Answer:
0.407
Step-by-step explanation:
<u>0. 4 0 7</u>
2 0 /8. 1 4 0
−<u> 0</u>
8 1
<u>− 8 0 </u>
1 4
<u> − 0 </u>
1 4 0
−<u> 1 4 0</u>
0
Answer:
Option 2
Step-by-step explanation:
¼Y - ½
= ¼Y - 2/4
= ¼(Y - 2)
Answer:
It will take 146 days to earn an interest of $80.
Step-by-step explanation:
The simple interest formula is:
![I=\frac{P\times r\times t}{100}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7BP%5Ctimes%20r%5Ctimes%20t%7D%7B100%7D)
It is provided that:
I = $80
P = $4,000
r = 5% p.a.
Compute the time required as follows:
![I=\frac{P\times r\times t}{100}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7BP%5Ctimes%20r%5Ctimes%20t%7D%7B100%7D)
![t=\frac{I\times 100}{P\times r}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7BI%5Ctimes%20100%7D%7BP%5Ctimes%20r%7D)
![=\frac{80\times 100}{4000\times 5}\\\\=0.4\ \years\\\\=0.4\times 365\ days\\\\=146\ days](https://tex.z-dn.net/?f=%3D%5Cfrac%7B80%5Ctimes%20100%7D%7B4000%5Ctimes%205%7D%5C%5C%5C%5C%3D0.4%5C%20%5Cyears%5C%5C%5C%5C%3D0.4%5Ctimes%20365%5C%20days%5C%5C%5C%5C%3D146%5C%20days)
Thus, it will take 146 days to earn an interest of $80.
Answer with explanation:
Let us assume that the 2 functions are:
1) f(x)
2) g(x)
Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that
![\frac{d}{dx}\cdot f(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20f%28x%29%3C0%5C%5C%5C%5C%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20g%28x%29%3C0)
Now the sum of the 2 functions is shown below
![y=f(x)+g(x)](https://tex.z-dn.net/?f=y%3Df%28x%29%2Bg%28x%29)
Diffrentiating both sides with respect to 'x' we get
![\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20f%28x%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20g%28x%29%5C%5C%5C%5C)
Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3C0)
Thus the sum of the 2 functions is also a concave function.
Part 2)
The product of the 2 functions is shown below
![h=f(x)\cdot g(x)](https://tex.z-dn.net/?f=h%3Df%28x%29%5Ccdot%20g%28x%29)
Diffrentiating both sides with respect to 'x' we get
![h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)](https://tex.z-dn.net/?f=h%27%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20%28f%28x%29%5Ccdot%20g%28x%29%29%5C%5C%5C%5Ch%27%3Dg%28x%29f%27%28x%29%2Bf%28x%29g%27%28x%29)
Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
<h3 /><h3>The volume of the cube is found by the formula </h3><h2>V = s³, </h2><h3>where s is the side length (called the edge in this problem)</h3><h3>Since V = 125 cm³, we can take the cube root of 125 to find the edge length.</h3><h3>The cube root of 125 is 5, ( 5³ = 125)</h3><h3>So the edge of the cube is 5 cm</h3><h3 /><h3>The are of a square is found by the formula </h3><h2>A = s² , </h2><h3>where s is the side length (called the edge in this problem) </h3><h3>Since A = 64 cm², we can take the square root of 64 to find the edge length.</h3><h3>The square root of 64 is 8 (8² = 84)</h3><h3>So the edge of the square is 8cm</h3><h3 /><h3>Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.</h3>