Sequences & Series Questions and Answers

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation be ī 32, where / is the length of the pendulum in feet What is the approximate length of a pendulum that takes 2.4 seconds to swing back and forth? O 1.72 ft 3.05 ft 38.40 ft 46.08 ft

Use the intercepts to graph the equation. 2x + 5y = 10

Rounding to the nearest tenth, what is the mean of 85, 85, 100, 90, 100, 85, 80, 100, 90?

What is the solution to the following system? [x+2y+z= 9 x-y+3z=13 2z = 10 x = 10, y = 2, z = 5 4, y = 2, z = 5 O x = 0, y = 2, z = 5 O x = 4, y = 6, z = 5 O O x = An

4U Unit 6 Test Lines and Planes Date, These planes might intersect in a line, or perhaps they are coincident, or they are parallel and don't intersect. Determine how ₁ and ₂ intersect. ₁: 3x + 4y - 5z + 5 = 0 and #₂: x=3+1s + 2t y = 4 + 4s+t z = −5+ 5s + 2t [5 marks]

Graphyx-2x+1. Letx=0, 1, 2, 3, 4 to generate ordered pair solutions. Choose the correct graph below A B. C. D.

Write the domain of each function in interval notation. 3 X + 2 f(x) =

Find the domain of f. (Enter your answer using interval notation.) x-9 √x-7 f(x)

An object is thrown upwards at time t = 0. The object's height, fin feet, t seconds later is given by the formula below: f (t) = -16t² + 128 t = Answer the following. Note: When relevant, keep your answers exact. Decimal approximations will be marked as incorrect. (a) Determine the height of the object t = 0.8 seconds after it was launched. Answer: 92 feet (b) Determine the number of seconds required for the object to reach a height of 3 ft on its way up. 128 + √16192 32 t = seconds

True or False. Determine whether the statement provided is a true or false The equation (x + 3)² + (y-2)² = 16 defines y as a function of x.

A spherical water tank holds 9000 ft³ of water. What is the diameter of the tank? Round to the nearest foot. (Hint: V = d³T The diameter of the tank is feet.

The optimal height h of the letters of a message printed on pavement is given by the formula h = 0.00252d2.27 . Here e d is the distance of the drive from the letters and e is the height of the driver's eye above the pavement. All of the distances are in meters. Find h if d = 50 m and e = 1.2 m. Round to the nearest meter. The optimal height for the given values is meters.

9 The formula for converting from Celsius to Fahrenheit temperatures is F = C+ 32. a. Find the inverse of the formula. Is the inverse a function? b. Use the inverse to find the Celsius temperature that corresponds to 30°F. a. Find the inverse of the formula. C= (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Write the following number in standard notation. 3.075× 108

An object is thrown upward. The height, h, in feet, at time t, in seconds, is given by the formula h = -16 t² + 160 t Determine the time required for the object to reach a height of 40 feet on its way up. Enter an exact answer, approximation.

Divide, (16xy² + 4xyz +20x²yz) + (-4x²y)

1 Suppose that $85,000 is invested at 35% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years. b) Find the amount of money in the account at t=0, 3, 7, and 10 years. *** a) The function for the amount to which the investment grows after t years is A(t) =. (Simplify your answer. Type an expression using t as the variable.)

- 34 xy4 Classify the given polynomial. Otrinomial monomial O binomial Onone of these The degree of the polynomial is

1. (a) Find the eigenvalues and eigenvectors of the following matrix 52 22 = (b) Using your answer from part (a) of this question, find the principal axes of the following ellipse 5x² + 4x₁x₂ + 2x² = 36 (c) Sketch the ellipse in the original ₁, 2 coordinate system, and mark the principal axes of the ellipse on your sketch.

Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance. P r compounded 1 1 $50,422 79 -% Quarterly 85 t The account balance is approximately $ (Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)

The graph of g (x) = -1/2f(x-6)-3 is the graph of y = f (x) Select the correct answer below: vertically stretched by a factor of 2, reflected across the y-axis, and shifted right 6 units and down 3 units vertically compressed by a factor of 2, reflected across the y-axis, and shifted left 6 units and down 3 units vertically compressed by a factor of 2, reflected across the x-axis, and shifted right 6 units and down 3 units vertically stretched by a factor of 2, reflected across the x-axis, and shifted left 6 units and down 3 units

Let f(x)=x² + 3x - 4 and g(x)= x - 1. Perform the function operation and then find the domain. (f+g)(x)

Let f(x) = 4x² + 13x + 10 and g(x)= x + 2. Perform the function operation and then find the domain of the result.

