Mathematical Induction Questions and Answers

Required Information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Let P n be the statement that 1 1 n 2 3 n n 1 n 1 Multiple Choice O 1 2 O entify the Inductive hypothesis ou must provide an answer before moving to the next part In the Inductive hypothesis we assume P K for some Integer k k 0 2 2 3 the Inductive hypothesis we assume P K for some integer k k 0 12 2 3 In the Inductive hypothesis we assume P K for some integer k k 0 12 23 In the Inductive hypothesis we assume P K for some integer k k 0 1 2 2 3 1 k k 1 1 le k 1 1 k k 1 1 k k 1 k 1 k 1 k k 1 k 1 k 1 k 1 k 2

The daily temperature in degrees Fahrenheit of Phoenix in the summer can be modeled by the function T x 94 10 cos x 6 12 where x is hours after midnight Find the rate at which the temperature is changing at 2 4 p m O a 2 1180 O b 1 4122 O c 2 4612 O d 4 8466 e 0 1534 O f 0 8820

A fungal colony grows on a flat surface starting with a single spore The shape of the colony edge is circular with the initial site of the spore at the centre of the circle Suppose the radius of the colony increases at a constant rate 13 3 units per unit time At what rate does the area covered by the colony change when the radius is 17 8 units O a 1990 7644 O b 26477 1670 O c 1487 4813 O d 743 7406 O e 1111 4326 O f 41 7832

5 The 100 kg stone shown in Fig a is originally at rest on the smooth horizontal surface If a towing force of 200 N acting at an angle of 45 is applied to the stone for 10 s determine the final velocity and the normal force which the surface exerts on the stone during this time interval a 200 N 45 6 If motor M exerts a force of F 10t 100 N on the cable where t is in seconds determine the velocity of the 25 kg crate when t 4 s The coefficients of static and kinetic friction between the crate and the plane are 0 3 and 0 25 respectively The crate is initially at rest M 7 The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20 from the horizontal as shown Determine the crate s acceleration in t 2 s if the coefficient of static friction is us 0 4 the coefficient of kinetic friction is 0 3 and the towing force is P 90t N where t is in seconds

Problem 8 Let B be the surface of the solid sphere M centered at the origin and having radius 3 Let w r y dx dy xz dy dz Use Stokes theorem to evaluate fw Explain how you know your answers are correct

12 Harrison loaned his friend Mattson 100 for one year at a simple interest rate of 5 The total amount of money that Mattson will pay back at the end of the year is a 5 00 b 100 00 c 105 00 d 120 00

Find an SVD of the matrix A A 2 2 2 1

Increasing the horizontal velocity of a projectile can be done by... A. increasing the launch angle B. decreasing the launch angle C. increasing the hang time

Let F be a finite field. Prove that any element of F can be expressed as the sum of two squares.

6. By Utah statute, responsibility for licensing procedures belongs to the (a) real estate education coordinator (b) Utah Association of REALTORS® (c) Utah attorney general (d) Real Estate Commission

The product of two consecutive positive integers is 210. Write the equation that would be used to find x, the smaller number. What are the two integers?

Simplify and write the results in standard form (3 - 2!) (8 + 3i)

Julie is designing a rectangular poster for her Youth Group that will have have a margin have margins of 5 cm, while the top and bottom will each the dimensions of the poster if the area of print should be as large as possible. an area of 4250 cm². of 8 cm. Determine, She using has determined the the methods shown sides will in this activity,

5. Find the general solution of the differential equation y"(t) - 5y' (t) + 4y(t) = e^2t [Hint: First determine the solution for the corresponding homogeneous equation by computing the roots of the associated quadratic equation, then guess a particular solution]

A tree casts a shadow 36 ft long. At the same time, the shadow cast by a vertical 6-ft post is 4 ft long. Find the height of the tree. The tree's height is _______ft.

Each wheel shown is divided into congruent sections. Find the measure of each arc.

In Exercise 10-12, find the value of x.

A die is rolled and a card is chosen. What is the probability that the die will be a multiple of 3 and the card will be red? (nearest tenth of a percent) P(mult of 3, red card) = ____

You add 5.2 g iron to 20.40 mL of water and observe that the volume of iron and water together is 21.06 mL. Calculate the density of iron. Express your answer to two significant figures with the appropriate units.

Consider the rectangle prism below, if LK=u, LH=v, LG=w. Q is in the middle of the face DEFG. Write the following in terms of u, v, w, A. LQ B. JQ C. Determine <JQL

The scores for 20 students on a 50-point math test are 27, 43, 33, 35, 42, 50, 47, 40, 41, 44, 37, 34, 38, 36, 39, 48, 46, 32, 45, and 49. (a) Find the percentile rank for a score of 41. A test score of 41 is equivalent to the____percentile

Two dice are rolled and their sum recorded. What is the probability of rolling a sum that is less than 7 or a sum that is divisible by 3?

Prove by mathematical induction that n³ + 5n is divisible by 6 for all n = 1, 2, 3, ....

Convert the polar coordinate (6, 7π/6) to Cartesian coordinates. Enter exact values.

Consider this argument: Ax Ey Fxy / Ey Ax Fxy You can prove it's invalid by finding a domain and a predicate F for which the premise is true and the conclusion is false. We choose the domain (of discourse) to be the natural numbers (0, 1, 2, ...). Which of the following definitions of F would show the argument is invalid? Fxy x != y None Both Fxy x <= y

Economics The Pita Pit sells about 5000 sandwiches a month when they sell their sandwiches for 8 5. They ran a sale one month and sold 6500 sandwiches for $4. (a) If the relationship is linear, how much should the sandwiches be sold for in order to maximize the revenue (5 points) (b) If their monthly overhead costs are $ 7.000 a month, and it cost $.95 to make each sub, how much should they sell the sandwiches for in order to maximize their profit (5 points)

Let f be harmonic on a simply connected domain D in the plane and let C be the boundary of D oriented counterclockwise. Show that if f = 0 on the boundary of D then ffVf²dA= 0. Hint: Apply the divergence form of Green's theorem to F = ƒVƒ.

