Answer:
<em>The water is leaking at the rate of 0.0625 gal/min.</em>
Step-by-step explanation:
<u>Rate of change</u>
The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.
The container holds 8 gallons of water and is leaking at a constant rate to be calculated later.
When 48 minutes have passed, the container has 5 gallons of water left. This means it has leaked 8 gallons - 5 gallons = 3 gallons.
Calculating the rate at which it's leaking:
![\displaystyle r=\frac{3\ gallons}{48\ min}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Cfrac%7B3%5C%20gallons%7D%7B48%5C%20min%7D)
r = 0.0625 gal/min
The water is leaking at the rate of 0.0625 gal/min.
Answer:
![A = 16 + 16\sqrt{10 }](https://tex.z-dn.net/?f=A%20%3D%2016%20%2B%2016%5Csqrt%7B10%20%7D)
Step-by-step explanation:
Given dimensions of a pyramid:
Length = l = 4 feet
Width = w = 4 feet for square base (w=l)
Height = h = 6 feet
The formula to find the area of square pyramid is =
=> ![A = 4^{2} + 2(4)\sqrt{\frac{4^{2} }{4} + 6^{2} }](https://tex.z-dn.net/?f=A%20%3D%204%5E%7B2%7D%20%2B%202%284%29%5Csqrt%7B%5Cfrac%7B4%5E%7B2%7D%20%7D%7B4%7D%20%2B%206%5E%7B2%7D%20%7D)
=>![A = 16 + 8\sqrt{{4 + 36 }](https://tex.z-dn.net/?f=A%20%3D%2016%20%2B%208%5Csqrt%7B%7B4%20%2B%2036%20%7D)
=> ![A = 16 + 8\sqrt{{40 }](https://tex.z-dn.net/?f=A%20%3D%2016%20%2B%208%5Csqrt%7B%7B40%20%7D)
=>![A = 16 + 8\sqrt{{2^{2} *10 }](https://tex.z-dn.net/?f=A%20%3D%2016%20%2B%208%5Csqrt%7B%7B2%5E%7B2%7D%20%2A10%20%7D)
=> ![A = 16 + 16\sqrt{10 }](https://tex.z-dn.net/?f=A%20%3D%2016%20%2B%2016%5Csqrt%7B10%20%7D)
Answer:
42° and 138°.
Step-by-step explanation:
Here we use the identity that
.
Now, to find
, we make use of the inverse sine function:
![x = sin^{-1}(0.0091)](https://tex.z-dn.net/?f=x%20%3D%20sin%5E%7B-1%7D%280.0091%29)
![\boxed{ x = 42^o.}](https://tex.z-dn.net/?f=%5Cboxed%7B%20x%20%3D%2042%5Eo.%7D)
Another solution to this is
Thus, the values of
in the interval
for which
are 42° and 138°.
Answer:
Step-by-step explanation:
Time taken = 9.77/100 = 0.0977 seconds