Answer:
1. y = (⅔)x - 3
2. y = 3x + c
3. 1) non-proportional
2) can be proportional if c = 0
Step-by-step explanation:
1. What is the equation of a line that has a slope of ⅔ and a y-intercept of -3?
y = (⅔)x - 3
2. What is the equation of a line that has a slope of 3?
y = 3x + c
3. Lable the 2 equations as proportional or non-proportional and why.
A proportional relation should pass through the origin, i.e the y-intercept should be 0
X=2
You add 3x and 4x which is 7x then divide 14 by 7 which is 2
You solve for the domain by setting the radicand less than or equal to 0 and solving for x. Dividing by a -x, we switch the sign so we have that the domain is less than or equal to 0, or all negative numbers. We know that it breaks every law in math to have a negative radicand with an even index, so if the domain is all negative values of x, taking a negative of a negative gives us a positive. The negative sign OUTSIDE the radical means you are flipping the graph upside down. So instead of having a range of y is greater than or equal to 0 as does the parent graph, you have flipped it upside down so it heads more negative in regards to the range. Therefore, the domain and the range both have the same sign, thee last choice from above.
Answer: The required solution is 
Step-by-step explanation:
We are given to solve the following differential equation :
where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.
From equation (i), we have
Integrating both sides, we get
![\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]](https://tex.z-dn.net/?f=%5Cint%5Cdfrac%7Bdy%7D%7By%7D%3D%5Cint%20kdt%5C%5C%5C%5C%5CRightarrow%20%5Clog%20y%3Dkt%2Bc~~~~~~%5B%5Ctextup%7Bc%20is%20a%20constant%20of%20integration%7D%5D%5C%5C%5C%5C%5CRightarrow%20y%3De%5E%7Bkt%2Bc%7D%5C%5C%5C%5C%5CRightarrow%20y%3Dae%5E%7Bkt%7D~~~~%5B%5Ctextup%7Bwhere%20%7Da%3De%5Ec%5Ctextup%7B%20is%20another%20constant%7D%5D)
Also, the conditions are
and
Thus, the required solution is
Answer:
10
Step-by-step explanation:
Plug in 0 where x is
See image below:)
