Hello!
This is a problem about the general solution of a differential equation.
What we can first do here is separate the variables so that we have the same variable for each side (ex. 
with the 
term and 
with the 
term).
Then, we can integrate using the power rule to get rid of the differentiating terms, remember to add the constant of integration, C, to at least one side of the resulting equation.
Then here, we just solve for and we have our general solution.
![y=\sqrt[3]{\frac{1}{2}x^2-x+C}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7Dx%5E2-x%2BC%7D)
We can see that answer choice D has an equivalent equation, so answer choice D is the correct answer.
Hope this helps!
the discriminant formula is b^2-4ac
so plug the values from each equation into the formula and solve, the result is the value of the discriminant
if the number is negative, there are no real roots/x-int
if it is 0 there is one real root/x-intercepts
if it is positive it has 2 real roots/x-int
and to find the actual solutions you have to plug the values into the quadratic formula
Step-by-step explanation:
uhm you know the excrotery system to the factor
To answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:
35/50 >= 3/4
that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:
<span>35/50 >= 3/4
</span>7/10 <span>>= 3/4
</span>now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:
7/10 <span>>= 3/4
</span>(2/2)(7/10) >= (5/5)(3/4)
2*7/2*10 >= 5*3/5*4
14/20 >= 15/20
we can see that the inequality does not hold, so,
<span>35/50 >= 3/4
</span>does not hold either, therefore the Constitution cannot be ammended
To find the gradient of the tangent, we must first differentiate the function.
The gradient at x = 0 is given by evaluating f'(0).
The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
So the point (0, -1) lies on the tangent. Substituting into the tangent equation:
