Find the angle between the plane 3x+y+z=10 and x-2y+2x=-1.

Q: Use the formal definition of the limit of a sequence to prove the following limit.

A: use the formal definition of the limit of a sequence to we have to following limit    limn→∞1n=0 usi...

Q: In Exercises 55–57, determine whether the given points are coplanar.55. A(1, 1, 1), B(-1, 0, 4), C(0...

A: Concept - In order to check whether points are coplanar or not, if the determinant of three vectors ...

Q: Find the slope of the line passing through each pair of points or state that the slope is undefined....

A: Given that, The points (6, -4) and (4, -2). By using the formula of the slope, m=y2-y1x2-x1 Take (x1...

Q: Use a vertical shift to graph one period of the function.

A:

Q: = 5x- 14/15 dx Find the function y(x) satisfying and y( - 1) = - 7.

A: Given, dydx=5x-1415   and  y(-1) = -7  

Q: 6. The present value of a sum of money is the amount that must be invested now, at a given rate of i...

A: givenP=$20000R=4.2%n=8 yearssince compounded quarterly tjerefore we apply this formulaAmpont or pres...

Q: Solve the initial-value problem -2 x' = -1 х, 1 -2 x(0) 3

A: Given information: x' =-201-2x  and x0=-13

Q: Evaluate the following integral. tan x x sec 2x tan x sec x dx =

A:

Q: Find two different sets of parametric equations for the rectangular equation. (Enter your answer in ...

A:

Q: At the surface of the ocean, the water pressure is the sameas the air pressure above the water, 15 l...

A: Given: At the surface of the ocean, the water pressure is the same as the air pressure above the wat...

Q: A square changes its area at a rate of 300 units^2/s. If a circle is always inscribed in this square...

A: Suppose S be the area of the square and r be the radius of the circle.   Draw the figure of the prob...

Q: Evaluate the integral. integral    (x 3   - x + 6 ) / (x  2  +2)  (  x2  + 1) dx

A: To evaluate:  ∫x3-x+6(x2+2)(x2+1)dx

Q: An equation of a quadratic function is given f(x) = 5x2 - 5x. Solve; a. Determine, without graphing,...

A:

Q: Use the quotient rule to simplify the expressions.Assume that x > 0. √200x3/√10x-1

A: Consider the given expression as 200x310x-1

Q: The rate of change in data entry speed of the average student is ds/dx = 4(x + 1)¬1/2, where x is th...

A: Given: The rate of change in data entry speed of the average student is dsdx=4(x+1)-12 Now, ds=4(x+1...

Q: a. Find the slope of the tangent line to the graph of f at the given point. b. Find the slope-interc...

A: Given, f(x)=23x at (3,6)

Q: Determine whether the series converges or diverges

A:

Q: 2a.

A: Given:        (a): ∫0ln(3)e2t+5etdt

Q: 4. Finding one-sided limits (both left-hand and right-hand) first, evaluate each limit below (you ma...

A: Here given as (a) limx→-22x+2x+22 find left-hand limit  L.H.S=limh→02(-2-h)+2-2-h+22         =limh→0...

Q: consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle...

A: Given, the position of the particle is  r(t) =b(ωt-sinωt)i^+b(1-cosωt)j^ The velocity vector is foun...

Q: Given the derivative of f, use sign chart to determine the interval(s) where f is increasing/decreas...

A: The derivative of a function may be used to determine whether the function is increasing or decreasi...

Q: Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the grid...

A: In this question, we have a given graph 

Q: The volume of a right-circular cone of radius r and height h is represented by V = (1/3)r2h.        ...

A: Given that, The volume of a right circular cone of radius r and height h is represented by V=13πr2h ...

Q: Find the integrating factor of the differential equation dy + 2xy = x³ dz %3D a. b. c. 2 In (r) d.

A:

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircl...

A:

Q: 12. A parking lot has visitor spaces, numbered from 0 to 30. Visitors are assigned parking spaces us...

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any s...

Q: #30) find the absolute extremum, if any, given by the second derivative test for each function

A:

Q: 5. Solve the following equation. Find the exact solution(s). anoiluloe auoensike yns ylitnebl noilsu...

A: Given 32x+1 = 78x-2 We have to find the value of x

Q: Calculate the consumers' surplus at the indicated unit price p for the demand equation. HINT [See Ex...

A:

Q: why first derivative is zero at local maximum and local minimum of function in an open interval

A: The first derivative is zero at local maximum and local minimum of function in an open interval beca...

Q: #46)

A: Given, AB = 5 miles BD = 10 miles BC = x CD = 10-x In ∆ABC, using Pythagoras theorem AC2=AB2+BC2AC2...

Q: Given that f(x) = 2x^3+9x^2-60x+70, find it's second derivative and its sign chart. Find when f is c...

A: Given, f(x) = 2x3 + 9x2 - 60x + 70  Differentiating the both sides f'(x) = 6x2 + 18x - 60           ...

Q: Write the first six terms of the arithmetic sequence: a1 = -7, d = 4

A: Given: a1=-7,d=4

Q: The annual net sales (revenue) earned by Nintendo in the fiscal years 2000 - 2014, can be approximat...

A: R(t) = Annual net sales revenueR(t) = -3.75t3 +65.8t2-206t + 578    (billion yen per year)When start...

Q: Differentiate the function.   f(x)  =π2

A: Given:fx=π2

Q: A company needs 150,000 items per year. It costs the company $720 to prepare a production run of the...

A: From given, the preparation for the production cost is $720. The cost of producing an item is $18. C...

Q: Find a power series representation for the function. (Give your power series representation centered...

A: Given: The function, fx=89-x.

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t ...

A: To write the gcd(117, 213) as a linear combination.

Q: Let f(t) measure the level of oxygen in a pond, where f(t) = 1 is the normal (unpolluted) level and ...

A:

Q: Solve the equation cos 2x = √2/2  on the interval [0, 2π).

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.