Sequences & Series Questions and Answers

Let f(x) =1/x-7 and g(x)=( 4/x)+7. Find the following functions. Simplify your answers. f(g(x)) = g(f(x)) =

tan(x) + cot(x) = 2 csc (2x) i have the answer but could you please explain each step thoroughly as i am stuck on this question and how did it get there. 2/sin2x = 2 csc (2x)

The height y (in feet) of a ball thrown by a child is y= -(1/14)x²+6x+3 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? (b) What is the maximum height of the ball? (c) How far from the child does the ball strike the ground?

Simplify the following expression. (2-3√-2) (2+3√2)

Jen really hates spiders. Her house is infested and her exterminator tells her that the pesticide has a continuous kill rate of 0.90%. (a) If the exterminator estimates that there are 10,000 spiders in her basement (gross), how long until half of the spiders are gone? Round your answer to two decimal places.

You attend the ULC Valentine's Day Dance and stay to help clean up afterwards. To help, you collect the soda cans, Coca-Cola and Sprite, and organize them. Some cans were on the table, and some were in the garbage. Seventy-two total cans were found. 42 total cans were found in the garbage and fifty total cans were Coca-Cola. 14 Sprite cans were found on the table. Complete the two-way frequency chart, then answer the questions below. Coca-Cola Sprite Total Party Table Type Garbage Total a) How many more cans were found in the garbage than the table? b) True or False, there were more Sprite cans found at the part than Coca-Cola. Provide evidence.

The following is a graph of which inequality? (a) x <= -6 (b) x >= -6 (c) x < -6 (d) x > -6

The graph represents a function. Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function? (A) (2, -3) (B) (-3,-1) (C) (3,0 ) (D) (-2, 1)

Find the indicated term for the sequence whose general term is given. an=(-1)ⁿ/(n+2) ;a21=

A trainee in a computer company takes 0.8 times as long to assemble each computer as he took to assemble the preceding computer. If it took him 40 minutes to assemble the first computer, find how long it takes him to assemble the seventh computer. Find the total time he takes to assemble the first seven computers. It takes _______ minutes to assemble the seventh computer. The total time to assemble the first seven computers is _______ minutes.

Rachel has two coupons for a chair. Coupon A:15% off of a $45 chair Coupon B:$4 rebate on a $45 chair Choose the coupon that gives the lower price. Then fill in the blank with the correct value. Coupon A gives the lower price. The price with coupon A is $ _less than the price with coupon B. Coupon B gives the lower price. The price with coupon B is $_ less than the price with coupon A.

The population size of a culture of bacteria triples every hour such that its size is modeled by the sequence an = 150(3)^(n-1), where n is the number of the hour just beginning. Find the size of the culture at the beginning of the fourth hour and the size of the culture at the beginning of the first hour. At the begining of the fourth hour, the size of the colony is ___ bacteria. At the begining of the first hour, the size of the colony is ______ bacteria.

Match what you type in Desmos for each type of relationship. Column A Column B 1. Line of Best Fit a. yl-ax1^2+bx1+c 2. Curve of Best Fit b. yl-mx1+b 3.Quadratic- 4.Linear

Find the vertex of the parabola and then graph it. x = 7y² The vertex is (Type an ordered pair.) Use the graphing tool to graph the parabola.

Identify the domain for the rational function: y = [2/(x+2)]+1 Explain how to tell where the horizontal asymptotes are.

Find the difference quotient (f(x+h)-f(x))/h for the function f(x)=3/(x-5) Simplify your answer.

A ship was sighted from a lighthouse on a foggy night. When the ship was first sighted, the bearing of the ship was N 13° E. The ship then sailed for 5.9 miles due south. The new bearing was N 28° E. Find the distance between the ship and the lighthouse at each location. The ship was first sighted at ____ miles from the lighthouse. The new location of the ship was ____ miles from the lighthouse.

Let f(x) = 1/(x-7) and g(x) = (4/x)+7. Find the following functions. Simplify your answers. f(g(x)) = _________________ g(f(x)) = _________________

Solve the inequality -7 ≥ x - 12 (A) x ≥ 5 (B) x ≥ -19 (C) x ≤ 5 (D) x ≤ -19

Approximate √(-0.33) in terms of the imaginary unit, i, rounded to two decimal places.

Find the twenty-ninth term of the arithmetic sequence 24, 22, 20, ... a29=_______(Simplify your answer.)

How many possible arrangements are there for a deck of 52 playing cards? (Consider only the order of the cards, and not whether they are turned upside-down.) Suppose you start with a sorted deck and shuffle it repeatedly, so that all arrangements become "accessible." How much entropy do you create in the process?

The arch of a bridge can be modeled by y = -0.002x² +1.06x, where z is the distance (in meters) from the left pylons and y is the height (in meters) of the arch above the water. The road can be modeled by the equation y = 52. To the nearest meter, how far from the left pylons are the two points where the road intersects the arch of the bridge?The road intersects the arch of the bridge about meters from the left pylons and about [ meters from the left pylons.

