[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

[LekhB]

Stuck with those 3. If anyone could help, it'll be greatly appreciated. Thanks!

[astarmathsandphysics]

Shortly

[astarmathsandphysics]

q6 in attachment

[astarmathsandphysics]

q7 in attahment

[astarmathsandphysics]

q3 in attachment

[sameer210394]

Let 'a' and 'b' be the straight lines with equations y=m1x+c1 and y=m2x+c2 where m1m2 not equal to zero. Use appropriate trigonometric formulae to prove that 'a' and 'b' are perpendicular if and only if m1m2 = -1.

[astarmathsandphysics]

The trig formulae is tan
m1=tan theta 1 and m2=tan theta 2
Two lines are perprendicular is theta 2 = theta 1 +90
tan theta 2 = tan (theta 1 +90) =- 1/(tan theta 1)
so m1 m2 =tan theta 1 tan theta 2 =-1

[Mrsmart1017]

Help pleazzz

[sameer210394]

Use the inequality sinx < x < tanx for a suitable value of x to show that Pi lies between 3 and 2(root3)

[sameer210394]

p/q = root3

(cosx + sinx) / (cosx - sinx) = root3

divide numerator & denominator by cosx

(1 + tanx) / (1 - tanx) = root3

tanx = (root3 -1) / (root3 +1)

x = 15, 195

[astarmathsandphysics]

Use the inequality sinx < x < tanx for a suitable value of x to show that Pi lies between 3 and 2(root3)

Take x=pi/6
sin (pi/6)<pi/6<tan (pi/6)
1/2<pi/6<sqrt(3)
Multiply by 6
3<pi<2 sqrt(3)

[Mrsmart1017]

Thanks sameer

[acash09]

i need help with question here, and please with full explanation if it is not too much... Thanks

[astarmathsandphysics]

here

[whale95]

Please check the attachments...