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Question Number 152715 Answers: 0 Comments: 2

By eliminating θ, show that x^2 = − y^2 , if x sin^3 θ + y cos^3 θ = sinθ and x sinθ − y cosθ = 0

$By eliminating θ, show that x^{2} = - y^{2},$ $if x \sin^{3} θ + y \cos^{3} θ = \sin θ and x \sin θ - y \cos θ = 0$

Question Number 152692 Answers: 0 Comments: 0

If b and h are two integers with b>h, and b^2 +h^2 =b(a+h)+ah, find the value of b.

$If b and h are two integers with b > h,$ $and b^{2} + h^{2} = b (a + h) + a h,$ $find the value of b .$

Question Number 152691 Answers: 1 Comments: 0

If a,p,q are primes with a<p, and a+p=q, find the value of a.

$If a, p, q are primes with a < p, and$ $a + p = q, find the value of a .$

Question Number 152683 Answers: 1 Comments: 0

The probability that athlete will win a race is (1/6) and that he will be second and third are (1/4) and (1/3) respectively.what is the probability that he will not be first in the first three place! Please,help me out

$T h e p r o b a b i l i t y t h a t a t h l e t e w i l l w i n a r a c e i s \frac{1}{6} a n d t h a t$ $h e w i l l b e s e c o n d a n d t h i r d a r e \frac{1}{4} a n d \frac{1}{3}$ $r e s p e c t i v e l y . w h a t i s t h e p r o b a b i l i t y t h a t h e w i l l n o t b e f i r s t$ $i n t h e f i r s t t h r e e p l a c e!$ $P l e a s e, h e l p m e o u t$

Question Number 152682 Answers: 1 Comments: 0

Question Number 152672 Answers: 1 Comments: 0

Question Number 152671 Answers: 3 Comments: 2

Question Number 152670 Answers: 1 Comments: 0

Question Number 152678 Answers: 2 Comments: 0

Find the sum of the real roots of equations: a^3 -6a^2 +15a-17=0 and a^3 -6a^2 +15a-11=0

$Find the sum of the real roots of equations :$ $a^{3} - {6 a}^{2} + 15 a - 17 = 0 and$ $a^{3} - {6 a}^{2} + 15 a - 11 = 0$

Question Number 152663 Answers: 1 Comments: 0

If x^3 -x+3=0 has the roots a, b and c. determine the monic polynomial with the roots a^5 , b^5 and c^5 . [Q152396]

$If x^{3} - x + 3 = 0 has the roots a, b and c .$ $determine the monic polynomial with$ $the roots a^{5}, b^{5} and c^{5} .$ $[Q 152396]$

Question Number 152660 Answers: 1 Comments: 0

∫ (x/( (√(1 + x^3 )))) dx

$\int \frac{x}{\sqrt{1 + x^{3}}} dx$

Question Number 152653 Answers: 1 Comments: 0

Ω :=∫_0 ^( ∞) (( e^( −x^( 3) ) . sin (x^( 3) ))/x)dx= ((ζ (2 ))/2) m.n...

$Ω := \int_{0}^{\infty} \frac{e^{- x^{3}} . s i n (x^{3})}{x} d x = \frac{ζ (2)}{2}$ $m . n . . .$

Question Number 152652 Answers: 0 Comments: 1

Question Number 152647 Answers: 1 Comments: 1

Question Number 152631 Answers: 1 Comments: 0

Question Number 152626 Answers: 1 Comments: 0

Solve for real numbers: (1/(x-1)) + (2/(x-2)) + (3/(x-3)) + (4/(x-4)) = 2x^2 -5x-4

$Solve for real numbers :$ $\frac{1}{x - 1} + \frac{2}{x - 2} + \frac{3}{x - 3} + \frac{4}{x - 4} = {2 x}^{2} - 5 x - 4$

Question Number 152625 Answers: 1 Comments: 2

x^4 +c_3 x^3 +c_2 x^2 +c_1 x+c_0 =0 for c_n ∈R this can have 4 unique zeros ∈R 2 unique zeros + 1 double zero ∈R 2 double zeros ∈R 1 triple + 1 unique zeros ∈R 1 fourfold zero ∈R 2 unique zeros ∈R + 1 pair of complex zeros 1 double zero ∈R + 1 pair of complex zeros 2 pairs of complex zeros 2 double imaginary zeros for given c_n ; can we decide which case we have without solving?

$x^{4} + c_{3} x^{3} + c_{2} x^{2} + c_{1} x + c_{0} = 0$ $for c_{n} \in R this can have$ $4 unique zeros \in R$ $2 unique zeros + 1 double zero \in R$ $2 double zeros \in R$ $1 triple + 1 unique zeros \in R$ $1 fourfold zero \in R$ $2 unique zeros \in R + 1 pair of complex zeros$ $1 double zero \in R + 1 pair of complex zeros$ $2 pairs of complex zeros$ $2 double imaginary zeros$ $for given c_{n}; can we decide which case we$ $have without solving ?$