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3 years ago

The scale model of the car is 1:18 the length of the model is 9 1/2 inches how many feet long is the actual

Mathematics

2 answers:

galina1969 [7]3 years ago

6 0

Answer: The length of the car is 14 and 1/4 (or 14.25 ) feets long.

Step-by-step explanation:

The scale is 1:18.

The lenght of the car is 9 and 1/2 inches.

Then, for the ratio relation, we have that each inch in the model car we have that corresponds to 18 inches in the car, so the length of the car is:

L = (9 +1/2)*18 in = 9.5*18 in = 171 inches.

Now, remember that 1ft = 12 inches, so if we want to write this in feet we must divide this by 12.

L = (171/12) ft = 14.25 ft = (14 + 1/4) ft

Y_Kistochka [10]3 years ago

5 0

Answer:

14.25 ft

Step-by-step explanation:

1 inch of the model represents 18 inches of the real car. The car's dimensions are 18 times larger than the model's dimensions. Multiply the model dimension by 18 to find the corresponding real dimension.

9 1/2 * 18 = 9.5 * 18 = 171

The actual car is 171 inches long.

Now we need to convert 171 inches to ft.

1 ft = 12 in.

Since we want to eliminate inches and end up with feet, we divide both sides by 12 in.

(1 ft)/(12 in.) = 1

The conversion factor is (1 ft)/(12 in.) to go from inches to feet.

171 in. * (1 ft)/(12 in.) = 14.25 ft

Answer: 14.25 ft

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3 years ago

The daily average temperature in Santiago, Chile, varies over time in a periodic way that can be modeled approximately by a trig

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a) the trigonometric function is;

$y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5$

b) $y = 28.36^0 \ C$ ( to two decimal places)

Step-by-step explanation:

This data can be represented by the sinusoidal function of the form :

$\mathbf{y = A sin (Bt -C)+D}$

where A = amplitude and which can be determined via the formula:

$A = \dfrac{largest \ temperature - lowest \ temperature}{2}$

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where B = the frequency;

Since the data covers a period of 3 days ; then $\dfrac{2 \pi}{B } =365$

$B = \dfrac{2 \pi}{365}$ ( where 365 is the time period )

The vertical shift is found by the equation D;

D = $\frac{largest \ temperature + lowest \ temperature}{2}$

D = $\frac{29+14}{2}$

D = 21.5

Replacing the values of A ; B and D into the above sinusoidal function; we have :

$y = 7.5 sin (\frac{2 \pi}{365}t -C) + 21.5$

From the question; when it is 7th of the year ( i.e January 7);

t = 7 and the temperature (y) = 29° C

replacing that too into the above equation; we have:

$29= 7.5 sin (\frac{2 \pi}{365}*7 -C) + 21.5$

$29= 7.5 sin (\frac{14 \pi}{365} -C) + 21.5$

$\frac{29-21.5}{7.5}= sin (\frac{14 \pi}{365} -C)$

$1= sin (\frac{14 \pi}{365} -C)$

$sin^{-1}(1)= (\frac{14 \pi}{365} -C)$

$\frac{\pi}{2}= (\frac{14 \pi}{365} -C)$

$C= (\frac{14 \pi}{365} -\frac{\pi}{2})$

$C= (\frac{28 \pi- 365 \pi}{730} )$

$C= \frac{-337 \pi}{730}$

Thus; the trigonometric function is;

$y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5$

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$y = 7.5 sin ( \frac{2 \pi}{365}*31+ \frac{337 \pi}{730})+ 21.5$

$y = 7.5 sin ( \frac{62 \pi}{365}+ \frac{337 \pi}{730})+ 21.5$

$y = 7.5 sin ( \frac{124 \pi+ 337 \pi }{730})+ 21.5$

$y = 7.5 sin ( \frac{461 \pi }{730})+ 21.5$

$y = 7.5 *( 0.915)+ 21.5$

$y = 6.8689+ 21.5$

$y = 28.36^0 \ C$ ( to two decimal places)

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