Determine the amplitude, period, and phase shift of the function y = 3 sin(2πx + 4). Then graph one period of the function.

Q: Solve the system x2 + y2 = 25, (x - 8)2 + y2 = 41 by the addition method.

A: Consider the given system of equation, x2+y2=25                             ⋯⋯1 x-82+y2=41          ...

Q: Find the areas of the shaded regions

A: From the figure, shaded region lies above the x-axis and below the x-axis as well.Above the x-axis, ...

Q: Determine whether the statement, given in inverted commas" is trueor false. If the statement is fals...

A: we have to determine whether the given statement is true or false. Statement: "5 + 3(x - 4) = 8(x - ...

Q: Find the least squares regression quadratic for the points (−2, 0), (−1, 0), (0, 1), (1, 2), (2, 5)....

A: Least square method:

Q: Write the first four terms of the sequence {an} defined by the following recurrence relation. an + 1...

A: Given: an+1=an+an-1  ,a1=1,a0=1

Q: (b) What is an approximate value for e ?

A: we have to determine the approximate value of e.  

Q: 4) Evaluate the following sin (x) -dx 1+ cos (x) 1 ex dx (4x³ + 7*)dx --

A: Consider the following integral: I=∫sinx1+cosxdx Substitute 1+cosx=t→-sinxdx=dt→sinxdx=-dt in I: I=-...

Q: The edge x of a cube is measured with an error of at most 0.5%.What is the maximum corresponding per...

A: Given: Let x be the edge of the cube with an error of 0.5%.  

Q: . Find the domain and range of the function whose graph is shown on the right. Give 1. your answer u...

A: A graph

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance 

Q: Find the value of constant K that makes the function below continuous at x = 4. x2 - 4x X< 4 f(x) = ...

A:

Q: What is a polynomial inequality?

A: An equality having both the sides of it as polynomials, are said to be Polynomial Inequality. The in...

Q: Solve:(x + 3)/4 =[(x - 2)/3 +1/4]

A: x+34=x-23+14

Q: Find the area of the region bounded by the ellips

A:

Q: Evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits th...

A: Given: limx→b x3-b3x-b.

Q: write the sum using sum characters (sigma Σ )

A:

Q: Differentiate implicitly cos(x³y³) = 9

A: Given,         cosx3y3=9

Q: please show all your work step by step. Given a = 4i + 5j and b = 6i + 7j, express i and j in terms ...

A:

Q: Evaluate the integral. integral       x +4 / (x  2 + 2  x  + 5 ) dx

A: The given integral ∫x+4x2+2x+5dx can be evaluated as, ∫x+4x2+2x+5dx=∫x+4x+12+22dx                   ...

Q: For what values of c are the vectors &lt;2c,4&gt; and &lt;c,-4&gt; perpendicular?

A: we will use dot product of two vector.

Q: Solve the absolute value equation or indicate the equation has no solution :      2x - 3 = 11

A: Consider the given absolute value equation, 2x-3=11 As we know that x=c is equivalent to x=c or x=-c...

Q: Describe one similarity and one difference between the graphs of y2 = 4x and (y - 1)2 = 4(x - 1).

A: Describe one similarity and one difference between the graphs of y2 = 4x and (y - 1)2 = 4(x - 1).

Q: Evaluate the limit.

A: Consider the given limit, limx→-∞2x5+3x4-31x8x4-31x2+12 take x5 common from the numerator and x4 fro...

Q: If limxS1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude anything ab...

A: Given limx→1fx=5

Q: Use the result in Example 3 to find dx6

A: Let,f(x) = x-1          ............(1)We have to find ,d6dx6x-1 = ?Differentiating equation (1) wit...

Q: Locate the critical points of the following function. Then use the Second Derivative Test to determi...

A: Consider the provided function, fx=6x4lnx2-7x4 Locate the critical points of the following function....

Q: The position of an object in circular motion is modeled by the parametric equations x =3 sin 2t y = ...

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

Q: Graph the solution set of the system 3x + y ≤ 6, 2x - y ≤ -1, x &gt; -2, y &lt; 4 of inequalities or...

A: Given inequalities are 3x+y≤6                                 ……(1)2x-y≤-1                          ...