The following numbers of people attended the last 11 screenings of a movie. 114, 196, 196, 203, 205, 206, 208, 210, 211, 212, 294 Identify all values that are outliers. If there is more than one outlier, separate them with commas. If there are no outliers, click on "None".

BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 943 hours. Suppose that this mean applies to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries. (a) According to Chebyshev's theorem, at least? of the lifetimes lie within 1.5 standard deviations of the mean, 943 hours. (b) Suppose that the distribution is bell-shaped. If approximately 68% of the ifetimes lie between 852 hours and 1034 hours, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .

The red blood cell counts (in 105 cells per microliter) of a healthy adult measured on 6 days are as follows. 48, 50, 55, 53, 52, 48 Send data to calculator Find the standard deviation of this sample of counts. Round your answer to two decimal places.

You SELL 4 e-mini S&P500 Index futures contracts with a futures price (FO) of 2753 and you close the position when the S&P (FT) is 2886.8 What is your profit or loss on the trade? See the notes for the multiplier on this contract. -66,900.00 -21,408.00 133,800.00 -535.20 -26,760.00

Convert the polar coordinate (5, π/4) to cartesian coordinates X= y =

Evaluate (-2)^6 = -3^4 =

(1 point) Use the simplex method to maximize P = 2x₁ + 3x2 + x3 subject to P = -X1 -X1 X1 + X2 + 2x3 ≤ 9 + 2x2 + 6x3 ≤ 8 + 7x2 + 10x3 ≤ 11 x₁ ≥ 0 X₂ 20 X3 20

A company wants to have $60,000 at the beginning of each 6-month period for the next 4 1 2 years. If an annuity is set up for this purpose, how much must be invested now if the annuity earns 6.89%, compounded semiannually? (a) Decide whether the problem relates to an ordinary annuity or an annuity due. ordinary annuity annuity due (b) Solve the problem. (Round your answer to the nearest cent.)

The apr of a 30 year mortgage loan varies based on a persons credit score. calculate $1475 monthly morgagw with execellent credit apr 2.92% and calculate fair credit apr 5.2% show work

Find the singular value decomposition for A A = [13].

Complete parts (a) through (c) below. (a) At mail time, you receive a check for $26 and an envelope with neither a bill nor a check. What addition-by-0 fact has been illustrated? (b) At mail time, you receive a postcard from your friend and a bill for $25. What addition fact is illustrated? (c) What is illustrated if your mailbox has a bill for $10 and a check for $10?

Find the projection from R³ onto its subspace spanned by (1, 2, -1) and (1,1,2).

In an experiment to test the effectiveness of low- phosphate detergents, 20 pieces of soiled denim are prepared. We want to wash some with regular Tide and some with low-phosphate Tide and compare cleaning ability. a) Label the denim pieces and carry out the randomization. Enter Table I Random Numbers at row 04 column 16 b) Make a diagram showing the design of the experiment.

Show that if E is L-non-measurable,then 3 a proper subset B of E such that 0<u" (B)<∞

If f(x) = 3x² + 9 and g(x) = x - 4, what is (f+g)(5)? 89 84 1 85

Let n(A) = 4 and n(A U B) = 8. (a) What are the possible values of n(B)? (b) If A∩B=Ø, what is the only possible value of n(B)?

Find the complex conjugate of the given complex number. 9 + 2i

Explain why the scratch algorithm works. Choose the correct answer below. A. The scratch marks represent the exchanges and a way to keep track of them. B. The scratch method adds the same amount to both numbers to make addition easier. C. The scratch method does not work. D. The scratch method scratches out numbers that are difficult to add.

find an arc distance between 0 and 2 (0 < bar under t < bar under, pie) such that sin t= sin (11pie/6)

FIFO and LIFO Costs Under Perpetual Inventory System The following units of an item were available for sale during the year: Beginning inventory 39 units at $46 Sale 22 units at $69 First purchase 18 units at $48 Sale 17 units at $70 Second purchase 25 units at $50 Sale 18 units at $71 The firm uses the perpetual inventory system, and there are 25 units of the item on hand at the end of the year. a. What is the total cost of the ending inventory according to FIFO? b. What is the total cost of the ending inventory according to LIFO?

A debt of $14 000.00 with interest at 6% compounded semi-annually is to be repaid by equal payments of $1453 at the end of every three months for two years. a) What is the number of payments to amortize the debt? Round up to the nearest integer b) What is the outstanding principal after 6th payment? c) What is the interest paid on the 7th payment? d) How much principal is repaid in the 7th payment?

Find the number of distinct arrangements of the 9 letters in CHOCOLATE. Two of the same letter are considered identical (not distinct).

True or False? Justify your answer. Answers without correct justification will receive no credit.¹ (a) Let A and B be two square matrices of the same dimension and A be an invertible matrix then (A-¹BA) 2020 = A-¹B2020 A. Justification: True False (b) Let A be an nxn matrix. The set of all nxn matrices X that satisfies (A+ A²)X = 0 is not be closed under the matrix multiplication. Justification: True False (c) If A and B are n x n matrices of rank n, then AB also has rank n. Justification: True False