Find an equation of a parabola that has curvature 10 at the origin. (Assume the parabola has its vertex at the origin, and opens upward.)

Step-by-step explanation:

The equation of a parabola is:

We know that the vertex is at the vertex, so b and c are 0.

Then, our quadratic equation is rewritten as:

  (1)

Now, the equation of the curvature related to a function is given by:

 (2)

Here:

y'' is the second derivative of the function

y' is the first equation of the function

κ is the curvature

Let's find the first and the second derivative of y whit respect to x.

Putting these values in equation (2), we have:

We can evaluate the curvature at the origin to find the parameter a. Which means x=0. (Let's recall that κ = 10 at the origin)

Now, we have two options for the equation:

or

But we know that this parabola opens upward, so the value of a must be positive.

Therefore, the equation is:

I hope it helps you!

i dont know if you cant find a way its best to actually add all of them start from 105 tho

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.