Calc

posted by .

Suppose Y1 is a function of x which dy1/dx=3y1. Suppose y2 is a function of x which dy2/dx=8x+5. If the graphs of y1 and y2 have the same y-intercept and they intersect at x=2, then determine the value of the y-intercept.

  • Calc -

    if dy1/dx = 3y1
    then y1 = ae^(3x) , where a is a constant, a≠ 0

    (check: dy1/dx = 3a(e^(3x)) = 3y1 )

    if dy2/dx = 8x + 5
    then y2 = 4x^2 + 5x + c

    the y-intercept of y1 is (0,a), but that is also the y-intercept of y2

    so in y2:
    a = 0 +0 + c
    a = c

    when x=2
    y1 = a(e^6) , y2 = 16+10+c = c + 26

    but a=c, so
    a(e^6) = a+26
    a(e^6) - a = 26
    a(e^6 - 1) = 26

    a = 26/(e^6 - 1) , which would be the y-intercept

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. discrete math

    1. let A and B be sets. Show that A U (B - A)=A U B 2. determine whether f is a function from Z to R if a) f(n)= +n b) 1/(n square -4) For 1. B-A is the same as B intersect ~A (That's the complement of A) So A U B = A U (B int ~A) …
  2. calculus

    Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two curves. …
  3. Calculus

    Suppose you have a rational function that its denominator is (X-c) and numerator can be any function. Suppose you need to find the limit of this rational function given as x goes to value c. Can you always say that for this problem …
  4. math

    Suppose you have a rational function that its denominator is (X-c) and numerator can be any function. Suppose you need to find the limit of this rational function given as x goes to value c. Can you always say that for this problem …
  5. Algebra/Math

    The graphs of a function f(x)=3x+b and its inverse function f^-1(x) intersect at the point (-3,a). Given that b and a are both integers, what is the value of a?
  6. Algebra 1

    Describe how the graphs of y = absolute value of x,and y = absolute value of X -15 are related. 1- Them graphs have the same shape. The y intercept of y = absolute x is 0, and them x intercept of the 2nd graph is -15. 2-m The graphs …
  7. Math

    Determine whether the following relation is a function. {(3,7),(3,8),(3,-2),(3,4),(3,1)} a. It is a function because the ordered pairs all have the same x-value*** b. It is NOT a function because there are multiple y-values paired …
  8. Math

    For each function, i) determine the corresponding reciprocal function, y =1/f(x) ii) state the non-permissible values of x and the equation(s) of the vertical asymptote(s) of the reciprocal function iii) determine the x-intercepts …
  9. economics

    suppose Y=100 is fixed,suppose the consumption function is c(Y-T)=20+M(Y-T), where M is constant between 0&1,suppose the investment function is I(r)=30-50r,suppose we leave G&T as un specified constant.drive equilibrium interest rate&predict …
  10. Math

    A function f is defined by the equation f(x)=4x−8. Suppose that the state variables T and Q are related by this function according to the mapping f:Q↦T. Suppose that T=3. Use the equation of the function to find the value …

More Similar Questions