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AlgebraQuestion and Answers: Page 31

Question Number 206795 Answers: 0 Comments: 3

Question Number 206773 Answers: 0 Comments: 3

∫_0 ^∞ (e^(−x^2 ) /((x^2 +(1/2))^2 ))dx= I^2 =∫∫_( D) (e^(−x^2 −y^2 ) /((x^2 +(1/2))^2 (y^2 +(1/2))^2 ))dA x=rcos(θ) y=rsin(θ) J=∣((∂(x,y))/(∂(r,θ)))∣drdθ=rdrdθ ∫∫_( D) ((re^(−r^2 ) )/((r^2 cos^2 (θ)+(1/2))^2 (r^2 sin^2 (θ)+(1/2))^2 ))drdθ

$\int_{0}^{\infty} \frac{e^{- x^{2}}}{{(x^{2} + \frac{1}{2})}^{2}} d x =$ $I^{2} = \int \int_{D} \frac{e^{- x^{2} - y^{2}}}{{(x^{2} + \frac{1}{2})}^{2} {(y^{2} + \frac{1}{2})}^{2}} d A$ $x = r \cos (θ) y = r \sin (θ)$ $J =∣ \frac{\partial (x, y)}{\partial (r, θ)} ∣ d r d θ = r d r d θ$ $\int \int_{D} \frac{{r e}^{- r^{2}}}{{(r^{2} \cos^{2} (θ) + \frac{1}{2})}^{2} {(r^{2} \sin^{2} (θ) + \frac{1}{2})}^{2}} d r d θ$

Question Number 206695 Answers: 1 Comments: 0

If (2)^(1/(10)) (cos 9° + i sin 9°) Find: z^5 = ?

$If \sqrt[10]{2} (\cos 9 ° + i \sin 9 °)$ $Find : z^{5} = ?$

Question Number 206679 Answers: 1 Comments: 0

if f(x)+2g(1−x)=x^2 and f(1−x)−g(x)=x^2 then f(x)=?

$i f f (x) + 2 g (1 - x) = x^{2}$ $a n d f (1 - x) - g (x) = x^{2}$ $t h e n f (x) = ?$

Question Number 206637 Answers: 1 Comments: 0

Question Number 206622 Answers: 2 Comments: 0

Σ_(n=2) ^4 (((2n)/3) −1) = ?

$\sum_{n = 2}^{4} (\frac{2 n}{3} - 1) = ?$

Question Number 206614 Answers: 1 Comments: 1

Question Number 206613 Answers: 2 Comments: 0

If f(x) = { ((x^2 , x ≤ 2)),((f(x−3) , x > 2)) :} Find ∫_(−1) ^( 53) f(x) dx = ?

$If f (x) = {\begin{cases} x^{2}, x ⩽ 2 \\ f (x - 3), x > 2 \end{cases}$ $Find \int_{- 1}^{53} f (x) dx = ?$

Question Number 206609 Answers: 0 Comments: 0

let matrix A_(n×n) and B_(n×n) satisfying A^2 = A & B^2 = B then prove ρ(A−B) = ρ(A−AB)+ ρ(B−AB) here ρ = rank

$let matrix A_{n \times n} and B_{n \times n} satisfying$ $A^{2} = A & B^{2} = B then prove$ $ρ (A - B) = ρ (A - AB) + ρ (B - AB)$ $here ρ = rank$

Question Number 206532 Answers: 3 Comments: 0

Find the nth term of the sequence 0,3,8,15,24,......

$F i n d t h e n t h t e r m o f t h e s e q u e n c e$ $0, 3, 8, 15, 24, . . . . . .$

Question Number 206501 Answers: 0 Comments: 9

If x^(log_3 x − 1) = log_3 x + 3 Find: log_3 x_1 + log_3 x_2 = ?

$If$ $x^{\log_{3} x - 1} = \log_{3} x + 3$ $Find : \log_{3} x_{1} + \log_{3} x_{2} = ?$

Question Number 206477 Answers: 3 Comments: 0

If a>b>0 and 4a^2 + b^2 = 4ab Find: ((a − b)/(a + b)) = ?

$If a > b > 0 and {4 a}^{2} + b^{2} = 4 ab$ $Find : \frac{a - b}{a + b} = ?$

Question Number 206475 Answers: 1 Comments: 0

If (a^2 /(12)) − 5b^3 = −30 Find: (2/(45)) a^2 − (8/3) b^3 = ?

$If \frac{a^{2}}{12} - {5 b}^{3} = - 30$ $Find : \frac{2}{45} a^{2} - \frac{8}{3} b^{3} = ?$

Question Number 206473 Answers: 4 Comments: 0

If 4^p = 5 Find: 2^(3p) = ?

