For simple interest
i=prn
where i= interest p=amount invested, r=rate n=time period
i= 970*4 and 1/4 * 2
i= $8245<span />
Answer:
Yes
Step-by-step explanation:
We are given that a function ![\phi(x)=x^2-x^{-1}](https://tex.z-dn.net/?f=%5Cphi%28x%29%3Dx%5E2-x%5E%7B-1%7D)
We have to find that given function is an explicit solution to the linear equation
![\frac{d^2y}{dx^2}-\frac{2}{x^2}y=0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D-%5Cfrac%7B2%7D%7Bx%5E2%7Dy%3D0)
If given function is an explicit solution of given linear equation then it satisfied the given differential equation
Differentiate w.r.t x
Then we get ![\phi'(x)=2x+x^{-2}](https://tex.z-dn.net/?f=%5Cphi%27%28x%29%3D2x%2Bx%5E%7B-2%7D)
Again differentiate w.r.t x
Then we get
![\phi''(x)=2-\frac{2}{x^3}](https://tex.z-dn.net/?f=%5Cphi%27%27%28x%29%3D2-%5Cfrac%7B2%7D%7Bx%5E3%7D)
Substitute all values in the given differential equation
![2-\frac{2}{x^3}-\frac{2}{x^2}(x^2-x^{-1})](https://tex.z-dn.net/?f=2-%5Cfrac%7B2%7D%7Bx%5E3%7D-%5Cfrac%7B2%7D%7Bx%5E2%7D%28x%5E2-x%5E%7B-1%7D%29)
=![2-\frac{2}{x^3}-2+\frac{2}{x^3}=0](https://tex.z-dn.net/?f=2-%5Cfrac%7B2%7D%7Bx%5E3%7D-2%2B%5Cfrac%7B2%7D%7Bx%5E3%7D%3D0)
Hence, given function is an explicit solution of given differential equation.
Therefore, answer is yes.
A) the Johnson family will travel 300 miles in 5 hours
Assuming 5, represents the amount of hours & 300 representing miles
Answer:
34.4 miles
Step-by-step explanation:
Mathematically;
z-score = x-mean/SD
from the question, we have mean as 29 and standard deviation as 3.6 with z-score as 1.5
So we need to find the z-score here
1.5 = x-29/3.6
3.6 * 1.5 = x-29
5.4 = x-29
x = 29 + 5.4
x = 34.4
Answer:
(x - 1)(3x - 5)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x-term.
product = 3 × 5 = 15 and sum = - 8
The factors are - 3 and - 5
use these factors to split the middle term
3x² - 3x - 5x + 5 ( factor the first/second and third/fourth terms )
= 3x(x - 1) - 5(x - 1) ( take out the common factor (x - 1) )
= (x - 1)(3x - 5)