personal income I (in billions of dollars) from 1970 and projected to 2024 can be…

A: We are given the U.S personal income from 1970 to 2024 can be approximated by where t is the number…

Q: Solve the equation tan(x) = -2.4 on the interval 32 EX²47

A: In this question, we will solve the given equations.

Q: Consider the logistic equation dy dz (b) Find the time t when yi(t) = 6. t = = y(1-y) (a) Find the…

A: The given differential equation

Q: Sketch the graph of the function. O -2 f(x) = x - 1 (In(x) -1 if x ≤ 0 if 0 < x < 1 if x 2 1 y 444…

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Q: Consider the following. f(x) = √5-x 2x - 3 Find each limit. (If the limit

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Q: Let f(x)=x² - 2x + 6, g(x)= and h(x) = √26-x. Find f(0), g(0), h(0), f(a), and f(-x). √x

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Q: Given the series: Σ [In(2(k+ 1)) - In(2k)] k=4 does this series converge or diverge? O diverges O…

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Q: B. A parabola has its vertex at the origin, its axis is along the x-axis, and passes through the…

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Q: Given: f(x) = 3x² a) Show the steps of how you find the limit of the difference quotient to find the…

A: The given function is; f(x)=3x2,, point (2,12).

Q: The following integral may be evaluated by using integration by parts. Note: e can be entered by…

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Q: Consider the following. x - 5, f(x) = x² + 5, 7-X, for x ≤-1 for-1 1 Find lim f(x). (If the limit…

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Q: Rewrite the following equation with the variables separated. y' = 6xy² + 2xy + 6y² + 2y

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Q: 18 Find the product of -2 + 1i and its conjugate. The answer is a + bi where The real number a…

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Q: Given the tables for f & g below, find the following: x f(x) g(x) 0 1 2 3 4 5 6 7 8 9 1 3 9 8 0 4 2…

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Q: Determine whether the improper integral converges, and, if so, evaluate it. ∞ x -3 dx

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The upper curve is,The lower curve is,.The lower and upper limits are:

Q: In a right-angled triangle, one of the angles is 40°. If the side adjacent to this angle is 50.0cm,…

A: 1)                           From pythagerous theroem,…

Q: Write the standard form of the equation of the circle with the given characteristics. Center: (4,…

A: Standard Form of Equation of a circle is given as follows Where ( h , k ) are the coordinates of…

Q: 19. Let P denote the unit circle, parametrized in the usual way. Compute Jp F-dr, where F(x, y) =…

A: To compute

Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

A: Given

Q: 7. Use Newton's method to find the positive root of 3 sin x = x correct to six decimal places.

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Q: Find the values of a and b that make f continuous everywhere. x² - 4 x-2 a = 3 b = f(x)= ax² - bx +…

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Q: Obtain the General Solution of the following differential equations. 1. x²y y' = ey

A: x2yy'=ey be the differential equationWe have to find general solution

Q: He graph (a) lim f(x) = (b) lim f(x) = →2 (c) lim f(x) = (d) lim f(x) = (e) lim f(x) = -8+#

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Q: [22¹ sin (2³ - 1) da

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Q: Find the quotient a+bi. 1 + 2i 7i The real number a equals The real number b equals and write the…

A: Since you have asked multiple questions in a single request ,we will be answering only first…

Q: using integration by parts, evaluate the following: ∫ arctan4tdt

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Q: 3 B d The following integral may be evaluated by using integration by parts. Notes: • powers can be…

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Q: Let V R. For u, v EV and a ER define vector addition by uv :-u+v-1 and scalar multiplication by a Eu…

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Q: Suppose f: R³. → R is a differentiable function which has an absolute maximum value M # 0 and an…

A: We need to find correct option.

Q: Find the product of -2 + 1i and its conjugate. The answer is a + bi where The real number a equals…

A: To find the product of  and its conjugate.Note: Since the student has posted two questions and has…

Q: Establish an integral to compute the Laplace transform of the subsequent function: 0≤ t ≤6 6 ≤t f(t)…

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Q: Is this statement true explain why, if false explain why if x² te=10, then y'= -2x

A: find dy/dx

Q: Complete the square of the given quadratic expression. Then, graph the function using the technique…

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Q: Find the solution to the boundary value problem: d'y dy dt2 Y -13- +36y= 0, y(0) = 8, y(1) = 9 dt

A: Given Boundary Value Problem

Q: Name: Example 9: Prove that lim(4x - 5) = 7. Example 10: Prove that lim √√x = 0. x→0+

A: 9)limx-3(4x-5) =710)limx-0+ sqrt(x)=0

Q: C -6 -5 -3 O -10 -9 -8 -7 -6 -5 -4 -3 -2 -10 -1 -2 1 10 5 9 B 76 5 4 3 2 1 Use the graph to fill in…

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Q: Evaluate the limit: lim h→0 (1 + h)² - 1 h

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Q: The graph of a polynomial function y = f(x), is shown at right. Identify the properties and…

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Q: Find the area of the shaded region. 1(1, 1) 5 10 y=√x y = 15 20 X = 27 25 X

A: The region bounded by curves  and  The given graph