Danielle is using 2 quarts of water in a recipe. How many cups of water is she using ?
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S = ax
It is required to find the value of a which make:
0 ≤ s ≤ 1 when <span>0 ≤ x ≤ 15
∴ s = 0 when x = 0 ⇒⇒⇒ a = 0 (unacceptable)
or s = 1 when x = 15 ⇒⇒⇒ a = s/x = 1/15
Similarly, t = by </span>
<span>It is required to find the value of b which make:
0 ≤ t ≤ 1 when <span>0 ≤ y ≤ 60
∴ t = 0 when y = 0 ⇒⇒⇒ b = 0 (unacceptable)
or t = 1 when y = 60 ⇒⇒⇒ b = t/y = 1/60
</span></span><span>
</span><span>∴ x = 15s and y = 60t
![J ( \frac{x,y}{s,t}) = \left[\begin{array}{ccc} \frac{dx}{ds} & & \frac{dx}{dt} \\ & & \\ \frac{dy}{ds} & & \frac{dy}{dt} \end{array}\right] = \left[\begin{array}{ccc}15& &0\\ & & \\0& &60\end{array}\right] = 900](https://tex.z-dn.net/?f=J%20%28%20%5Cfrac%7Bx%2Cy%7D%7Bs%2Ct%7D%29%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cfrac%7Bdx%7D%7Bds%7D%20%26%20%26%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%5C%5C%20%26%20%26%20%5C%5C%20%5Cfrac%7Bdy%7D%7Bds%7D%20%26%20%26%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D15%26%20%260%5C%5C%20%26%20%26%20%5C%5C0%26%20%2660%5Cend%7Barray%7D%5Cright%5D%20%3D%20900)
Note: it is not matrix it is determinant</span>
It is required to find the value of a which make:
0 ≤ s ≤ 1 when <span>0 ≤ x ≤ 15
∴ s = 0 when x = 0 ⇒⇒⇒ a = 0 (unacceptable)
or s = 1 when x = 15 ⇒⇒⇒ a = s/x = 1/15
Similarly, t = by </span>
<span>It is required to find the value of b which make:
0 ≤ t ≤ 1 when <span>0 ≤ y ≤ 60
∴ t = 0 when y = 0 ⇒⇒⇒ b = 0 (unacceptable)
or t = 1 when y = 60 ⇒⇒⇒ b = t/y = 1/60
</span></span><span>
</span><span>∴ x = 15s and y = 60t
Note: it is not matrix it is determinant</span>