Nigel paints 5/4 square yards in 1/3 hour.How much did he paint in 5 hours

Mathematics

1 answer:

White raven [17]3 years ago

6 0

Answer:

$18\frac{3}{4}\ yd^{2}$

Step-by-step explanation:

we know that

using proportion

$\frac{(5/4)}{(1/3)}\frac{yd^{2}}{hours}=\frac{x}{5}\frac{yd^{2}}{hours}\\\\x=5*(5/4)/(1/3)\\\\x=\frac{75}{4}\ yd^{2}\\\\x=18\frac{3}{4}\ yd^{2}$

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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9

Naddika [18.5K]

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

$y=A\sin[\omega(x-\alpha)]+C$

where, A = amplitude; $\omega=\dfrac{2\pi}{period}$ , α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= $C=\dfrac{73+97}{2}=85$ [midline is average of upper and lower limit.]

A= 97-85 = 12

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Period = 24 hours;

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Substitute all values in sinusoidal function, we get

$y=12\sin[\dfrac{\pi}{12}(x-10)]+85$

Put y= 82, we get

$82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03$