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Basic Algebra

Various Calculations of Geometry

1. Find the distance d (p1,p2) between the points p1 and p2 p1=(-2,4), p2=(5,6) d(p1,p2)= 2. Find the midpoint of the line segment joining the points p1 and p2 p1=(4,3) p2=(-1,4) midpoint is __________ 3. List the intercepts and test for symmetry y= -2x^7/x^8-2 4. Find the intercepts and use them to graph the equa

Simple Algebra: Determining Line Equations

1. The equation of the line L is parallel to y=5x. What is the equation for line L? 2. If (a,-2) is a point on the graph of y=x^2+3x, what is a? 3. Find the equation for the line with the given properties. Express the equation in slope intercept form. The points are P=(-1,-3) and Q=(1,-2). What is the equation of the li

Moment of Force about given points

9. A force of magnitude 3 units acts at the point with coordinates (1,2,3). The force is applied in the direction of the vector 3i - j + 4k. Find the moment of the force about O. Also find the moment of the force about the point with coordinate (1,2,3)

Voltage Across an Inductor

1. The voltage v across an inductor L, in LR electrical circuit drops exponentially over time t (s). The relationship is: See attached. Where the emf, E, and τ are constants. Use the table of values for t and v and logarithms to plot an appropriate straight line graphs. See attached for table. Use your graph to est

Optimal Solution to Maximum Height Problem using Derivative

A projectile is launched from a platform 20 feet high with an initial velocity of 112 feet per second, The height h of the projectile at t seconds after launch is given h= - 16t^2 + 112t +20 feet. a. How many seconds after launch does the projectile attain maximum height? b. What is the maximum height?

geometry and quadratic equation based problems

1) Solve equation r=sqrt(A/pi) 2) Discuss everyday objects that have shapes described by conic section. Remember, the conic sections are the circle ellipse, parabola, and hyperbola. 3) Give examples of quadratic relationship in either nature of business. Remember a quadratic relationship has the form V=a*x^2+b*x+c 4

Radicals, Polynomials, and Nomenclature

The most common business application involving exponents is the calculation of compound interest. Let's introduce some nomenclature. PV = present value ; the money you pay into the plan today. t = the duration of an investment program, in years. FV = future value ; that is, the money you expect to have after n years.

Quadratic Formula Based Questions

This SLP provides some insight into the use of quadratic formulas in business and natural science. 1.A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items? 2.A company's costs, in

Quadratic Factoring and Solving

Show all of your work in a Word document and submit by the end of the module. 1-4: Solve by factoring: 1. 4x2 - 25 = 0 2. x2 - 12x + 36 = 0 3. x2 + 14x + 45 = 0 4. 6x2 - x - 15 = 0 5-7: Solve by completing the square. 5. x2 - 4x + 3 = 0 6. x2 + 5x - 1 = 0 7. 2x2 + 7x - 15 = 0 8-10: Solve by using the quadratic formula:

Simplifying indicated operations

Show all your work in a Word document and submit by the end of the Module. Perform the indicated operations and simplify. (A radical in simplest terms contains no perfect squares; do not use decimals.) 1. 2 √12+ √27 2. 4 √3+ 6√75 3. 2 √y+ √(8z) 4. (√3)( √15) 5. (√8)( √12) 6. (3√y)( -2√y) 7

Sequences and Series of Functions

1. Write the following in expanded for then find the sum a) ^7(Sigma sign) k=0 (k=1)(k+2) b) ^7(Sigma sign) k=4 3k Note: The sigma sign does not show up when pasted here. The 7 is on top of the sigma sign and the k= 0 or k=2, respectively, lies below the sigma sign. 2. Express the following series using sigma notation: a

Racial Inequalities: An Analysis

See the attachments. - White households have on average 22 times the wealth of average Black households and 18 times the wealth of average Latino households - On average, more money is spent on White children than Black and other non-White children in public schools - Public schools are nearly as segregated today as the

Reflection of a line across the line y = x

(a) Write the equation of a line that intersects the negative x-axis and the positive y-axis at points not equidistant from the origin (0, 0). (b) Draw the line. (c) Draw the line that is the reflection of your line across the line y=x. (d) Find the equation of the line drawn in Part (c). Do not convert fractions, if a

Solving equations algebraically

Solve the following equations algebraically. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may ty sqrt 3 (x) as cuberoot (x) and shraising to the nth power as ^n, like x ^3 is typed x^3. a) t sqrt (2/3) =4 b)5 sqrt (x + 1 )= 3 c)

Algebra: Celebrity Body Mass Index

The United States is becoming more health conscious, and as a result, the problem of obesity has gotten more attention. The Body Mass Index (BMI), relates a person's height and weight, and is often used to determine if someone is overweight. The table below tells the weight status for a given BMI. BMI Weight Status Below 18.5

Let A and B be arbitrary n x n matrices whose entries are real numbers. (a) Use basic matrix laws only to expand (A + B)^2. Explain all steps. (b) Is (A - B)(A + B) = A^2 - B^2 ? Explain as you did in part (a).

