This question is the application of differential eqns in order to derive a model for the temperature dependence with time. Actually, a general equation has already been derived for this type of cases. This equation is known as the Newton's Law of Cooling. The equation is
(T - Ts) / (To -Ts) = e^(-kt)
where T is the the temperature at any time t
Ts is the surrounding temperature
To is the initial temperature
k is the constant
t is the time
several assumptions have been made to arrive at this form, i suggest you trace the derivation of the general formula.
First we need to look for k using the initial conditions that is @t = 1.5 min, T = 50 F
substituting we get a k = 0.2703
therefore @ t = 1 min, T = 55.79 F
@ T = 15 F the time required is 9.193 min.
3/4 is greater. you have to change the 3/4 to 12/16 which proves that 3/4 is greater than 11/16
product of 4/5 and 5/7 is 4/7
What is ocean expansion:
Eustatic change is the expansion of the ocean due to the addition of water. The extra amount of water released into the ocean body is due to melting ice sheets and glaciers. Warmer temperatures accelerates the melting, adding more water into ocean the than previous decades.
Answer:
It will be seen in every place close to the sea or beaches also many island will go under.
let's firstly convert the mixed fractions to improper fractions and then to do away with the denominators, let's multiply both sides by the LCD of all denominators.
![\stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{4}-\cfrac{4}{5}=\cfrac{35}{20}-\boxed{?}\implies \stackrel{\textit{multipling both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{7}{4}-\cfrac{4}{5} \right)=20\left( \cfrac{35}{20}-\boxed{?} \right)} \\\\\\ 35-16=35-20\boxed{?}\implies 19=35-20\boxed{?}\implies -16=-20\boxed{?} \\\\\\ \cfrac{-16}{-20}=\boxed{?}\implies \cfrac{4}{5}=\boxed{?}](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B7%7D%7B4%7D-%5Ccfrac%7B4%7D%7B5%7D%3D%5Ccfrac%7B35%7D%7B20%7D-%5Cboxed%7B%3F%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultipling%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B20%7D%7D%7B20%5Cleft%28%20%5Ccfrac%7B7%7D%7B4%7D-%5Ccfrac%7B4%7D%7B5%7D%20%5Cright%29%3D20%5Cleft%28%20%5Ccfrac%7B35%7D%7B20%7D-%5Cboxed%7B%3F%7D%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%2035-16%3D35-20%5Cboxed%7B%3F%7D%5Cimplies%2019%3D35-20%5Cboxed%7B%3F%7D%5Cimplies%20-16%3D-20%5Cboxed%7B%3F%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B-16%7D%7B-20%7D%3D%5Cboxed%7B%3F%7D%5Cimplies%20%5Ccfrac%7B4%7D%7B5%7D%3D%5Cboxed%7B%3F%7D)
Given:
Length of the circular arc with circle radius=49cm
θ=135°
Now,
Length of arc = θ/360°×2πr
49=2× 22/7×r×135°/360°
49×20×7/3×22×2
51.96cm