$If 4^{p} = 5$ $Find : 2^{3 p} = ?$

Question Number 206458 Answers: 3 Comments: 0

if f(x)=(√(x−x^2 )) then f^(−1) (x)=?

$i f f (x) = \sqrt{x - x^{2}} t h e n f^{- 1} (x) = ?$

Question Number 206443 Answers: 0 Comments: 4

Question Number 206425 Answers: 1 Comments: 0

If cos𝛂 = (3/5) (0<𝛂<(𝛑/2)) Find: ((tan^2 (45° + (𝛂/2)))/3) = ?

$If \cos α = \frac{3}{5} (0 < α < \frac{π}{2})$ $Find : \frac{\tan^{2} (45 ° + \frac{α}{2})}{3} = ?$

Question Number 206391 Answers: 2 Comments: 0

Find: ∫_(−3) ^( −2) (∣x∣ + ∣x − 4∣) dx = ?

$Find :$ $\int_{- 3}^{- 2} (∣ x ∣ + ∣ x - 4 ∣) dx = ?$

Question Number 206365 Answers: 2 Comments: 4

Number series: a_3 = 2a + b − 6 a_9 = a + b + 5 a_(15) = 3a + b − 7 Find: a = ?

$Number series :$ $a_{3} = 2 a + b - 6$ $a_{9} = a + b + 5$ $a_{15} = 3 a + b - 7$ $Find : a = ?$

Question Number 206363 Answers: 0 Comments: 2

If 0<a<1 Compare: (1/(a−1)) , (a/(a−1)) , (1/(1−a)) , (a/(1−a)) , (a/(2a))

$If 0 < a < 1$ $Compare :$ $\frac{1}{a - 1}, \frac{a}{a - 1}, \frac{1}{1 - a}, \frac{a}{1 - a}, \frac{a}{2 a}$

Question Number 206357 Answers: 2 Comments: 0

Find: 1 + cos444° − cos84° + cot45° = ?

$Find :$ $1 + \cos 444 ° - \cos 84 ° + \cot 45 ° = ?$

Question Number 206355 Answers: 2 Comments: 0

if the sum of three positive real numbers is equal to their product, prove that at least one of the numbers is larger than 1.7.

$i f t h e s u m o f t h r e e p o s i t i v e r e a l$ $n u m b e r s i s e q u a l t o t h e i r p r o d u c t,$ $p r o v e t h a t a t l e a s t o n e o f t h e$ $n u m b e r s i s l a r g e r t h a n 1.7 .$

Question Number 206339 Answers: 1 Comments: 0

E ⊆ Y ⊆ ( X , d )∣_(metric space) prove E is open in Y if and only if ∃ G (open set ) in X such that E = G ∩ Y .... (mathematical analysis (I))

$E \subseteq Y \subseteq (X, d) ∣_{m e t r i c s p a c e}$ $p r o v e E i s o p e n i n Y i f a n d o n l y i f$ $\exists G (o p e n s e t) i n X s u c h t h a t$ $E = G \cap Y . . . . (m a t h e m a t i c a l a n a l y s i s (I))$

Question Number 206367 Answers: 4 Comments: 2

Find: (1/6) + (1/(24)) + (1/(60)) + ... + ... (1/(720)) = ?

$Find :$ $\frac{1}{6} + \frac{1}{24} + \frac{1}{60} + . . . + . . . \frac{1}{720} = ?$

Question Number 206332 Answers: 1 Comments: 0

If log(a + b + c) = loga + logb + logc then prove that log(((2a)/(1 − a^2 )) + ((2b)/(1 − b^2 )) + ((2c)/(1 − c^2 ))) = log(((2a)/(1 − a^2 ))) + log(((2b)/(1 − b^2 ))) + log(((2c)/(1 − c^2 ))).

$If \log (a + b + c) = \log a + \log b + \log c$ $then prove that$ $\log (\frac{2 a}{1 - a^{2}} + \frac{2 b}{1 - b^{2}} + \frac{2 c}{1 - c^{2}}) =$ $\log (\frac{2 a}{1 - a^{2}}) + \log (\frac{2 b}{1 - b^{2}}) + \log (\frac{2 c}{1 - c^{2}}) .$

Question Number 206328 Answers: 2 Comments: 0

f(x)= ⌊ (( 1+ x +x^2 )/(x+ x^( 2) )) ⌋ is given. ⇒ { (( D_f = ? (domain ))),(( R_( f) = ?( range))) :}

$f (x) = ⌊ \frac{1 + x + x^{2}}{x + x^{2}} ⌋ i s g i v e n .$ $\Rightarrow {\begin{cases} D_{f} = ? (d o m a i n) \\ R_{f} = ? (r a n g e) \end{cases}$

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