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Question Number 36049 Answers: 0 Comments: 0

A triangle △ABC is constructed such that ∠B= 90° and AB= 5cm Given that ∠C= 45° . show that the point (2,0) lie on the line BC and is perpendicular to AB but meet at 45^ ° with the line AC.

$A triangle △ ABC is constructed$ $such that ∠ B = 90 ° and AB = 5 cm$ $Given that ∠ C = 45 ° . show that$ $the point (2, 0) lie on the line$ $BC and is perpendicular to AB but$ $meet at 45^{} ° with the line AC .$

Question Number 36034 Answers: 1 Comments: 1

Question Number 36011 Answers: 0 Comments: 2

simplify: ′interval number′ (1,6)∪(3,7)

$simplify :^{'} i n t e r v a l {n u m b e r}^{'}$ $(1, 6) \cup (3, 7)$

Question Number 35987 Answers: 0 Comments: 4

let f(x) = (1/(1+x^3 )) 1) calculate f^((n)) (x) 2) developp f at integr serie.

$l e t f (x) = \frac{1}{1 + x^{3}}$ $1) c a l c u l a t e f^{(n)} (x)$ $2) d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 36003 Answers: 2 Comments: 0

x [(2),(1) ]+y [(3),(5) ]+ [((−8)),((−11)) ]=0 find x and y

$x [\begin{matrix} 2 \\ 1 \end{matrix}] + y [\begin{matrix} 3 \\ 5 \end{matrix}] + [\begin{matrix} - 8 \\ - 11 \end{matrix}] = 0$ $f i n d x a n d y$

Question Number 35960 Answers: 0 Comments: 3

Solve using Residue Theorem I = ∫_(−∞) ^(+∞) (x^2 /(x^4 + 16)) dx

$Solve using Residue Theorem$ $I = \int_{- \infty}^{+ \infty} \frac{x^{2}}{x^{4} + 16} d x$

Question Number 35915 Answers: 1 Comments: 0

if P(A) and P(B) are independent events then P(A∣B)=??

$i f P (A) a n d P (B) a r e i n d e p e n d e n t$ $e v e n t s t h e n P (A ∣ B) = ? ?$

Question Number 35811 Answers: 3 Comments: 6

Multiple Choice Questions Rio Mike. Q_1 . The value of 6 + 2 × 4 −15 ÷ 3 is; A) 3 B) 9 C) 4 D) 27 Q_2 . 80 as a product of its prime factor is. A) 2^3 × 5 B) 2 × 5^(3 ) C) 2^2 × 5^2 D) 2^4 × 5 Q_3 . The deteminant of (((6 4)),((3 2)) ) is A) 18 B) 0 C) 24 D) −24 Q_4 . the value of ((1/(16)))^(−(1/2)) is A) −(1/4) B) 4 C) −4 D) (1/2) Q_5 . if −8,m,n,19 are in AP then (m,n) is A) (1,10) B) (2,10) C) (3,13) D) (4,16)o Q_6 . if cos θ = ((12)/(13)) then cot^2 θ is; A) ((169)/(25)) B) ((25)/(169)) C)((169)/(144)) D) ((144)/(169)) Q_7 . the solution set of 3 ≤ 2x−1≤5 is; A) ]x≥−2,x≤(8/3)[ B) [x≥2,x≤−(8/3)[ C) ]x>−2,x≤(3/8)] D) [x≥−2,x≤(8/3)] Q_8 . Which is a factor of f(x)= x^2 −3x + 2 A) (x−1) B) (x−2) C) (x+1) D)(x+3) Q_(9 ) . The sum of the sum of roots and product of roots of the quadratic equation 3x^2 + 6x + 9=0 A) 1 B) −1 C) 32 D) 5 Q_(10) . 2log2−log2 = A) log 8 B) log 6 C) log 3 D) log 2. Q_(11) . Σ_(r=1) ^∞ 3^(2−r) = A) (9/4) B) (9/2) C) ((13)/3) D) (1/2) Q_(12) . The constand term in the binomial expansion of (x^2 + (1/x^2 ))^8 is A) 3^(rd) B) 4^(th) C) 5^(th) D) 6^(th) Q_(13) . cos(180−x) = A) −sinx B) sin x C) cos x D) −cos x Q_(14) . The value of p for which (2,1) , (6,3), and (4,p) are collinear is ; A) 2 B) 1 C)−1 D) −2 Q_(15) . ∫_1 ^2 x^3 dx = A) −sin 7x B) sin 7x C) −7sin7x D) 7sin7x Q_(16) . Given that g : → px −5, the value of p for which g^(−1) (3)=4 is A) (1/2) B) −(1/2) C) −2 D) 2 Q_(17) . The value of θ in the range 0°≤θ≤90° for which sinθ = cos θ is A) 90° B) 60° C) 30° D) 45° Questions