In many classes, a passing test grade is 70. Using the formula A = 10 SR, what raw score R would a student need to get a passing grade after her score is adjusted? The student would need a raw score of

Gandalf the Grey started in the Forest of Mirkwood at the point (-1, 2) and arrived in the Iron Hills at the point (0, 7). If he began walking in the direction of the vector v = 5i + 1j and made one right angled turn, what are the coordinates of the point where he changed direction?

Find all the real fourth roots of 0.0081. Choose all that apply. Select one or more: a. There are no real fourth roots of the number. b. 0.3 c. -0.3 d. -0.03 e. 0.03

Let f(x)=x² and g(x)=x-1. Find (fog)(-3). (fog)(-3)= (Simplify your answer.)

If a linear equation is in the form y=mx+b, the slope of the line is and the y-intercept is

The dosage in milligrams D of a heartworm preventive for a dog who weighs x pounds is given by D(x)= 136 -x. Find the proper dosage for a dog that weighs 28 pounds. 25 The dosage is milligrams. (Type an integer or a decimal.) CIB

The function c(x) = 72 (1.04) models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory. a represents the number of years since 2010. a. Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so? b. How much does an ounce of the chemical cost in 2018? Show your reasoning.

A savings account earns 8% interest each year, compounded quarterly (4 times a year). If a person invests $100 and makes no further deposits or withdrawals, what is the balance in the account after 3 years?

These equations represent the number of bacteria in four different dishes as a function of time, t, in days. Which equation represents the population with the greatest growth factor? a. a(t) = 1,000. (5/6) t b. b(t) = 800 (1/50)t c. c(t) = 600 (5/2)t d. d(t) = 400.3t

Find the midpoint between the pair of points. (3,0) and (-5,4) The midpoint between (x₁, y₁) and (x₂. ₂) is (*¹2*2*¹*) 0 (-14) (-2,2)

What is the rate on an investment that triples $9465 in 35 years? Assume interest is compounded monthly. a.) 3,9% b.) 3,1% c.) 2.1% d.) 2,6% Group of answer choices

How do the graphs below compare? Choose all that apply. 1 f(x) = g(x)= Select one or more: a. -5 X e. b. c. d. shifted down 5 units f. vertical stretch of 5 shift up 5 units vertical shrink of 5 reflections across the x-axis reflection across the y-axis

Find the point(s) of discontinuity and determine if the discontinuities are removable or non removable. x² + 7x + 12 x + 4 Select one: a. x = 4, non-removable b. x = -4, non-removable c. x = 4, removable d. x = -4, removable e. There are no points of discontinuity.

Trent jogged to his friend's house 4.8 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 10 mph slower than the rate when he was riding. What was his jogging rate?

Determine the equation of a rational function with vertical asymptote a hole and a horizontal asymptote at

A company finds that it can make a profit of P dollars each month by selling x patterns, according to the formula P(x) = - .002x² +5.5x - 1400. How many patterns must it sell each month to have a maximum profit? To attain maximum profit they must sell patterns. What is the maximum profit? The max profit is S

(Solving, Simplifying) In College Algebra, you learned the at the Quadratic Formula is x = a) You need to have this formula memorized. Write down what technique you plan to use to memorize the formula. b) Fill in the blanks below to setup the Quadratic Formula for 6x² + x - 2 = 0. c) Simplify your answer from part (b).

A contractor hires out machinery. In the first year of hiring out of equipment the profit is 8250, but this diminishes by 3% in successive years. Find the total of all the profit for the first 3 years. Round your answer to the nearest pound.

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function ()=-16f² +48t, where t is the time in seconds since the rocket was shot and f(t) is the rocket's height in feet. What is the maximum height the rocket reaches? O 16 ft O 36 ft O48 ft O144 ft