Solve the following inequalities and write the solution in interval form i) 2|2x+7| +2 ≤24 ii) 3 3x-2 >24 Given f(x)= x+1 and g(x)= x2 + 4x, find (fg)(x) and write the domain of (fg)(x) in interval notation.

Q: For the following population model (in billions):…

A: As we can see these three are different questions and do not depend on each other. According to the…

Q: Evaluate the definite integral: 3 dr 3

A: We need to evaluate the following integral ∫13x3-3xdx

Q: The graph of x +y = 100 is a circle having center at the origin and radius 10. a. Write the equation…

A: The graph of the circle x2+y2=100 having center at the origin and radius 10

Q: Find the slope of the tangent line to the curve of intersection of graph of f and the plane x =2 at…

A:

Q: area of the region enclosed by y = 4 – x and y = -x+2, identit X'

A:

Q: Find the point on the line y = 1 – 6 that is closest to the origin. Give your answer in the form (a,…

A: We have to find a point on line which is closest to the origin.

Q: d) L{e f, sin dr}

A:

Q: xsin-1x dx V1-x2

A: We know, ∫udv=uv-∫u'vdv ddxsin-1x=11-x2

Q: Determine whether the planes are parallel, orthogonal, or neither. 2x - 10y - 2z - 1 2x - 10y - 2z =…

A:

Q: Find the area of the surface generated when the indicated arc is revolved about the x-axis.…

A:

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: The objective of the question is evaluate the vector with given magnitude and same direction vector.

Q: 6.26. у - 3у %3D0

A:

Q: | (u + 2)(3u + 4) du :

A:

Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

A:

Q: x² dx (3x3-4)5

A:

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

A:

Q: 11. The graph below represents the graph of y = csc x. -5 -10 -5 10 True False

A:

Q: Find the interval of convergence of the series. (3x)" Σ n· 2" n=1 (Use symbolic notation and…

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: S xsin²xdx 2. х

A:

Q: Evalua fe the integral 7) Of xy dx sübjcct to the functional relation X = at and

A:

Q: 25. Let OP be the position representation of vector A, 0Q be the position representation of vector…

A:

Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: Counting An employee group requires 6 people be chosen for a committee from a group of 16 employees.…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the average value TEX of the function f (x) =4sin cos on - 2 the interval [1,4].

A: Given problem:- f(x) =4 sin(πx/2) cos(πx/2)  To find:- Average value of the function over interval…

Q: Find the arc length of the parametric curve: x = e'(sint + cos t), y = e'(cost - sint) OstsIn3

A:

Q: Use the Ratio Test to determine the radius of convergence of x" Σ Vn : 11" n=1 Then determine…

A: Let's find.

Q: can you please and write and understand text

A: Apologies for the inconvenience. Here is the solution with improved explanation.    From the graph,…

Q: Find the area of the region between the graphs of f(x) = 6x + 8 and g(x) = x² + 3x + 2 over [0, 2].…

A:

Q: Evaluate the integral. |cos *x sin xdx Scos 4 cos "x sin xdx =

A: To find the value of given integral .

Q: - 1)*dx

A: ∫02 (x-1)2dx ∫02 x2 -2x +1dx [x3/3 -x2 +x ]02 8/3 - 4+2 -0 8/3 -2 (8-6)/3 2/3

Q: In Exercises 22 through 24, find an equation of the sphere satisfying the given conditions. 22. A…

A:

Q: Prove by contrapositive. if x and y are integers such that x > 1, and x divides y, then x / (y +1)

A:

Q: denote In°(x) dæ

A:

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

A:

Q: Evaluate x +1)?dx = [{(x+ 1}dx+ f{(x+ 1}°dx %3D

A: ∫13x+12dx=∫12x+12dx+∫23x+12dx⇒563=∫12x+12dx+∫23x+12dx⇒563=193+∫23x+12dx⇒563=193+373

Q: (ポ-2) X1 X

A: ∫12(x2 -2x)dx/x here now diivide by x ∫12 (x -2)dx [x2/2 - 2x]12 (2)2/2 - 2*2 - 1/2 + 2 2 -4 -1/2+2…

Q: Find the Jacobian of the transformation. x = 4e sin(20), y = er cos(20) a(x, y) a(r, 0)

A:

Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. 2x x* +7 xp-…

A:

Q: Consider the curve 5 sin(y) + 3 cos(x) = 2. %3D Find y' by implicit differentiation. Find y" by…

A:

Q: Find the limit. Use l'Hospital's Rule if it is appropriate. If there is a more elementary method,…

A:

Q: Determine whether the given differential equations are homogenous and, if so, solve them. 2x + y…

A:

Q: Find the area of all the regions bounded by ALL of the following: y = x, x + y = 0 and y = 2 - x².…

A: Given figure:

Q: Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the…

A:

Q: Let f(x) = cx3.4 and suppose that f(6) = 48. Find the value of c. (Round your answer to two decimal…

A: Given query is to find the value of c.

Q: 9! Calculate 7. 4! 5! 3024 15120 1814400 126

A:

Q: cosx dx sin²x-5sinx-6

A: Find your answer below

Q: For each sign chart for f'. Carefully sketch the graph of both functions f and f'. Upload your work…

A:

Q: 4. Evaluate y = sin¬1 (x) when x = 1 %3D O 37 2 -1

A:

Q: Use algorithm to sketch the curve given by the function f(x) = 1 4 x +2x2 +1 [A:6] a) Determine the…

A:

Q: How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n > 2…

A: