The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If th
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Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
You mean 
or 
?
If you had meant,, then the simplest form of this fraction would be - 
Divide both parts of the fraction by 4, and you getthe simplest form of the fraction.
Finding out the simplest form of a given fraction is nothing else than cancelation.
Flop it, you have with you -
Flop the simplest form of the previous fraction, that's
If you had meant, then this will certainly be of any use to you.
HOW TO UNDERSTAND THAT THE FRACTION IS IN ITS SIMPLEST FORM?
Maybe, you are just simplifying and simplifying...but you don't even know when to stop. You can understand whether a fraction is in its simplest form or not by seeing that the numerator and the denominator have a common factor to divide it by, or not.
For instance, consider the case here - or <span>. We can't divide it any further. So, we know that it is in its simplest form.
</span>
L O N G Process:
Well, if you want to divide it by the smallest common factor to its larger, then --
or
1) Divided by 2 =
or 
2) Next, also by 2 = or
That took much longer, right.<span> So, it is more preferable to divide the fraction by the possible largest common factor, you can guess of.</span>
If you had meant,
Divide both parts of the fraction by 4, and you get
Finding out the simplest form of a given fraction is nothing else than cancelation.
Flop it, you have with you -
Flop the simplest form of the previous fraction, that's
If you had meant
HOW TO UNDERSTAND THAT THE FRACTION IS IN ITS SIMPLEST FORM?
Maybe, you are just simplifying and simplifying...but you don't even know when to stop. You can understand whether a fraction is in its simplest form or not by seeing that the numerator and the denominator have a common factor to divide it by, or not.
For instance, consider the case here -
</span>
L O N G Process:
Well, if you want to divide it by the smallest common factor to its larger, then --
1) Divided by 2 =
2) Next, also by 2 =
That took much longer, right.<span> So, it is more preferable to divide the fraction by the possible largest common factor, you can guess of.</span>
