Pre calculus Definition and 30 Threads

In mathematics education, precalculus or college algebra is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.

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  1. brotherbobby

    Proving a sum of three squared terms, cyclic in #a,b,c#, is equal to 1

    Problem statement : I copy and paste the statement of the problem from the text. (Given ##\boldsymbol{a+b+c=0}##) Attempt : I am afraid I couldn't make any meaningful progress. With ##a = -(b+c)##, I substituted for ##a## in the whole of the L.H.S, both numerators and denominators. I multiplied...
  2. brochesspro

    The given function is an even or an odd function?

    I think the answer is an even function as the function ##x^2## is an even function and thus, is symmetrical w.r.t. Y axis. The question I have is how to do this problem algebraically. I tried to graph some functions on GeoGebra to verify my answer. a) ##y = ln(x^2)## b) ##y = sin(x^2)##...
  3. A

    How Should Compass Bearings Be Notated in Navigation Problems?

    150 km tan(35)=150/x Hyp=316.58 I know this isn't right where did I go wrong or did I even start correctly
  4. M

    Problem involving a system of equations

    Homework Statement If an amount of $1000 is deposited in a savings account that pays 3.2% interest per year compounded monthly, the amount in the account after nmonths is given by: The amount in the account after 2 years (rounded to one decimal point) will be??
  5. T

    Complex Analysis prerequisite material review

    Homework Statement Identify the set of points satisfying ##1<\vert 2z-6\vert <2## such that ##z\in\Bbb{C}##. My pre-caculus is very rusty, so I am not sure if I am doing this correctly. Homework Equations ##x^2 +y^2= r^2## ##\forall z,z'\in\Bbb{C}, \vert zz'\vert =\vert z\vert\vert z'\vert##...
  6. L

    Find the smallest value for the polynomial

    The graph below shows a portion of the curve defined by the quartic polynomial P(x) = x^4 + ax^3 + bx^2 + cx + d. Which of the following is the smallest?https://imgur.com/a/1VuGSiA(A) P(-1) (B) The product of the zeros of P (C) The product of the non-real zeros of P (D) The sum of the...
  7. rishi kesh

    What is significance of eulers number

    Thread moved by mentor why is 'e' so important number. e^x is said to be natural language of growth. Why isn't 2^x a 100% growth.Can anyone explain me the difference between both of these and also bit more about number e which known as famous constant.please explain clearly. I will appreciate it.
  8. B

    Solve equation |f^-1(x)|= 1+f^-1(x)

    Homework Statement f(x) = (2x-3)/(x-1) Solve the equation |f^-1(x)|= 1+f^-1(x) Homework Equations I'm pretty sure f^1(x) = (-3+x)/(x-2) The Attempt at a Solution I am not sure what solve means. Do i need to plug in values?
  9. Bunny-chan

    Supremum and infimum of specific sets

    Homework Statement I'm in need of some help to be able to determine the supremum and infimum of the following sets:A = \left\{ {mn\over 1+ m+n} \mid m, n \in \mathbb N \right\}B = \left\{ {mn\over 4m^2+m+n^2} \mid m, n \in \mathbb N \right\}C = \left\{ {m\over \vert m\vert +n} \mid m \in...
  10. Schaus

    What's the Error in Solving Radical Equations?

    Homework Statement √3x - 5 +2 = -3 Underlined is under square root. √2x - 3 = -x + 3 Underlined is under square root. Homework EquationsThe Attempt at a Solution √3x - 5 +2 = -3 -2 -2 (√3x - 5)2 = (-5)2 3x - 5 = 25 3x = 30 x = 10 Solution says no answer but I got one... I tried...
  11. liluiass

    Prove: |x+y|<|xy+1| for |x|,|y|<1

    Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1|Homework EquationsThe Attempt at a Solution |x+y|<2 I couldn't prove that |xy+1| >2 And couldn't find a way to solve the problem Please help
  12. T

    Proving theorem for polynomials

    Homework Statement Prove the following statement: Let f be a polynomial, which can be written in the form fix) = a(n)X^(n) + a(n-1)X^(n-1) + • • • + a0 and also in the form fix) = b(n)X^(n) + b(n-1)X^(n-1) + • • • + b0 Prove that a(i)=b(i) for all i=0,1,2,...,n-1,n Homework Equations 3. The...
  13. Kupkake303

    How to find the inverse of a function

    T(t) = Ts+(98.6 – Ts)e-kt rewrite in the form t=g-1(T) In trying to understand how to find the inverse of this but am having a hard time, please advise. Thanks, Kupkake303
  14. C

    Trig Identities: Simplifying Expressions with Cotangent, Secant, and Cosecant

    I have re-post this forum as I should have paid closer attention to rules. I apologized for that. Homework Statement 1) The expression tan^3 θ + sinθ/cosθ is equal to: (a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ 2) Simplify (cos θ/1+ sin θ - cosθ/sinθ-1)^-1 (a)...
  15. Y

    How Sin(90° + θ) =sin θ of triangle P'OM'

    Hello everyone. I'm learning Trigonometry right now with myself and at current about how to find the trigonometric ratio of the angle (90° + θ) in terms of θ. I'm quite confused in the Figure. How sin(90° + θ) become equal to sin (90° - θ) of triangle P'OM'. I know that triangle P'OM' and POM...
  16. Ryaners

    Finding inverse of a Sin function (problem from Mooculus)

    I'm working through the problems in the Mooculus textbook as revision for Calculus I & there seems to be something wrong with how I'm manipulating the function to find its inverse in the following example. Homework Statement The height in meters of a person off the ground as they ride a Ferris...
  17. Ricky_15

    Argument of a random complex no. lying on given line segment.