$M u l t i p l e C h o i c e Q u e s t i o n s$ $R i o M i k e .$ $Q_{1} . T h e v a l u e o f 6 + 2 \times 4 - 15 \div 3$ $i s;$ $A) 3 B) 9 C) 4 D) 27$ $Q_{2} . 80 a s a p r o d u c t o f i t s p r i m e$ $f a c t o r i s .$ $A) 2^{3} \times 5 B) 2 \times 5^{3} C) 2^{2} \times 5^{2}$ $D) 2^{4} \times 5$ $Q_{3} . T h e d e t e m i n a n t o f (\begin{matrix} 6 4 \\ 3 2 \end{matrix}) i s$ $A) 18 B) 0 C) 24 D) - 24$ $Q_{4} . t h e v a l u e o f {(\frac{1}{16})}^{- \frac{1}{2}} i s$ $A) - \frac{1}{4} B) 4 C) - 4 D) \frac{1}{2}$ $Q_{5} . i f - 8, m, n, 19 a r e i n A P t h e n$ $(m, n) i s$ $A) (1, 10) B) (2, 10) C) (3, 13) D) (4, 16) o$ $Q_{6} . i f c o s θ = \frac{12}{13} t h e n {c o t}^{2} θ i s;$ $A) \frac{169}{25} B) \frac{25}{169} C) \frac{169}{144} D) \frac{144}{169}$ $Q_{7} . t h e s o l u t i o n s e t o f 3 ⩽ 2 x - 1 ⩽ 5$ $i s;$ $A)] x ⩾ - 2, x ⩽ \frac{8}{3} [B) [x ⩾ 2, x ⩽ - \frac{8}{3} [$ $C)] x > - 2, x ⩽ \frac{3}{8}] D) [x ⩾ - 2, x ⩽ \frac{8}{3}]$ $Q_{8} . W h i c h i s a f a c t o r o f f (x) =$ $x^{2} - 3 x + 2$ $A) (x - 1) B) (x - 2) C) (x + 1) D) (x + 3)$ $Q_{9} . T h e s u m o f t h e s u m o f$ $r o o t s a n d p r o d u c t o f r o o t s o f t h e$ $q u a d r a t i c e q u a t i o n 3 x^{2} + 6 x + 9 = 0$ $A) 1 B) - 1 C) 32 D) 5$ $Q_{10} . 2 l o g 2 - l o g 2 =$ $A) l o g 8 B) l o g 6 C) l o g 3$ $D) l o g 2 .$ $Q_{11} . \underset{r = 1}{\sum^{\infty}} 3^{2 - r} =$ $A) \frac{9}{4} B) \frac{9}{2} C) \frac{13}{3} D) \frac{1}{2}$ $Q_{12} . T h e c o n s t a n d t e r m i n t h e$ $b i n o m i a l e x p a n s i o n o f {(x^{2} + \frac{1}{x^{2}})}^{8} i s$ $A) 3^{r d} B) 4^{t h} C) 5^{t h} D) 6^{t h}$ $Q_{13} . c o s (180 - x) =$ $A) - s i n x B) s i n x C) c o s x$ $D) - c o s x$ $Q_{14} . T h e v a l u e o f p f o r w h i c h$ $(2, 1), (6, 3), a n d (4, p) a r e c o l l i n e a r$ $i s;$ $A) 2 B) 1 C) - 1 D) - 2$ $Q_{15} . \int_{1}^{2} x^{3} d x =$ $A) - s i n 7 x B) s i n 7 x C) - 7 s i n 7 x$ $D) 7 s i n 7 x$ $Q_{16} . G i v e n t h a t g : \to p x - 5, t h e$ $v a l u e o f p f o r w h i c h g^{- 1} (3) = 4 i s$ $A) \frac{1}{2} B) - \frac{1}{2} C) - 2 D) 2$ $Q_{17} . T h e v a l u e o f θ i n t h e r a n g e$ $0 ° ⩽ θ ⩽ 90 ° f o r w h i c h s i n θ = c o s θ i s$ $A) 90 ° B) 60 ° C) 30 ° D) 45 °$ $Q u e s t i o n s$