Select ALL that apply. The figure shown is a quadrilateral. Determine which sequences of transformations performed on the figure result in a figure that is similar but not congruent. A) Translation right and up followed by a dilation with a scale factor 1.5 B) Translation up and to the left followed by a reflection across a horizontal line. C) Dilation with a scale factor of 3 followed by a reflection across a vertical line. D) Reflection across a vertical line followed by a dilation with a scale factor of 1/2. E) Rotation 180° clockwise around the origin followed by a translation to the right.

Find a, for the arithmetic sequence with a₁ = 5,d = −4, n=98. (a) -392 (b) -387 (c) -383 (d) 393 Determine the seating capacity of an auditorium with 30 rows of seats if there are 25 seats in the first row, 28 seats in the second row, 31 seats in the third row, and so on. (a) 1635 (b) 1792 (c) 2055 (d) 3125

Consider the equation x₁ + x₂ + x₃ + x₄ = 16 . How many solutions are there with 2 ≤ Xi ≤ 6 for all i ∈ {1,2,3,4} ?

Multiply. (2√3-4) (3√6+1) Provide your answer below:

Simplify. (Assume all variables represent positive real numbers.) √(a³b³)/√(ab)

Consider the following piecewise function. -3x + 2 , x < 2 f(x) = 2x-7, x≥2 Evaluate f(6) (A) -16 (B) 5 (C) -11 (D) -4

Solve the inequality (x-2)(x − 3)² > 0 Select all the intervals below that are included in the solution. x<2 x<3 2<x<3 x>2 x>3

Express using rational exponents.∛ 9 Provide your answer below:

The school's flagpole has been bent at the base 12" from vertical as shown in the figure. If a 22-ft rope that is attached to the top of the pole touches the ground, what is the actual length of the flagpole?

For each polynomial, find all roots of the function and simplify them as much as possible. Then sketch the complete graph, indicating the viewing window, the x-intercepts and the relative maximum and minimum. (a) f(x)=x³+2x²-3x-6 (b) f(x)=2x³-7x²-3x+8 (c) f(x)-x³-8x²+21x-20

Solve the equation [9]17 X+ [4]17 = [6]17 X + [8]17 for XE Z17. Write your answer as X = [X]17 where 0<x< 17. What is x?

The graph of y=f(x) is shown. Draw the graph of y=f(2x) (b) The graph of y=g(x) is shown. Draw the graph of y=1/2g(x)

Find the equation for the parabola that has its focus at the(-11/4,-2) and has directrix at x =51/4

The number of species born each year in a new aquarium forms a sequence whose general term is an = (n +9)(n+2). Find the number of species born in the fourth year, and find the total number born in the first four years. The number of species born in the fourth year is The number of species born in the first four years is

Determine the simple interest rate if an investment of Php65,000.00 accumulates to Php100,000.00 in 45 months. Round off answer to two decimals. A) 12.17% B) 12.18% C) 14.35% D) 14.36%

Each side of an equilateral triangle has a length of d inches. The area of the equilateral triangle is given by A = √³/4d². Identify the equation(s) that represent the length of a side. b=2 x 3³/⁴ A¹/₂ d= 4√3/3 A¹/₂ d= 3√3/4 A¹/₂ d = 3√3/4 A¹/₂

Multiply, simplify your answer. ∛9x²y² ( ∛4xy + ∛x²y³ )

Rationalize the denominator. Assume all variables represent positive real numbers. (-2√2) / (4-3√2)

10).Find f(g(x)) when f(x) = 2x + 1 and g(x) = x² + x

Solve the system. y = x² + 7x+7 y=x+2 The solutions are and.

Simplify sec(t) - cos(t)/tan(t) to a single trig function.

Which of the following is a parameterization of the line that passes through the point (-1,-6) with a slope of 4? (a) z = t and y = 4t - 6, for any t (b) z = tan t and y=4 tan t + 2, for π/3 < t < π/2 (c) z = 3t and y = 12t - 2, for any t (d) z = t + 3 and y = 4t + 1, for any t

Consider the equation x₁ + x₂ + x₃ + x₄ = 16. How many solutions are there with 2 ≤ Xi ≤ 6 for all i = {1,2,3,4} ?

A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick. Let y represent the ice sheet's thickness (in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks.

Test the series for convergence or divergence. ∞ Σ(−1)^(n-1)e^(4/n) n=1 Identify bn. ________________ Evaluate the following limit. lim (bn) n→∞ ________________ Since lim bn =____ 0 and b(n +1) ____ bn for all n, ____________________ n→∞

Solve the inequality. Express the solution both on the number line and in interval notation. Use exact forms (such as fractions) instead of decimal approximations. a) x² - 2x - 3 ≥ 0 b) 6x - 2x² > 0 c) (3x-4)/(9x+17) ≤ 0 d) (6x + 5)/(7x - 13) (2) Solve the inequalities algebraically and write the solution as an interval. a) |3x - 2| < 4 b) |5 - 2x| ≥ 9

Perform the operation and simplify. Leave answers in exponential form. 5^3/2.5 ½ Provide your answer below: