First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.
If we need the vertex to be at 
, the equation will contain a 
term.
If we start with 
we have a parabola, concave down, with vertex at and a maximum of 0.
So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be 
We have
Now we only have to fix the fact that this parabola doesn't land at 
, because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want
such that:
Plugging these values gets us
As you can see in the attached figure, the parabola we get satisfies all the requests.
Answer:
She will use 13 quarter cups of oatmeal
Step-by-step explanation:
3 1/4 = 13/4
x/4 = 13/4
4(x/4) = 4(13/4)
x = 13
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
<span>the 30°-60°-right triangle theorem states that the
</span>In a right triangle, the hypotenuse is twice as long as a leg if and only if the measure of the
<span>angle opposite that leg is 30°
so the option C is correct from above all
</span>see the figure
hope it helps
The answer is B. 0.25 inch. Lets multiply all of them by the same factor. Since A. and B. have 3 decimals, lets divide all numbers by 1000: A. 0.026 * 1000 = 26, B. 0.25 * 1000 = 250, C. 0.24 * 1000 = 240, D. 0.025 * 1000 = 25. So, by comparing the whole numbers, it can be concluded that the biggest steel rod is B. 0.25 inch.
, we have
