Sequences & Series Questions and Answers

If caffeine leaves the body at a continuous rate of about 16% per hour. How much caffeine is left in the body 8 hours after drinking a cup of coffee containing 100 mg of caffeine?

Use the sum-to-product identities to rewrite the following expression as a product. cos (45°) - cos (70) Answer 4 Points cos (45) - cos (70) =

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x

Given a circle of radius 12 in., find the length of the arc subtended by a central angle of 270°. Round decimals to the nearest hundredth.

Rewrite the following polar equation in rectangular form. r = -9sin0

Let g(x) = 7(x + 2)³(x - 3)²(x + 1). Which of the following has the same end behavior as g(x)? f(x) = -5(2-1)³ (+5) f(x)=3(x - 3)²(x+3) f(x) = f(x)=1 f(x) = 2x³(x - 1)²(x + 1) (x + 2)(x − 3)(x + 1)

The following is the graph y = f(x). Graph the transformation image of the graph that is represented by the equation y + 2 = -2f(2(x + 3)). State the domain and range. (5 marks)

What is the average rate of change of f(x) = 2x³ 3x² + 7 from x = 0 to x = 4? -

Given f(x) = e which of the following is the equation of the graph of f shifted left 3 and then reflected vertically? g(x) = 3e-2 g(x) = e* - 3 g(x) = - e + 3 g(x) = e + 3 g(x) = - e²+3

Simplify the following, using only positive exponents. Do not evaluate.

Show that if f is a bounded function on [a, b] then for any two measurable partitions of [a, b] we have U(P₁,f) ≥ L(P₂, f) and Lof(x) dxzLf(x)dx [7]

Use the formula for S₁ to find the sum of the first five terms of the geometric sequence 15, -5, 5/3, -5/9, ...

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point Con land such than ZCAB 43.3". Find the distance across the lake from A to B.

The length of a parking lot is 5 yards more than the width. If the area of the parking lot is 50 square yards, find the dimensions of the parking lot.

Using L'Hospital's rule evaluate: (a) lim 2-1 sin(πz) In z (b) lim Z-00 e1/2 - 1 1/z

Write the following expression as a single trigonometric ratio: sin4x/cos2x

12. If cos(θ)+sin(θ)=(1+√3)/2 and cos(θ)-sin(θ)=(1-√3)/2 find the value of sin(2θ).

A professor gives two types of quizzes: objective and recall. He plans to give at least 18 quizzes this quarter. The student preparation time for an objective quiz is 12 minutes and for a recall quiz 36 minutes. The professor would like a student to spend at least 4 hours (240 minutes) preparing for these quizzes above and beyond the normal study time. The average score on an objective quiz is 6, and on a recall quiz 4. The professor would like the students to average at least 88 points. It takes the professor 1.5 minutes to grade an objective quiz, and 2.5 minutes to grade a recall type quiz. How many of each type should he give in order to minimize his grading time?

Determine the sum of the geometric series 15-45+ 135 - 405 +... - 32 805

The ramp of a moving truck touches the ground 17 feet away from the end of the truck. If the ramp makes an angle of 14 relative to the ground, what is the length of the ramp? Round your answer to two decimal places.

According to the Rule of 72, how long would it take to double an $11,000 investment at a 1.5% compound interest rate? A. 11 years B. 18 years C. 27.3 years D. 48 years

Determine in which of the four quadrants angle θ is located given cos(θ)>0 and cot(θ) < 0

Given the graph of f(x) =3x+8/6x-5 shown here, determine the values of x that solve 3x+8/6x-5≥0

Find the 15th term of an arithmetic sequence if the first term is 27 and the common difference is. Round your answer to 2 decimal places as needed.

Suppose Roberto, Travis and Deandre go to a donut shop. Roberto buys 6 amaretto pumpkin, 6 black forest and 8 cotton candy donuts and ends up spending $48.70. Travis gets 5 of the amaretto pumpkin, 6 black forest and 6 cotton candy donuts for a total cost of $41.33. Lastly, Deandre spends $31.67 on 4 amaretto pumpkin, 4 black forest, and 5 cotton candy donuts. Write this scenario as a system of equations, then solve that system using an augmented matrix and RREF on your calculator before answering the question below. How much does a single amaretto pumpkin donut cost? Round your answer to 2 decimal places.

