- Solve x = log[3] 81 + log[3]1/9
For what value of x, the following matrix is singular ?
(5-x) (x + 1)
(2) ( 4)
3.. The matrix A =
3 2 satisfies the relation A2 - 4A + I = 0. Find A-1.
1 1
4. cosθ sin θ sinθ - cosθ
Simpliy cosθ + sinθ
- sinθ cosθ cosθ sinθ
5. Evaluate
-1
∫ 1/x dx
-4
6. A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
7. A window is in the form of a rectangle surmounted by a semi-circular opening.
The total perimeter of the window is 10m. Find the dimensions of the window to
admit maximum light through the whole opening
8. A square piece of tin of side 48 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off, so that the volume of the box is the maximum possible? Also find the maximum volume.
Solve x = log[3] 81 + log[3]1/9
ReplyDeletex= log[3] (81*1/9)
x= log[3] 9
x= log9/log 3
x= 2
for singular matricies major- minor = 0
ReplyDeletemiss i dont understand, please help, if u say Simpliy cosθ + sinθ
ReplyDeletesince cosθ = -sinθ
and sinθ= cosθ
then cosθ + sinθ simplifies to be
-sinθ+cosθ
i not sure if that rite
using the technique i used b4 to simpliy - sinθ cosθ cosθ sinθ
ReplyDeletesince cosθ = -sinθ
and sinθ= cosθ
then - sinθ cosθ cosθ sinθ
equals cosθ- sinθ - sinθ cosθ
these not looking rite, i dont think this is the wway to simplify the question, sum1 please help
when evaluating -1
ReplyDeleteis equal to -1x since if u diff. -1x u get -1, i ent sure, please help sum1
when evaluating ∫ 1/x dx
ReplyDeleteu increse the power by 1
so u get 1 cuz 1/x*by x = 1
where i dont understand, cuz the next step is to divide the co-effecient by the power and there is no power so i gues u get 0, i lost with this step so please help.
Q1
ReplyDeleteSolve x = log[3] 81 + log[3]1/9
rule: loga + log b = log ab
so, x= log[3] (81*1/9)
x= log[3] 9
rule: log mv = log m / logv
so, x= log9/log 3
hence, x= 2
well ram i'm kinda confused too but i think u were rite with d 1st sin cos question, as for d other 1 with
ReplyDelete- sinθ cosθ cosθ sinθ
equals cosθ- sinθ - sinθ cosθ
i was wondering if we can further simplify it as
-2sin@ + 2cos@
i'm not sure!
Q5. Evaluate
ReplyDelete-1
∫ 1/x .dx
-4
-1
∫ x^-1 .dx
-4 since -1 + 1 = 0 we get...
-1
∫ 1/0 x^0 .dx
-4
-1
∫ 1 + c
-4
this is my answer...not sure if its correct though..any ideas anyone?
attempting Q8. lol
ReplyDeletev = sxsxs or s^3
s = 48 - 2x
so, v = (48 - 2x)^3
v = (2340 -192x +4x^2)(48 -2x)
v = 110592 - 13824x + 576x^2 -8x^3
this is a strange answer!
anyone wants to try Q6 and Q7 i dont kno how to start! help!
ReplyDelete