Posted by **weloo_volley** on Tuesday, May 8, 2012 at 6:11pm.

weloo

Consider the two parabolas :y1=2x^2-3x-1 and y2=x^2+7x+20.

(a) Find the points of intersection of the parabolas and decide which one is greater than the other between the intersection points.

(b) Compute the area enclosed by the two parabolas.

(c) Use Mathcad to draw the graphs of the parabolas and find their intersection points graphically .

(d) Solve the differential equation dy/dx = -exp(5-x)+3/5x^2 ; y(5)=3.

- math -
**Reiny**, Tuesday, May 8, 2012 at 6:57pm
for their points of intersection...

2x^2 - 3x - 1 = x^2 + 7x + 20

x^2 - 10x - 21 = 0

x^2 - 10x + 25 = 21 + 25 , I completed the square

(x-5)^2 = 46

x-5 = ± √46

x = 5 ± √46

so x = 5+√46 and x = 5-√46

or appr. 11.8 and -1.8

so I will take any value of x between these two values, x = 0 seems like a good choice, and find their y values

if x=0, y1 = -1, and if x=0 , y2 = 20

so the parabola y2 = .... is greater for all values of x between the two values we found

So the height of the region is

x^2+7x+20-(2x^2-3x-1) = -x^2 + 10x + 21

Area = ∫(-x^2 + 10x + 21) dx from x = 5-√46 to 5+√46

= [(-1/3)x^3 + 5x^2 + 21x] from x = 5-√46 to 5+√46

= ...

I will let you do the button-pushing arithmetic

Obviously we cannot demonstrate Mathcad on this webpage.

## Answer This Question

## Related Questions

- math - hilp meeee trying .... Consider the two parabolas :y1=2x^2-3x-1 and y2=x^...
- math - hilp meeee trying .... Consider the two parabolas :y1=2x^2-3x-1 and y2=x^...
- math - Question-2; Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...
- Math - Find the points of intersection of the parabolas y=1/2x^2 and y=1-1/2x^2...
- calculus - find the points of intersection of the parabolas Y=(1r2 x^2) and Y=...
- calculus - find the points of intersection of the parabolas Y=(1r2 x^2) and Y=...
- Math - If f(x)=x^2-6x+14 and g(x)=-x^2-20x-k, determine the value of k so that ...
- Math - If f(x)=x^2-6x+14 and g(x)=-x^2-20x-k, determine the value of k so that ...
- Math- How many points of intersection are there? - Let x1, x2,..., x20 be ...
- Calculus - Find the points of intersection for y=e^x and y=sin(2x). are there an...

More Related Questions