A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it has grown 9.67 inches, and after seven weeks it had grown 14.67 inches. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1) what is the slope of the function? m = 2) What is the initial value for the function 3) write the function I(w) = = 4) How tall will the vine maple be after 4 months? (If needed, round to 2 decimal places.)

Graph the function using the slope and intercept. f(x) = 1/3 x + 2 The slope is The y-intercept is

Solve the system. Give your answer as (x, y, z) 6c+y+4z = -55 2x+6y + 6z = - 54 6c – 5y + 2z = -29 (x, y, z) =

Is (2, 4) a solution of the inequality y < - 2x + 4 Yes, (2, -4) is a solution to y < - 2x +4 No, (2, -4) is NOT a solution to y < -2x + 4

Given f(x) = |-4 -3x|, find the following: f(-1) = f(-8)= f(- 6) = f(15) =

Find the domain and range of the relation: {(-5,5), (5, 4), (-5,3), (-5, 2)}. Then determine whether the relation is a function. Domain = { Range = { } Separate your answers by commas. } Separate your answers by commas. Is the relation a function? Yes No

Solve the inequality: -17≥ x + 29 Enter your answer as an interval, such as [a, ∞).

Find the intercepts of -3x + 4y = - 12. x-intercept = y-intercept = Using the intercepts from above draw the graph of -3x + 4y = - 12

Write the following in interval notation: x ≤ 20 and x ≥ 11 If no solutions exists enter No solutions. Use reduce fraction in your answer - no decimals!

Solve. Write your answer in interval notation. 2x+2 12 or 3x +3> 54 If no solutions exists enter No solutions. Use reduce fraction in your answer no decimals!

Solve the inequality: 12 ≥ x + 7 Enter your answer as an interval, such as [a, co).

Solve for x: -2 ≤-5x + 15 < 8 Write your answer in interval notation:

Write and inequality describing all the real numbers on the number line that are greater than or equal to 4. Inequality: Now draw the corresponding graph.

Use interval notation to indicate all the real numbers on the number line that are less than -27.

Which property is does 2(6 + 3) = 12 + 6 represent? commutative associative distributive identity inverse

Regular octagon ABCDEFGH is inscribed in a circle with radius r 7√/2 cm. Find the area (in square centimeters) of the circle. (Note: For the circle, use A-ar with = -3) x cm? Find the length (in centimeters) of one side of the square ACEG cm Find the area (in square centimeters) of the square ACEG. cm² Considering that the area of the octagon is less than the area of the circle and greater than the area of the square ACEG, find the two integers (areas in square centimeters) between which the area of the octagon must lie cm² mm² smaller value larger value

Solve. 3x + 3y + z = 5 x-3y + 2z=1 8x-2y+3z=4 The solution set is {} (Type an ordered triple.)

Find dy/da in terms of t if x = tet, y = 4t + 4et

Write the equation of the line with slope m = 7 and passing through the point (1,5). Write the final equation in slope-intercept form. .

Use the slope-intercept form of a line (y = mx + b) to graph the equation y = -3x/4 - 1 The slope is The y-intercept is

Values of c will the function y=x^2+6x+c have two x intercepts one x intercept no x intercept

Use the wrapping function to evaluate sins and coss for the real number s. S= -17x/3 Use the wrapping function to find the terminal point W(s) = (x,y) of the string of lengths with initial point at (1,0). (Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for a the expression.) 4 17x 3 COS any numbers in √3 sin 2 (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Find the domain of the function f(x) = x² + 17 In interval form, the domain of f is

A force of 3 pounds acts in the direction of 53 to the horizontal. The force moves an object along a straight line from the point (1,7) to the point (8,8), with distance measured in feet. Find the work done by the force The work done is approximately fool-pounds (Round to the nearest hundredth as needed)

Would the graph for f(x) = - 9x² + x + 5 open up or down, and why?, find g(). Down, because a (the coefficient of 2) is negative. Up, because b (the coefficient of x) is positive. Down, because b (the coefficient of a) is positive. Up, because a (the coefficient of 2) is negative.