Math - Others Questions

Miguel is judging an essay contest He has to select the best second best and third best If there are 13 essays entered how many ways could he choose the top essays

In year 2020 Jim was traveling for work He packed 7 unique masks 3 unique shirts 2 unique pairs of pants and 3 unique pairs of shoes How many outfit combinations has he packed Your answer is

Dwight is packing for a vacation He is deciding which books to bring He wants to bring one book from each genre Given he has 2 science fiction 5 business ethics and 9 beet farming books how many unique combinations of books could be bring with him Your answer is

How many ways can a teacher select a group of 3 students to sit in the front row if the class has 10 students

2 members of a gymnastics team are randomly chosen to compete in an invitational If there are 9 members on the team how many ways could be chosen Your answer

elw 8400X 400X

45 Points Determine the rate of seepage in cubic feet min under the dam by drawing flow net to scale and also determine the total uplift force in psf acting at the bottom of the dam at Point B per unit length of dam The permeability of the silty sand is 0 05 ft min The drawing is to scale Use the scaled drawing for your flow net sketching and pressure calculations evaluations Upstream water level is at El 200 ft Downstream water level is at El 162 ft Dam is 105 ft long and bottom is at el 146 ft Ground surfaces on both upstream and downstream sides are at El 150 ft T EL 200 FT EL 150 FT TH ht 52 5k 105 FEET LONG FLO F rock THEO by do 20 El 162 FT

Problem 4 Find the exact value of the expression or write an algebraic expression that is equivalent to the expression Show all your steps a arccos COS b sin arctan c sec arcsin 2 2 ese arctan 2 d csc e sec arcsin x 1 f cos arctan 2x

No late submissions will be accepted lem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20

lem 1 Suppose that cos lem 2 Suppose that sin 0 25 12 13 and 0 T Determine the values of sin COS and tan

Problem 6 Find all solutions in exact form expressed in radians 1 sin t cos 2t 0 2 sin 2t sin t 0 3 2 sin 2t sin 2t 1 0 4 tan 3x tan x 1 0 5 3 tan 2t 2 3 6 sec 4x 2

Problem 5 Solve each equation on the interval 0 27 Give exact answers a 3 sin 3 cos 3 3 cos 3 b 2 sin 3 sin 3 10 c 2sec x tan x 3 d 2 cos 6 3 cos B 1 0

6 In Figure 5 is the graph of f x ln x 1 for 0 x 4 It crosses the x axis at x e You will use Newton s method for f x 0 to create numerical estimates for e Y 1 SI Figure 5 Graph of y ln x 1 a Using Newton s method for the equation ln x 1 0 with x 1 tabulate an to find the first n for which n and n 1 agree to 5 digits after the decimal point b For the n you found in part a to how many digit

1 s2 4s 8 C Determine theinverse Laplace Transform

1 2 48 8 4s Determine theinverse Laplace Transform

s 7 L 5 1 8 2 Determine the nu

The smallest positive integer in the set 24x 60y 2000z x y ze is a

Determine 6 1 L 8 1 4 2 C 2 4 s 1 3 L 2s 10 10 1 4 L g 48 8 5 L 7 s 7 s 1 s 2

1 C 3 48 8 Determine theinverse Laplace Transform

5 The number is a solution of sin z 0 close to 3 see Figure 4 You will use Newton s method for sin z 0 to create numerical estimates for wh 10 Z2 Figure 4 Graph of y sin z a Write out the recursion for Newton s method used to solve sin z 0 b Using Newton s method for sin r 0 with z 3 find the first n for which z and Int1 agree to 5 digits after the decimal point Use radians not degrees

7 Determine if the shaded amount is more less or equal to half

2 20 16 24 0

1 and 4 Apply Newton s method to estimate the solution of x x 1 0 by taking finding the least n such that n and n 1 agree to three digits after the decimal point

Thursday 1 Find the number that makes an equivalent fraction 7 10 40 3 Use or to compare the fractions 4 3 5 10 2 Find the number that makes an equivalent fraction 1 10 4 4 Determine if the fraction shown is less more or equal to half 1

1 Recall the test IVP y Ay and y 0 a We consider the so called implicit Trapzoidal method h W 1 W 7 f t 1 W 1 f ti wi to solve the test IVP which is a stiff system a Write down the stability function Q hA for the implicit Trapzoidal method Hint Q hX is obtained by applying the implicit Trapzoidal method to the test IVP see Lec 11 Theorem 1 b For the stability function show that if hA is a real number and h 0 we have Q hA 1 c Optional For the stability function verify that for any h such that Re hA 0 we have Q hA 1 This shows the implicit trapezoidal method is A stable

Tuesday 1 Find the number that makes an equivalent fraction 2 2 S 4 12 3 Use or to compare the fractions 3 3771 100 5 Use or to compare the fractions 122 20 8 7 Determine if the shaded amount is more less or equal to half 2 Find the number that makes an equivalent fraction 3 7 1 10 3 3 4 Determine if the fraction shown is less more or equal to half 3 3 3 1 1 20 6 Determine if the fraction shown is less more or equal to half 23 24 6 14 8 Determine which letter best represents an equivalent fraction A B 6 00 3 5 C 5

