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4 years ago

Help on this problem?? please?

Mathematics

1 answer:

Reptile [31]4 years ago

5 0

MrBillDoesMath!

Answer to #4: 81/256 * s^8 * t^ 12

Comments:

(7x^3) ^ (1/2) = 7 ^ (1/2) * x^(3/2) where ^(1/2) means the square root of a quantity. The answer written (7x^3) is NOT correct.

---------------------

(1) (27s^7t^11)^ (4/3)

= 27^(4/3) * (s^7)^(4/3) * (t^11)^ (4/3)

As 27 = 3^3, 27 ^(4/3) = 3^4 = 81

(2) (-64st^2)^ (4/3) = (-64)^(4/3) * (s^4/3) * t(^8/3)

As 64 = (-4)^3, (-64)^(4/3) = (-4)^4 = +256

So (1)/(2) =

81 * s^(28/3)* t^(44/3)

------------------------------- =

256 s^(4/3) * t^((8/3)

81/256 * s ^ (28/3 - 4/3) * t^(44/3 - 8/3) =

81/256 * s^(24/3) * t (36/3) =

81/256 * s^8 * t^ 12

MrB

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cestrela7 [59]

(i):
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$t^{2}V^{2} = x^{2} + y^{2} + gt^{2}y + \frac{1}{4}g^{2}t^{4}$
$4t^{2}V^{2} = 4x^{2} + 4y^{2} + 4gt^{2}y + g^{2}t^{4}$
$4x^{2} + 4y^{2} + 4gt^{2}y + g^{2}t^{4} - 4t^{2}V^{2} = 0$
$4y^{2} + 4gt^{2}y + (gt^{2}t^{4} + 4x^{2} - 4t^{2}V^{2}) = 0$

(ii): Impact is when x = d.
$\text{Impact: } d = Vtcos\theta$
$t = \frac{d}{Vcos\theta}$

First impact occurs when t is minimised.
This means that Vcos theta is maximised, which means cos theta = 1, and theta = 0
$\therefore \text{First impact occurs at } \theta = 0\text{: }t = \frac{d}{V(1)} = \frac{d}{V}$

i'll do the rest later.

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