Answer: A) The United States felt if Europe was financially stable then communism would be less likely to spread.
Explanation: One of the major goal of the United States in giving financial aids to Europe and Latin America was to assist in rebuilding the war-torn regions, remove trade barriers, modernize industry, improve European prosperity, and prevent the spread of Communism. This was known as the European Recovery Plan in 1948 which was to send foreign aid to Western Europe. During this period, the United States transferred over $12 billion dollars in economic recovery programs to Western European economies after the end of World War II.
Answer:
The cost per month is increasing at a rate $365.
Explanation:
Differentiation Formula
Given that,
A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by
.
Again given that,
the rate of changing production is 13 unit per month
i.e ![\frac{dx}{dt}=13](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D13)
To find the cost per month, we need to find out the value
when production is changing at the rate 13 units per month and the production is 70 units.
![c=0.2x^2+10,000](https://tex.z-dn.net/?f=c%3D0.2x%5E2%2B10%2C000)
Differentiating with respect to t
![\frac{d}{dt}(c)=\frac{d}{dt}(0.2x^2)+\frac{d}{dx}(10,000)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%28c%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%280.2x%5E2%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%2810%2C000%29)
![\Rightarrow \frac{dc}{dt}=0.2\frac{d}{dt}(x^2)+\frac{d}{dx}(10,000)](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdc%7D%7Bdt%7D%3D0.2%5Cfrac%7Bd%7D%7Bdt%7D%28x%5E2%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%2810%2C000%29)
![\Rightarrow \frac{dc}{dt}=0.2\times 2x^{2-1}\frac{dx}{dt}+0](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdc%7D%7Bdt%7D%3D0.2%5Ctimes%202x%5E%7B2-1%7D%5Cfrac%7Bdx%7D%7Bdt%7D%2B0)
![\Rightarrow \frac{dc}{dt}=0.4x\frac{dx}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdc%7D%7Bdt%7D%3D0.4x%5Cfrac%7Bdx%7D%7Bdt%7D)
Plugging ![\frac{dx}{dt}=13](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D13)
![\Rightarrow \frac{dc}{dt}=0.4x\times 13](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdc%7D%7Bdt%7D%3D0.4x%5Ctimes%2013)
![\Rightarrow \frac{dc}{dt}=5.2x](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdc%7D%7Bdt%7D%3D5.2x)
[ plugging x=70]
=364
[ The unit of c is not given. Assume that the unit of c is dollar.]
The cost per month is increasing at a rate $365.