Question Number 35738 Answers: 2 Comments: 0

Given that ∫_0 ^k x^2 = 16 find the value of k

$G i v e n t h a t \int_{0}^{k} x^{2} = 16$ $f i n d t h e v a l u e o f k$

Question Number 35656 Answers: 0 Comments: 5

Following alphabet lacks one letter. abcdefghijklmnopqrstuvxyz I request that letter, please come and make the alphabet complete.

$Following alphabet lacks one letter .$ $abcdefghijklmnopqrstuvxyz$ $I request that letter,$ $please come and make the alphabet$ $complete .$

Question Number 35602 Answers: 2 Comments: 0

Q_1 .p(x) = 3x^3 + 4x^2 +5x − k and (x−1) is a factor of p(x) find the value of k and the remaining two factors. Q_2 . Evaluate Σ_(r=1) ^∞ 3^(2−r) .

$Q_{1} . p (x) = {3 x}^{3} + {4 x}^{2} + 5 x - k and$ $(x - 1) is a factor of p (x) find the$ $value of k and the remaining$ $two factors .$ $Q_{2} . E v a l u a t e \underset{r = 1}{\sum^{\infty}} 3^{2 - r} .$

Question Number 35595 Answers: 1 Comments: 0

Find the surface Area of a solid cone of raduis 3cm and slant height 4cm. (take π=3.1)

$F i n d t h e s u r f a c e A r e a o f a s o l i d$ $c o n e o f r a d u i s 3 c m a n d s l a n t$ $h e i g h t 4 c m . (t a k e π = 3.1)$

Question Number 35594 Answers: 1 Comments: 0

Given that 18,24,and k + 14 are three consecutive terms of an arithmetic progression Find a) the common difference b) the value of k c)the first term if the 4^(th) term is 12. d) the sum of the first twelve terms of the progression.

$G i v e n t h a t 18, 24, a n d k + 14 a r e$ $t h r e e c o n s e c u t i v e t e r m s o f a n$ $a r i t h m e t i c p r o g r e s s i o n F i n d$ $a) t h e c o m m o n d i f f e r e n c e$ $b) t h e v a l u e o f k$ $c) t h e f i r s t t e r m i f t h e 4^{t h} t e r m i s$ $12 .$ $d) t h e s u m o f t h e f i r s t t w e l v e t e r m s o f$ $t h e p r o g r e s s i o n .$

Question Number 35513 Answers: 1 Comments: 0

g(x)= 6x^2 − 5ax + b^2 given that g(x) has only two roots and are (x−1) and (x−2) find the value of a and b.Using (x−1) as a root detemine the extend to which (x−2) is a root (occurance as a root).

$g (x) = 6 x^{2} - 5 a x + b^{2}$ $g i v e n t h a t g (x) h a s o n l y t w o r o o t s$ $a n d a r e (x - 1) a n d (x - 2)$ $f i n d t h e v a l u e o f a a n d b . U s i n g$ $(x - 1) a s a r o o t d e t e m i n e t h e$ $e x t e n d t o w h i c h (x - 2) i s a r o o t$ $(o c c u r a n c e a s a r o o t) .$

Question Number 35512 Answers: 1 Comments: 0

Given that (x+1,3,x) are lengths of the sides of a right angled triangle(pythagoras tripple) find the value of x.

