math
posted by weloo_volley .
weloo
Consider the two parabolas :y1=2x^23x1 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(5x)+3/5x^2 ; y(5)=3.

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
(x5)^2 = 46
x5 = ± √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^23x1) = 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 buttonpushing arithmetic
Obviously we cannot demonstrate Mathcad on this webpage.
Respond to this Question
Similar Questions

Calculus
f(x)=x^2  5x +7 and g(x) 3/x 1) Indicate points of intersection 2) compute the area enclosed by the graphs of f(x) and g(x). 1) (1, 3) , (3, 1) 2)Area = âˆ« [1 to 3] [(3/x)  (x^2  5x + 7)] dx = [3 ln x  (1/3)x^3 + (5/2)x^2  … 
calculus
find the points of intersection of the parabolas Y=(1r2 x^2) and Y=10x  2. 
calculus
find the points of intersection of the parabolas Y=(1r2 x^2) and Y=10x  2. 
Math
If f(x)=x^26x+14 and g(x)=x^220xk, determine the value of k so that there is exactly one point of intersection between the two parabolas. 
Math
If f(x)=x^26x+14 and g(x)=x^220xk, determine the value of k so that there is exactly one point of intersection between the two parabolas. 
math
Question2; Consider the function f(x)= cos3x 4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. … 
math
hilp meeee trying .... Consider the two parabolas :y1=2x^23x1 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 … 
math
hilp meeee trying .... Consider the two parabolas :y1=2x^23x1 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 … 
Math How many points of intersection are there?
Let x1, x2,..., x20 be distinct points on the xaxis and let y1, y2,...,y13 be distinct points on the yaxis. For each pair xi, yi, draw the segment connecting xi yo y1. Assume that no three of these segments intersect in one point. … 
Math
Find the points of intersection of the parabolas y=1/2x^2 and y=11/2x^2. Show that at each of these points the tangent lines to the two parabolas are similar Answer (+1,1/2) Please show and explain all steps thank yo