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.
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...
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)##...
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??
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##...
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...
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.
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?
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...
Homework Statement
X and Y 2 real numbers / |x| <1 and |y|<1
Prove that |x+y|<|xy+1|
Homework Equations
The 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
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...
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
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...
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...
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...
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...
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...
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...
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...
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