$G i v e n t h a t (x + 1, 3, x) a r e l e n g t h s$ $o f t h e s i d e s o f a r i g h t a n g l e d$ $t r i a n g l e (p y t h a g o r a s t r i p p l e)$ $f i n d t h e v a l u e o f x .$

Question Number 35482 Answers: 0 Comments: 1

Let A and B are 3 ×3 matrices. The statements below which is True is ... (A) AB = BA (B) If AB = 0, then only A = 0 or B = 0 is true (C) If AB = I, then only A = I or A = −I is true (D) There exist A where A ≠ 0, and yet A^2 = 0 (E) ∣A + B∣ = ∣A∣ + ∣B∣

$Let A and B are 3 \times 3 matrices . The statements below$ $which is T r u e is . . .$ $(A) A B = B A$ $(B) If A B = 0, then only A = 0 or B = 0 is true$ $(C) If A B = I, then only A = I or A = - I is true$ $(D) There exist A where A \neq 0, and yet A^{2} = 0$ $(E) ∣ A + B ∣ = ∣ A ∣ + ∣ B ∣$

Question Number 35478 Answers: 0 Comments: 1

((3(√2)(2−i)))^(1/5) =...??

$\sqrt[5]{3 \sqrt{2} (2 - i)} = . . . ? ?$

Question Number 35460 Answers: 1 Comments: 1

Find the values of k for which the equation (((k −3)),((10 −k+1)) ) ((x),(y) ) = (((k−1)),(8) ) have a) a unique solution b) no solution c)an infinite solution hence Find the image of the point (3,1) after reflection in the line with equation a) x=1 b) y= −1 c) y+x= 1

$F i n d t h e v a l u e s o f k f o r w h i c h$ $t h e e q u a t i o n$ $(\begin{matrix} k - 3 \\ 10 - k + 1 \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} k - 1 \\ 8 \end{matrix})$ $h a v e$ $a) a u n i q u e s o l u t i o n$ $b) n o s o l u t i o n$ $c) a n i n f i n i t e s o l u t i o n$ $h e n c e$ $F i n d t h e i m a g e o f t h e p o i n t$ $(3, 1) a f t e r r e f l e c t i o n i n t h e l i n e$ $w i t h e q u a t i o n$ $a) x = 1 b) y = - 1 c) y + x = 1$

Question Number 35425 Answers: 1 Comments: 0

Given that a number is a factor of 144 and the square of the number added to five times the number is ≥ −6 find the number

$G i v e n t h a t a n u m b e r i s a f a c t o r$ $o f 144 a n d t h e s q u a r e o f t h e n u m b e r$ $a d d e d t o f i v e t i m e s t h e n u m b e r$ $i s ⩾ - 6 f i n d t h e n u m b e r$

Question Number 35426 Answers: 1 Comments: 2

find the value of x if the inverse of the matrix (((x+5 2)),((7 x)) ) is (((0 0)),((0 0)) )

$f i n d t h e v a l u e o f x i f t h e i n v e r s e$ $o f t h e m a t r i x (\begin{matrix} x + 5 2 \\ 7 x \end{matrix}) i s$ $(\begin{matrix} 0 0 \\ 0 0 \end{matrix})$

Question Number 35384 Answers: 1 Comments: 1

((−1+i(√3)))^(1/6) =....??

$\sqrt[6]{- 1 + i \sqrt{3}} = . . . . ? ?$

Question Number 35367 Answers: 2 Comments: 0

Q_(3 ) . a number is a factor of 6 the square of the number added to 5 times thenumber is same as −6 find the number.

