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Questions (23)

A thin triangle has vertices (0,0), (1,0), and (0,2). Let the density function at any given point on the triangle be represented
1. 0 answers
2. 1,259 views
Let z be a complex number such thatz=2(cos3∘+icos87∘). Then z^6 can be expressed as r(sinα∘+icosα∘), where r is a real
1. 3 answers
2. 455 views
Given w=2+2i and v=−5√3+5i,vw^2 can be expressed as r*(cos(α∘)+i*sin(α∘)), where r is a real number and 0≤α≤360.
1. 2 answers
2. 429 views
In polar coordinates,the graph r=sin(θ)/cos^2(θ) represents the function y=(a_n)*x^n+(a_(n−1))*x^(n−1)+…+a_0 in
1. 1 answer
2. 511 views
A polynomial function f(x) has degree 6 and has real coefficients. It is given that 3, 2, 11−3i, and 11+28i are roots of f(x).
1. 1 answer
2. 676 views
a and b are integers such that the polynomial f(x)=x^4−4x^3−8x^2+ax+b has 1+2i as a solution to f(x)=0. What is the value of
1. 1 answer
2. 374 views
If f(x) is a polynomial with real coefficients such that f(8+8i)=38+9i, then f(8−8i)=a+bi. What is the value of a+b?
1. 3 answers
2. 405 views
For how many ordered triples of positive real numbers (a,b,c), do the equations ax^2+2bx+c, bx^2+2cx+a and cx^2+2ax+b each have
1. 1 answer
2. 509 views
The following three sets A,B and C satisfy A ⊂ B and C ⊂ A:A={x∣(x−3)(x^2−20x+75)>0}, B={x∣x>α}, C={x∣x>β}. If
1. 0 answers
2. 401 views
What is the maximum integer value of n, where n<148,that satisfies the following inequalities: sin(pi/2+(pi*n)/74)<0 and
1. 2 answers
2. 415 views
Let f(x)=cos(pi*x/3)g(x)=1^x+(−1)^x h(x)=f(x)⋅g(x) where x is a positive integer. Given that h(x) has a range of exactly 3
1. 2 answers
2. 443 views
The remainder that the polynomial f(x) leaves upon division by x−1 and x−2 is 2 and 3, respectively. If the remainder f(x)
1. 0 answers
2. 463 views
Given that the quadratic polynomial f(x)=3x^2+ax+b has real coefficients and f(x)=0 has a complex root 8+5i, what is the value
1. 2 answers
2. 432 views
Suppose x and y are real numbers satisfyingx(x+i)+y(y+i)−6(8+i)=0. What is the value of x^3+y^3?
1. 1 answer
2. 477 views
1+(2/i)+(3/i^2)+(4/i^3)+⋯+(n/i^(n−1))=29+28iwhat is the value of n? n is positive value
1. 1 answer
2. 298 views
Given that a and b are real numbers such that the follwoing quadratic equation x^2+(a+6i)x+b+12i=0 has a repeated root, what is
1. 1 answer
2. 438 views
For how many ordered triples of positive real numbers (a,b,c), do the equations ax^2+2bx+c, bx^2+2cx+a and cx^2+2ax+b each have
1. 0 answers
2. 549 views
If z is a non-real complex number and z^2−26z is a real number, what is the value of z+z¯?z¯ denotes the conjugate of the
1. 1 answer
2. 451 views
What is the maximum integer value of n, where n<148,that satisfies the following inequalities: sin(pi/2+(pi*n)/74)<0 and
1. 0 answers
2. 365 views
Let f(x)=cos(pi*x/3)g(x)=1^x+(−1)^x h(x)=f(x)⋅g(x) where x is a positive integer. Given that h(x) has a range of exactly 3
1. 1 answer
2. 367 views
Let f(x)=x2−1. How many distinct real roots are there to f(f(f(x)))=0?
1. 1 answer
2. 442 views
A plane flies horizontally at constant ground speed v=720km/h. The pilot is informed by an air traffic controller that he must
1. 9 answers
2. 957 views
A helium-4 atom falls from a height h into a tank of gaseous helium atoms at 300 K. What is h in meters if the temperature of
1. 16 answers
2. 793 views