Which is longer 1/3 of a minute or 2/3 of a minute?
2 answers:
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Sarah has received £ 294
<u><em>Solution:</em></u>
Given that £980 is divided between Caroline, Sarah & Gavyn
Let "c" be the amount received by caroline
Let "s" be the amount received by sarah
Let "g" be the amount received by gavyn
<em><u>Caroline gets twice as much as Sarah</u></em>
amount received by caroline = twice as much as Sarah
amount received by caroline = 2(amount received by sarah)
c = 2s ---- eqn 1
<em><u>Sarah gets three times as much as Gavyn</u></em>
amount received by sarah = three times as much as Gavyn
amount received by sarah = 3(amount received by gavyn)
s = 3g ------- eqn 2
Given that total amount is 980
c + s + g = 980 --- eqn 3
<em><u>Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"</u></em>
From eqn 2,
--- eqn 4
Substitute eqn 1 and eqn 4 in eqn 3
Thus sarah has received £ 294
Given:- ;
, where a is any positive real number.
Consider the helix parabolic equation :
now, take the derivatives we get;
As, we know that two vectors are orthogonal if their dot product is zero.
Here, are orthogonal i.e,
Therefore, we have ,
take t common in above equation we get,
⇒ or
To find the solution for t;
take
The number determined from the coefficients of the equation
The determinant
Since, for any positive value of a determinant is negative.
Therefore, there is no solution.
The only solution, we have t=0.
Hence, we have only one points on the parabola i.e <1,0>