$Q_{3} . a n u m b e r i s a f a c t o r o f 6$ $t h e s q u a r e o f t h e n u m b e r a d d e d$ $t o 5 t i m e s t h e n u m b e r i s s a m e a s$ $- 6 f i n d t h e n u m b e r .$

Question Number 35363 Answers: 3 Comments: 0

Q_1 . A quadratic equation x^2 −3x+4=0 has roots α and β .without solving a)write down the values of α^2 +β^2 b) find the quadratic equation with integral coefficients,whose roots are (1/α^2 ) and(1/β^2 ) Q_2 . the first term of a GP is 32 and the sum to infinity is 48. find the common ratio and the 8^(th) term of the progression

$Q_{1} . A q u a d r a t i c e q u a t i o n x^{2} - 3 x + 4 = 0$ $h a s r o o t s α a n d β . w i t h o u t s o l v i n g$ $a) w r i t e d o w n t h e v a l u e s o f α^{2} + β^{2}$ $b) f i n d t h e q u a d r a t i c e q u a t i o n$ $w i t h i n t e g r a l c o e f f i c i e n t s, w h o s e$ $r o o t s a r e \frac{1}{α^{2}} a n d \frac{1}{β^{2}}$ $Q_{2} . t h e f i r s t t e r m o f a G P i s 32$ $a n d t h e s u m t o i n f i n i t y i s 48 .$ $f i n d t h e c o m m o n r a t i o a n d t h e 8^{t h}$ $t e r m o f t h e p r o g r e s s i o n$

Question Number 35357 Answers: 2 Comments: 0

Q_1 . find the term in x^6 in the expansion of (x^2 +(2/x))^9 Q_2 . in the binomial expansion of (x+(k/x))^6 , the term independent of x is 160 find the value of k. Q_3 . find the constand term in the binomial of (x+(3/x))^(12) .

$Q_{1} . f i n d t h e t e r m i n x^{6} i n t h e$ $e x p a n s i o n o f {(x^{2} + \frac{2}{x})}^{9}$ $Q_{2} . i n t h e b i n o m i a l e x p a n s i o n o f$ ${(x + \frac{k}{x})}^{6}, t h e t e r m i n d e p e n d e n t o f x$ $i s 160 f i n d t h e v a l u e o f k .$ $Q_{3} . f i n d t h e c o n s t a n d t e r m i n t h e$ $b i n o m i a l o f {(x + \frac{3}{x})}^{12} .$

Question Number 35419 Answers: 1 Comments: 0

Given that f(x)= x^3 −x^2 +ax+b and g(x)= 2x^3 −9x^2 −3ax + b have a common factor (x−1) where a and b are constands . Find the values of a and b hence find other factors of f(x)

$G i v e n t h a t$ $f (x) = x^{3} - x^{2} + a x + b a n d$ $g (x) = 2 x^{3} - 9 x^{2} - 3 a x + b h a v e a$ $c o m m o n f a c t o r (x - 1) w h e r e a a n d$ $b a r e c o n s t a n d s . F i n d t h e v a l u e s$ $o f a a n d b h e n c e f i n d o t h e r f a c t o r s$ $o f f (x)$

Question Number 35304 Answers: 2 Comments: 4

Q1. a) solve for x 9^x +5(3^x )=6 b)write down the first 4 terms in the binomial expansion of (1−3x)^7 c)the sum S_n of the first n^(th) terms is given by S_(n ) = 3(1−((2/3))^n ) find d) the common ratio e) the sum to infinity of the progression

$Q 1 . a) s o l v e f o r x 9^{x} + 5 (3^{x}) = 6$ $b) w r i t e d o w n t h e f i r s t 4 t e r m s$ $i n t h e b i n o m i a l e x p a n s i o n o f {(1 - 3 x)}^{7}$ $c) t h e s u m S_{n} o f t h e f i r s t n^{t h} t e r m s$ $i s g i v e n b y S_{n} = 3 (1 - {(\frac{2}{3})}^{n}) f i n d$ $d) t h e c o m m o n r a t i o$ $e) t h e s u m t o i n f i n i t y o f t h e p r o g r e s s i o n$

Pg 110 Pg 111 Pg 112 Pg 113 Pg 114 Pg 115 Pg 116 Pg 117 Pg 118 Pg 119

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