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This set spans P₃(

**R**) if an arbitrary vector in P₃(**R**) can be ...p, there are coefficients b, c, d ∈**R**such that b(1 + 2x - 4x³) + c(2 - x + x²...1 Answers · Science & Mathematics · 04/11/2015

8^

**r**= 16^2 (2^3)^**r**= (2^4)^2 2^(3r) = 2^8 3r = 8**r**= 8/3 Note that you ...rational numbers. Here's how you would do it in general. 8^**r**= 16^2 = 256 ln(8^**r**) = ln(256)**r***ln(8) = ln(256)**r**= ln(256)/ln(8...2 Answers · Science & Mathematics · 31/10/2007

**r**/15 -**r**/35 = 1/15 multiply equation by 15**r**- 15r/35 = 1**r**- 3r/7 = 1 multiply equation by 7 7r - 3r = 7 4r = 7**r**= 7/4 hope this helps keep practicing! good luck2 Answers · Science & Mathematics · 27/02/2011

"

**R**to**R**" or "**R**->**R**" (as I prefer it ... refers to the integers, so when we state "Z to**R**" (or "Z ->**R**") we mean that the domain is the set...2 Answers · Science & Mathematics · 07/07/2009

**r**= 5 sin 4θ dr/dθ = 5 cos 4θ (4) = 20 cos 4θ dy/dx = (dr/dθ sin θ +**r**cos θ) / (dr/dθ cps θ +**r**sin θ) dy/dx = ( (20...25√3 /4 -35/4 = (-25√3-35) / 4 When θ=π/3,**r**= 5 sin 4π/3 = -5√3/2 x=**r**cos θ = (-5√3/2)( 1/2...1 Answers · Science & Mathematics · 20/02/2013

**R**(sin x, cos x) essentially means that you have a ratio of polynomials... of sine and cosine. [More explicitly, the rational function is**R**(u, v) = v/(u + uv). So,**R**(sin x, cos x) = cos x/(sin x + sin x cos...1 Answers · Science & Mathematics · 01/04/2012

Unfortunately, the notation B(

**r**,a) has no standard meaning (even in the context... sort of a "standard" choice of a metric in**R**^2, this choice is by no means the *only* choice...1 Answers · Science & Mathematics · 29/05/2013

**r**^(-8) = 7/352**r**^8 = 352/7**r**= (352/7)^(1/8)**r**= (50.28571)^(1/8)**r**= 1.6318514 Answers · Science & Mathematics · 22/01/2014

∫((

**r**)/(2^(**r**^2)) dr Let u=**r**^2 du = 2rdr The integral simplifies to ∫1/(2^u...ln2))] + c But u =**r**^2 Integral = -[1/(ln(2)]e^(-(**r**^2)(ln2))] + c = -[1/ln(2)][1/2^(**r**^2)] + c = -1/[(2^(**r**^2))* ln(2...1 Answers · Science & Mathematics · 09/06/2007

first we assume that

**r**,**r**' are in A+B. then we check if**r**-**r**' is also... an additive subgroup of**R**. from our initial assumption, we may write**r**= a+b, for some a in A, b in B, and likewise**r**' = a'+b'...1 Answers · Science & Mathematics · 18/04/2012