Where does the line that passes through the point (1,0,2) in the direction of the vector <2,-1,4> intersect the xy-plane?

Q: Find the derivative of the function: F(x)=√x arctant dt

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Q: The "vertex" of the graph of a quadratic function is the point that corresponds to the minimum (or…

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

Q: What is the approximate value of log (812000 A 8000 B 162000 C 81000 D The value cannot be…

A: The given expression is

Q: Let f(t) be the population (in thousands of people) of Math City, as a function the time t (in…

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Q: Determine for the two vectors: x = ai+bj+ck and y = di+ej+Xk where a = 2.3, b = 3.5, c = -4.3, d =…

A: Given,Given,

Q: Find H′(x) for the given function.   ​H(x)=3/ x+2

A: The objective of the question is to find the derivative of the function H(x) = 3 / sqrt(x+2).

Q: 1. Consider the function f given by f(x) = 2x² - 3x + 6. *Make a table to show the following. a.…

A: Consider the function  given by (a) To determine the average rate of change on the interval .(b) To…

Q: Verify that y = re³ is a solution to the differential equation y" - 6y + 9y = 0.

A: Consider the differential equation

Q: 3. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

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Q: Find the indefinite integral. 10 (+/-) cot Select one: O a. O b. O c. O d. e. dr 10 - 20 sin()+c 10…

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Q: Use the substitution t = tanto transform the integrand into a rational function of t and then…

A: By using the substitution  to transform the integrand into a rational function of  and then to…

Q: 1. Express 3-² == in logarithmic form.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The dimension of a rectangular shape cardboard are 8 x 3 cm rotated about the axis of 8 cm to form a…

A: The dimension of a rectangular shape cardboard are 8 x 3 cm rotated about the axisof 8 cm to form a…

Q: From the set of provided options, select the correct coefficients for the factored form of the…

A: 6x2+x−1=(ax+b)(cx+d)

Q: Let f(x, y) vector (-1,-1) is 8 Then Vf= and Duf(-2,-4) in the direction of the

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Q: Determine the dot product for the two vectors: x = ai+bj+ck and y = di+ej+fk where a = 4, b = 5, c =…

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Q: A rock is thrown upward from a bridge that is 96 feet above a road. The rock reaches its maximum…

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Q: Write the equations of the horizontal and vertical asymptotes?

A: we have given graph to find the vertical and horizontal asymptotes.

Q: Obtain the following integral: 30x⁹ √ (210 + 8) dx as a function of a to within an additive constant…

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Q: A rhombus is inscribed in a rectangle that is w meters wide with a perimeter of 44 m. Each vertex…

A: Solution is following in explanation step.

Q: Find a simplified form of the difference quotient for the function. 9 X+9 f(x) = O A. (x+ B. O C. 9h…

A: Given,

Q: Evaluate the definite integral Select one: a. 5 O b. 0 o c. 2 O d. 6 O e. 1 sin³t cost dt.

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Q: f(x+h)-f(x) c) Find f'(x) by determining lim h h→0 d) Find f'(0) and f'(2). These slopes should…

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Q: A farmer has 600m of fencing to use for building a sheep pen in the shape of a semicircleon top of a…

A: The objective of this problem is to find the dimensions of a field, which is a combination of a…

Q: X 19. lim x→1x² + 4

A: To find:-The condition of existence of limit at

Q: Sketch a graph of f(x) = = 5 4 3 2 1 -5 -4 -3 -2 -1 Clear All Draw: 7 -1 -2 -3 -4 - 1 2x I 2 1 2 3 4…

A: The given function is: f(x)= (-1/2)x -2

Q: The temperature at a point (x, y) on a rectangular metal plate is given by T(x, y) = 100 - 2x2 - y2.…

A: Given: T(x,y) = 100-2x2 -y2We have to find the path a heat-seeking particle will take, starting at…

Q: The slope of the line below is -4 -3 -2 -1 5 4 3 2- 1 P -2 -3 -4 12 a

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Q: d dx -2x+1 √²2+¹ +11 dt S=2x

A: f(x)=ddx∫−2x2x+11t+1dt

Q: Step 5: Find the area of the region. Since, the area of the region bounded by the curve y=3x²-3 and…

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Q: X lim x→1x² + 4

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Q: I have 8 coins in my pocket, some are quarters and some are dimes. If I have $1.10 in my pocket, how…

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Q: 3. Find the total area between the region and the x-axis. a. y = -x² - 2x, -3 ≤ x ≤ 2 b. y = 3x² -3,…

A: To find the total area between the region and the x-axis.

Q: What is the product using Pascal's triangle : (m-n)^3(m+n)^3

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Q: 55. lim x →0 √x +5-√√5 X

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Q: Please re evaluate the integral. The provided answer is incorrect

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Q: f(x) = x²-6x+5, what is the domain of the inverse of the function  (f^(-1))?

A: f(x)= x2 -6x +5 f(x)= y= (x-3)2-4 Graph of f: f(x)= (x-3)2-4 is an upward parabola having veterc at…

Q: Find the work done by the force field F(x, y, z) = xyi+yzj+xz k on a particle that moves along the…

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Q: First find f' and then find f. f" (x) = 2x³ + 10x² + 6x +1, ƒ'(1) = 4, f(1) =-10.

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Q: A gasoline-powered lawn mower produces a sound of 98 decibels. An electric lawn mower produces a…

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Q: List the points in the graph in the interval -2<x<8 at which the function is not differentiable. 10…

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Q: Find the exact solution(s) to the following equation. 2e²x=5e*-2

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Q: Find the volume, V, of the solid formed, when the part of the curve y = 0.8x¹.5, is rotated about…

A: The objective of this question is to find the volume of the solid formed when the part of the curve…

Q: Find the limit. (If the limit is infinite, enter '' or '-', as appropriate. If the limit does not…

A: Given Expression is as follows

Q: For the given​ function, find the points on the graph at which the tangent line has slope 1.

A: The objective of this question is to find the points on the graph of the function y = 15x - x² where…

Q: Find X con. 76 lim 1x-61 x →6 X-61 -X-6

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Q: Consider the following linear equation: 2(x-3) + 1 = 4(x - 1)-5(x + 1) Which of the following…

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Q: A rock is thrown upward from a bridge into a river below. The function f(t) = 16t² + 38t+ 92…

A: A rock is thrown upward from a bridge into a river below. The function  determine the height of the…

Q: A flower store stocks three kinds of flowers: lillies, roses, and carnations. The lilies cost 0.4…

A: Let x be the number of lillies.Let y be the number of roses.Let z be the number of carnations.

Q: lim x 7-5 X vx2 +9 X =

A: The objective of the question is to find the limit of the function (5x / sqrt(x^2 + 9x)) as x…