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GeometryQuestion and Answers: Page 101

Question Number 19150 Answers: 1 Comments: 4

A semicircle is tangent to both legs of a right triangle and has its centre on the hypotenuse. The hypotenuse is partitioned into 4 segments, with lengths 3, 12, 12, and x, as shown in the figure. Determine the value of ′x′.

$A semicircle is tangent to both legs of a$ $right triangle and has its centre on the$ $hypotenuse . The hypotenuse is$ $partitioned into 4 segments, with lengths$ $3, 12, 12, and x, as shown in the figure .$ $Determine the value of^{'} x^{'} .$

Question Number 19104 Answers: 1 Comments: 1

Let ABC be an acute-angled triangle with AC ≠ BC and let O be the circumcenter and F be the foot of altitude through C. Further, let X and Y be the feet of perpendiculars dropped from A and B respectively to (the extension of) CO. The line FO intersects the circumcircle of ΔFXY, second time at P. Prove that OP < OF.

$Let ABC be an acute - angled triangle$ $with AC \neq BC and let O be the$ $circumcenter and F be the foot of$ $altitude through C . Further, let X and Y$ $be the feet of perpendiculars dropped$ $from A and B respectively to (the$ $extension of) CO . The line FO intersects$ $the circumcircle of Δ FXY, second time$ $at P . Prove that OP < OF .$

Question Number 18801 Answers: 0 Comments: 1

Question Number 18799 Answers: 1 Comments: 0

Question Number 18783 Answers: 1 Comments: 0

∫sin x

$\int \sin x$

Question Number 18967 Answers: 0 Comments: 3

Let PQRS be a rectangle such that PQ = a and QR = b. Suppose r_1 is the radius of the circle passing through P and Q and touching RS and r_2 is the radius of the circle passing through Q and R and touching PS. Show that : 5(a + b) ≤ 8(r_1 + r_2 )

$Let PQRS be a rectangle such that$ $PQ = a and QR = b . Suppose r_{1} is the$ $radius of the circle passing through P$ $and Q and touching RS and r_{2} is the$ $radius of the circle passing through Q$ $and R and touching PS . Show that :$ $5 (a + b) ⩽ 8 (r_{1} + r_{2})$

Question Number 18681 Answers: 1 Comments: 0

y = ∣sin x∣ + 2 y = ∣x∣ + 2 −π −π ≤ x ≤ π Find the area that have created from the equations above

$y = ∣ \sin x ∣ + 2$ $y = ∣ x ∣ + 2 - π$ $- π ⩽ x ⩽ π$ $Find the area that have created$ $from the equations above$

Question Number 18968 Answers: 1 Comments: 1

Find the side lengths of a triangle if side lengths are consecutive integers,and one of whose angles is twice as large as another.

$Find the side lengths of a triangle$ $if side lengths are consecutive$ $integers, and one of whose angles$ $is twice as large as another .$

Question Number 18625 Answers: 1 Comments: 1

x−5×+3=7

$x - 5 \times + 3 = 7$

Question Number 19238 Answers: 0 Comments: 4

Let ABCD be a parallelogram. Two points E and F are chosen on the sides BC and CD, respectively, such that ((EB)/(EC)) = m, and ((FC)/(FD)) = n. Lines AE and BF intersect at G. Prove that the ratio ((AG)/(GE)) = (((m + 1)(n + 1))/(mn)).

$Let A B C D be a parallelogram . Two$ $points E and F are chosen on the sides$ $B C and C D, respectively, such that$ $\frac{E B}{E C} = m, and \frac{F C}{F D} = n . Lines A E and B F$ $intersect at G . Prove that the ratio$ $\frac{A G}{G E} = \frac{(m + 1) (n + 1)}{m n} .$

Question Number 18527 Answers: 0 Comments: 0

from 1 to 100 isn′t(10,20,30,40,50,60,70,80,90,100), totalizing 10 times the number 0 apears from 1 to 100?

$f r o m 1 t o 100 {i s n}^{'} t (10, 20, 30, 40, 50, 60, 70, 80, 90, 100), t o t a l i z i n g 10 t i m e s t h e n u m b e r 0 a p e a r s f r o m 1 t o 100 ?$

Question Number 18477 Answers: 0 Comments: 0

F[topology]={G⊂X.G is finit.} please sol it

$F [t o p o l o g y] = {G \subset X . G i s f i n i t .}$ $p l e a s e s o l i t$

Question Number 18461 Answers: 1 Comments: 0

Question Number 18394 Answers: 0 Comments: 0

Question Number 18323 Answers: 0 Comments: 0

Σ((cos 2rθ)/(sin^2 2rθ−sin^2 θ))

$Σ \frac{\cos 2 r θ}{\sin^{2} 2 r θ - \sin^{2} θ}$

Question Number 18236 Answers: 0 Comments: 0

∫ (dx/(1 − sin x + cos x))

$\int \frac{d x}{1 - \sin x + \cos x}$

Question Number 20977 Answers: 0 Comments: 1

Imtegrate ∫e^(−ax^2 +bx+c) dx for a>0. It′s just for fun. If you have questions leave a comment. I′ll do my best to answer them.

$I m t e g r a t e \int e^{- {a x}^{2} + b x + c} d x f o r a > 0 .$ ${I t}^{'} s j u s t f o r f u n . I f y o u h a v e q u e s t i o n s$ $l e a v e a c o m m e n t . I^{'} l l d o m y b e s t t o a n s w e r t h e m .$

Question Number 17939 Answers: 1 Comments: 1

∫secxdx

$\int s e c x d x$

Question Number 17901 Answers: 1 Comments: 2

Question Number 17948 Answers: 1 Comments: 3

Question Number 17886 Answers: 0 Comments: 7

Question Number 17884 Answers: 1 Comments: 1

Question Number 17935 Answers: 0 Comments: 0

Ball A is dropped from the top of a building. At the same instant ball B is thrown vertically upwards from the ground. When the ball collide, they are moving in opposite directions and the speed of A(u) is twice the speed of B. The relative velocity of the ball just before collision and relative acceleration between them is (only their magnitudes) (A) 0 and 0 (B) ((3u)/2) and 0 (C) ((3u)/2) and 2g (D) ((3u)/2) and g

$Ball A is dropped from the top of a building .$ $At the same instant ball B is thrown$ $vertically upwards from the ground .$ $When the ball collide, they are moving in$ $opposite directions and the speed of A (u)$ $is twice the speed of B . The relative$ $velocity of the ball just before collision$ $and relative acceleration between them$ $is (only their magnitudes)$ $(A) 0 and 0 (B) \frac{3 u}{2} and 0$ $(C) \frac{3 u}{2} and 2 g (D) \frac{3 u}{2} and g$

Question Number 17771 Answers: 1 Comments: 1

Question Number 17743 Answers: 2 Comments: 0

Question Number 17692 Answers: 1 Comments: 0

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