The length of q, to the nearest 10th of a centimeter is 7.6 cm.
Given in question,
In ΔOPQ,
o = 9.2 cm
p = 2.4 cm
∠Q = 37°
Cosine formula ⇒ cos θ = ![\frac{o^{2}+p^{2}-q^{2} }{2op}](https://tex.z-dn.net/?f=%5Cfrac%7Bo%5E%7B2%7D%2Bp%5E%7B2%7D-q%5E%7B2%7D%20%20%7D%7B2op%7D)
Putting the values in equation,
cos 37 = ![\frac{(9.2)^{2}+(2.4)^{2}-q^{2} }{2*9.2*2.4}](https://tex.z-dn.net/?f=%5Cfrac%7B%289.2%29%5E%7B2%7D%2B%282.4%29%5E%7B2%7D-q%5E%7B2%7D%20%20%7D%7B2%2A9.2%2A2.4%7D)
0.799 = ![\frac{84.64 + 5.76-q^{2} }{44.16}](https://tex.z-dn.net/?f=%5Cfrac%7B84.64%20%2B%205.76-q%5E%7B2%7D%20%7D%7B44.16%7D)
0.799*44.16 = 90.4 - ![q^{2}](https://tex.z-dn.net/?f=q%5E%7B2%7D)
32.28 = 90.4 - ![q^{2}](https://tex.z-dn.net/?f=q%5E%7B2%7D)
= 90.4 - 32.28
= 58.12
![q = \sqrt{58.12}](https://tex.z-dn.net/?f=q%20%3D%20%5Csqrt%7B58.12%7D)
![q = 7.63](https://tex.z-dn.net/?f=q%20%3D%207.63)
q = 7.6 cm (to nearest 10th)
Hence, length of q is 7.6 cm.
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The domain is {0≤x≤200}.
This is because the domain is x, the number of cakes. The smallest number of cakes she can bake is 0.
Since she is buying enough materials to make 200 cakes, this number is the largest number of cakes she can bake.