1. Given the matrices A, B and C, compute: (a) AC + BC (It is much faster if you use the distributive law for matrices first.) (b) 2A - 3A (c) Perform the Boolean Product operation on the following zero-one matrices. Please refer to the attachment for the complete question. 2. We know that matrix algebra behaves si

Algebra: Weighted Average

Just to be clear, please do the math for me, I do not wish to know how to find out my grade, they show me online and I still can't get it right. Based on the information provided please tell me what my grade is. DF = 35% Assignments = 35% MT = 15% F = 15%, Grades%: DF1= 100 As1= 0 DF2= 100 As2= 100 DF3= 0 A

Exponential and Logarithmic Functions - Compound Interest

Examples of Exponential and Logarithmic Functions. Excercises to follow. Explanation: Start by writing the beginning amount into cell C1 (pink). The program automatically copies that number to cell B5 (pink), which is the beginning amount for the first period. Type the multiplier into cell C3 (blue). The program automa

Solving by Elimination and Dependent and Inconsistant Systems

1. Solving a system by elimination. Solve each system of equations: a. 2x - y + 3z = 14 b. X + y = 2z = -5 c. 3x + y - z = 2 d. x - 3y + 2z = -11 e. 2x + 4y + 3z = -15 f. 3x - 5y - 4z = 5 2. Dependent and Inconsitent systems. Solve each system: a. 4x - 2y - 2z = 5 b. 2x - y - z = 7 c. -4x + 2y + 2z = 6 3. Paranoia

Force diagrams, vectors and equations of motion

A parachutist and her parachute have a combined mass of 80 kg. She steps out from an aircraft travelling horizontally at 90m s−1 at a height of 300m above the ground, and falls for 5 seconds before instantaneously opening her parachute. In the free fall phase of the motion, take the origin of coordinates to be a point on the g

Monthly interest and balance on credit cards

It's time to go shopping! You grab your Best Purchase credit card, which has an annual interest rate of 18%. The unpaid balance on your card for the current billing cycle is $285.76. On your shopping trip, you purchase four items: a Blu-ray player, two 4-GB flash drives, and a 19-inch flat-screen television. You purchase all the

Introductory Algebra

1. Simplify by factoring. Assume that all variables under radicals represent nonnegative numbers. √(36x^6) Answer or note that the square root is not a real number. Show all work. 2. Use the quotient rule to simplify. Provide answer using exponential notation. Show all work. -12a^5b^6c^12 / 3a^2b^3c^9 3. The amo

Simultaneous Equations: Word Problems

For Halloween, Mr. Olowitz bought 8 bags of candy bars and 4 bags of lollipops for a total cost of $51.56. Later that day he realized he didn't have enough candy and went back to the same store and bought 3 more bags of candy bars and 3 more bags of lollipops for a total cost of $23.82. While in the store on his second trip, Mr.

Approximating real zero, free falling object and profit

Question #1 Given f(x)=6x^4-7x^3-23x^2+14x+3, graph using a graphing tool. Use the graph to approximate each real zero as a decimal, accurate to the nearest tenth. Question #2 For a body falling freely from rest (neglecting air resistance), the distance the body falls varies directly as the square of the time. If an objec

Algebraic Synthetic Division

See the attached file. In problems 1 through 4, write out the polynomial that has the listed factors: Example: (x), (x-1) ANS: x2-x 1. (x-2), (x+3) 2. x, (x-2), (x-1) 3. (x-2i), (x+2i) 4. x, (x-1), (x+1), (x-2) In problems 5 through 8, write the polynominal having the listed roots: 5. i 6. 2, 1,

Simplifying exponential equations

32. Zero exponent. Simplify each expression. 5y^2z(y^-3z^-1) 38. Changing the sign of an exponent. Write each expression without negative exponents and simplify. 5^-2xy^-3 3x^-2 52. The quotient rule for exponents. Simplify each expression. 2r^-3t^-1 10r^5t^2∙t^-3 64. Use the rules of exponents to simplify eac

measure theory: show is countable

Let {x_alpha}_[(alpha)(E)(gamma)] be an indexed collection of non-negative real numbers. The sum of this collection is defined to be the supremum of the set of all sums over finite subsets of gamma. This is The sum of_[(alpha)(E)(gamma)]x_(alpha) = sup{(the sum of)_(alpha)(E)(S)x_(alpha): S is finite subset of gamma} Prove t