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transforms 1 L 6e 3t t2 2t 8 2 L 5 e2t 6t 3 L t 3t e4t cost

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transforms 1 L 6e 3t t 2t 8 2 L 5 e2t 6t 3 Lt 3t et cost

Determine 6 1 L 8 1 4 2 2 C 344 4 3 L s 1 s 2s 10 10 1 4 L g 48 8

Use Definition to determine the Laplace transform of the given function 1 t 2 et

Determine the Laplace transform 1 L t et sin 2t 2 L e t cos 3t e6t 1

em 3 Let 0 arcsin 1 where x 0 and is in the first Quadrant Use this information to answer the following questions a Sketch and complete a right angle triangle containing the angle 0 b Use the triangle from part a to find the values of all the other trigonometric functions of 0

Use Definition to determine the Laplace transform of the given function 1 t 2 et 8

Problem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

Problem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

oblem 2 Suppose that sin 0 12 13 2 and T Determine the values of sin 2 cos and tan COS 2 2

coblem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

3 A line passes through point 8 9 and has a slope of 4 Write an equation in Ax By C form for this line Use integers for A B and C 7 0 0

Solve the following I V P by using the Laplace transform y y 2y 0 y 0 1 y 0 0

We can also use Laplace transforms to solve n th order differential equations As the simplest example solve the following first order differential equation using the Laplace transform y 0 1 2t y 3y e t

H

The three right triangles below are similar The acute angles LL LR and LZ are all approximately measured to be 62 4 The side lengths for each triangle are as follows Note that the triangles are not drawn to scale 19 73 cm L 62 4 9 15 cm J 17 48 cm K KL JL 118 38 cm P Osine O cosine Otangent R 62 4 177 57 cm che venn 62 4 54 9 cm 157 32 cm 104 88 cm Q a For each triangle find the ratio of the length of the side adjacent to 62 4 to the length c the hypotenuse Note that side adjacent cannot also refer to the hypotenuse Round your answers to the nearest hundredth QR PR X YZ XZ b Use the ALEKS Calculator to find sin 62 4 cos 62 4 and tan 62 4 Round your answers to the nearest hundredth sin 62 4 cos 62 4 tan 62 4 c Which trigonometric function gives each ratio of sides in part a 82 35 cm Y

002 Tal ASTTUD 2 American Swiss Ltd s common stock paid 10 00 in dividends last year The investors require a return of 8 What is the price of the share if a the dividends grow at a constant rate of 3 per year b the dividends grow at a constant rate of 0 per year Ef a super woll c the dividends grow at a constant rate of 3 per year d Explain the outcomes la 19q8E2 701 anillog al 00 M to sladda nom 03 9717 DE

1 MacroCorp s common stock paid 3 00 in dividends last year and is expected to grow indefinitely at an annual 5 percent rate a What is the value of the stock if you require a 10 percent return b What is the value of the stock if you require a 7 percent return c What is the value of the stock if you require a 5 percent return d What is the value of the stock if you require a 4 percent return e Explain the outcomes 2700 SL 63 and go 01 8

A four sided closed field traverse has the fol lowing angles A 81 53 30 B 70 28 30 C 86 09 30 D 121 30 30 The lengths of the sides are as follows AB 636 45 ft BC 654 45 ft CD 382 65 ft DA 469 38 ft The bearing of AB is S 17 17 W BC is in the N E quadrant a Balance the field angles b Compute the bearings or the azimuths

K The owners of the Phoenix Flames football team own different amounts of stock in the franchise so when they vote on an issue they have different amounts of voting power Assume that Alvarez s and Cianci s votes each will count once Belardo s will be counted three times Devlin s five times and Espinoza s six times In order for a motion to be passed the vote must be a total voting weight of at least eight How many different subsets of this group of owners have a voting weight of at least eight Type a whole number n

K Let A 3 4 5 6 7 9 10 11 a How many subsets does A have b How many proper subsets does A have a A has 256 subsets Type a whole number b A has proper subsets Type a whole number

A pizza parlor offers mushrooms onions and sausage as toppings for the plain cheese base How many different types of pizzas can be made different types of pizzas can be made KILD

Use the table to find the number of subsets of the set of students who are neither upperclassmen juniors or seniors nor have a GPA below 3 2 The number of subsets is Type a whole number Major Class Rank GPA Activitie Elston Music Freshman 3 8 Band Carmen Physics Senior 2 5 Yearboc Frank Business Freshman 1 3 Basebal Gina Music Senior 2 9 Soccer Dana Music Freshman 3 9 Tennis Brenda Business Freshman 3 8 Choir

A tree diagram that shows all subsets of set a b c is shown below Think of the top branch as branch 1 the next branch as branch 2 etc Complete parts a and b Choose Choose Choose element a element b element c Yes Yes No No No Yes No Yes No Yes No a Which branch corresponds to the subset c a branch