    Homework Statement In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options . A) -3∏/4 B) ∏/4 C) 5∏/6 D) ∏/6 2. MY ATTEMPT AT THE SOLUTION We get two points ( -3 , 5 ) & ( -5 , -3 ) => The...
  18. T

    Is it possible to learn pre-algebra to pre-calc in 9 months?

    I am currently in year 9 (9 grade for those in US) and I have a really rusty and a weak math background. I have 2 months of summer holidays coming up. I should be done with pre algebra in mid December. During my summer holidays I have more than 50 hours a week avalible for study and I was just...
  19. Unichoran

    Calculating Inverse Functions for Hourly Salary and Production Units

    Homework Statement Hello,I have some problems with my Pre-Calculus homework. The task is: You get paid 8$ per hour plus 0.85$ per unit you produced. 1.Set up an equation for it. 2.Find the inverse function. 3.What does each variable in the inverse function mean? Homework Equations See below...
  20. B

    Sin^4Ө =3/8-3/8cos(2Ө) Prove the following trigonometric identity

    Homework Statement Prove the following trigonometric identity. The question is sin^4Ө =3/8-3/8cos(2Ө) Homework Equations I think I'm supposed to use the power reducing formulas for trigonometric identities which are sin^2(u)= (1- cos(2u))/2 cos^2(u)=(1+cos(2u))/2 *Let u represent any...
  21. funlord

    Implicit Differentiation: two different answers

    Homework Statement with answers given: Homework Equations use implicit differentiation The Attempt at a Solution I always get this answer but not the second one PLs explain the second answer for I am very desperate. Thank You
  22. T

    Pre Calculus problem in need of help

    Homework Statement Solve for X in terms of Natural Logs; Both my friend and I (top scores in the class) are struggling with this problem. Homework Equations e^ax=c*2^bx The Attempt at a Solution We both decided to divide both sides by 2^bx which gave us e^ax / 2^bx = C Then...
  23. Jewish_Vulcan

    Learning integrals and derivitaves in pre calculus.

    Hello I am in pre-calculus which is the next math class after algebra 2 and there are many scientific equations that require a knowledge of calculus to solve. For example I do science olympiad maglev and many of the equations to solve for magnetic flux or magnetic fields etc.. use derivatives...
  24. M

    Changing Perspectives in Math Class: From Memorization to Understanding

    So my semester started yesterday, and my first class on: Monday, Tuesday, Thursday, and Friday is pre calculus. I walked in, sat down, and it began. My professor is the head of the math department at the college, and within 5 minutes of the intro lecture, it's clear that he really loves math...
  25. A

    Pre Calculus online with 2nd semester Algebra 2

    Hi, I am wondering if it would be better to do Pre-Calculus online with the 2nd semester Algebra 2. Or take college algebra online with 2nd semester Algebra 2. If I go the Pre-Calculus online with 2nd semester Algebra 2, my senior year I will be taking Calculus AB 1st semester and Calculus BC...
  26. X

    Online resources to study pre calculus.

    Tomorrow I'm taking a certification exam to become a college math tutor and I have to take a proficiency test in pre calculus. A lot of the stuff I don't remember because I haven't used it in a while. Anyone got some good online resources. I studied before but I just realized yesterday after not...
  27. I

    I really with this Pre Calculus problem =[

    sketch and graph 1. y= [x][/3] +2 2. y= squareroot x-3 3. y= Ix-2I 4. y= [y][/2] - 1
  28. J

    Why Is Pre-Calculus Challenging for Some Students?

    hello! I am a studen from sweden and i having some troble solves this kind of problems. i have tried but the book its really bad to expleain. and i really have to know this for the comming exan, so if anyone could help me i really be so happy :) here are some stuff i have hard time solving...
  29. S

    How Do You Solve a Pre Calculus Problem with Congruent Sides and Diagonals?

    [SOLVED] Pre Calculus Homework Problem...Help! [b]1. Homework Statement A quadrilateral has two pairs of congruent sides and a longer diagonal of length of 6, as shown. For what value of x will the area of the shaded region be 40% of the area of the unshaded region? [b]2. Homework...
  30. P

    Pre-Calc Help: Range & Exponents, Bacterial Growth

    Range of- (x)/((x^2)-9) please explain in detail also the properties of exponents to simplify the expression ((16x^-2)(y^4))^1/2 A bacterial culture starts with 20,000 bacteria, and the number doubles every 40 min. Find the number T of minutes required for the culture to have...
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