find the point at which the line g(x)=−1x+0g(x)=-1x+0 intersects the line k(x)=−4x+9

Q: Find the solution of the equation on the interval [0, 2π).

A: We have, cos (A+B) = cos A cos B - sin A sin B sin (A-B) = sin A cos B-cos A sin B

Q: Given the profit function P(x) = 1.3x – 0.01x² – 30, find the value of x at the function's optimum…

A:

Q: Obtain the general solution y

A:

Q: Find the relative maximum and minimum values. =x2 + y² - 6x + 12y - 9

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Q: Solve using the method of undetermined coefficients: x" – x' = te*;x(0) = 2,x'(0) = 1 %3| -

A:

Q: Solve for x and y simultaneously: x-2y -3 and y320

A:

Q: show that the 2x2-y2=C is a solution to yy'-2x=0.

A:

Q: Find a formula for the quadratic function whose graph has y-intercept at y=11 and zeros at x=1 and…

A:

Q: If the total revenue function for a blender is R(x) = 40x − 0.01x2   where x is the number of units…

A:

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: - Find the number of non negative solutions to x + y + z = 21.

A:

Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

A:

Q: Use Fixed-Point method to find solution accurate to within 10 for the following nonlinear equation:…

A: Given equation is, The given initial solution is,  To find the solution of the given equation…

Q: Find the equation of the line tangent to the graph of f(x)=5x^{3}+6x^{2}-6x-3

A: This question is related to functions, We will solve it using given information.

Q: 8. For the graph of the linear function H(z) = -4z + 3, the slope is %3D and the y-intercept is

A: Consider the given equation as Hz=-4z+3

Q: Find the general solution of (D3-D2+D-1)y = 15sin2x using method of undetermined coefficient.

A:

Q: Find the equilibrium point. D(x) = 7- 8x, S(x) = 3 + 8x

A: Equilibrium point is the point at which demand and supply function intersects. That means at…

Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: solve for y in terms of t or x, as appropriate.

A:

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Find the general solution to x”-3x’+2x = e^t

A: First we find complementary function then particular integral and then general solution.

Q: 2.a. Find the maximum and minimum values of the function: y = 3x² 18x +31 -

A: We have to find the maximum and minimum values of the given function y=3x2-18x+31 .

Q: Find the value/s of x for which y=3x^4-4x^3+1 is maximum?

A: y=3x4-4x3+1 Differentiating with respect to x, we get dydx=34x3-43x2+0=12x3-12x2 Now to find…

Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: ose the percent of males who enrolled in college within 12 months of high school graduation is given…

A: Given: y=-0.126x+55.72 y=0.73x+39.7

Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: The annual total revenue for a wis given by R(x)=24,000x-6x^2 dollars, where x is the number of…

A: To find maximum no of units sold. Also to find maximum possible annual revenue.

Q: Find the maximum value of ƒ(x, y) = 49 - x2 - y2 on the line x + 3y = 10.

A:

Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

A:

Q: The production function of a competitive firm is described by the equation y = 2.x26x,2. The factor…

A: Given the production function of the competitive firm : y=2x1126x212 The factor prices are p1=$3 and…

Q: Find the particular solution determined by the initial condition. f'(x) = rx) = 2x2/5 - 3x, f(1) =…

A:

Q: 16 Solve the equation for for y 3rex 1 r2 x - 0

A: 3xex+x2ex=0

Q: Solve (x + 2)x 4 geometrically by constructing a line segment of length x .

A: We can expand it by multiplying x inside bracket then it is parabola equation then draw the parabola…

Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: 24. Find the point of inflection of the curve x3 – 6x2 + 2x + 14.

A: Using formula of point of inflection of the curve.

Q: Find the particular solution y''-2y'-3y=0; when x=0, y=0, y'=-4

A: It is given that the differential equation  y''-2y'-3y=0,  y0=0 and y'(0)=-4     The given…

Q: Find the Particular Solution indicated. (Homogenous Linear Equation with Constant Coeffiecients)

A: Given : Homogenous Linear Differential Equation with Constant Coefficients               D2+D-12y=0…

Q: Find the solution of y-x =0 using separable variable method. dx

A:

Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

Q: Find the critical points of the function f(x)=x2−4x+3x−2.

A:

Q: Find the point at which the line f(x)=−5x−3f(x)=-5x-3 intersects the line g(x)=−x+1g(x)=-x+1

A: The given functions are fx=-5x-3gx=-x+1

Q: Find the maximum revenue for the revenue function  R(x) = 372x − 0.7x2.

A: To Determine :- The maximum revenue for the revenue function. Rx = 372x - 0.7x2

Q: Use variation of parameters to find the general solution of y′′−2y′+ 2y=(e^x)csc(x)

A:

Q: Find the point at which the line f(x) = - 3x +8 intersects the line g(x) = -5z + 16 %3D %3D

A: Given f(x)=-3x+8 g(x)=-5x+16

Q: Over the next 20 years, a company projects its continuous flow of revenue to be R(x) = 100e01z…

A: Consider the provided question,

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: Find the attractive fixed point of g(x) = 4x - x2 4 | 2

A: Fixed point: The point of intersection of y=f(x) and line y=x are known as fixed points: Example:…

Q: Find the general solution of (2x –y) = 2y – x

A:

Q: Find the general solution for y' = y – xy³e-2x

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.