# math

posted by .

Q=3x^2+4y^2 if x+y=7 what is minimum value for Q.
I have absolutely no idea how to solve this problem.

• math -

from the 2nd equation: y = 7-x
sub into the other

Q = 3x^2 + 4(7-x)^2)
= 3x^2 + 4(49 - 14x + x^2
= -x^2 + 196 - 56x + 4x^2
= 3x^2 - 56x + 196

The minimum of Q occurs at the vertex of the corresponding parabola

If you know Calculus ...
dQ/dx = 6x - 56 = 0 for a min of Q
6x=56
x = 56/6 = 28/3

Q = 3(28/3)^2 - 56(28/3) + 196 = -196/3

If no Calculus, then complete the square ...
Q = 3(x^2 - (56/3)x + 784/9 - 784/9) + 196
= 3( (x - 28/3)^2 - 784/9) + 196
= 3(x-28/3)^2 - 784/3 + 196
= 3(x-28/3)^2 - 196/3

so the min of -196/3 happens when x = 28/3

• math -

What is the distance between the parallel lines, whose equation are 3x + 4y = 2 and 3x + 4y = -5.

## Similar Questions

1. ### Math Absolutely no idea

Find the absolute maximum value and the absolute minimum value, if any, of the function. g(x)=(1/16)x^2-16sqrtx on [0,36]
2. ### pre calc

Find the values of b such that the system has one solution. x^2 + y^2 = 36 y= x+b and then they give me an answer box b=_________ (smaller value) b=_________ (larger value) i have absolutely no idea how to even begin this and what …
3. ### math

Consider the initial value problem, f(x,y) = y(18.06 - y), y(0) = 12. The exact solution of the problem increases from y(0) =12 to y = 18.06 as x increases without limit. Determine the minimum upper bound of h for the classical 4th-order …

I have absolutely NO IDEA how to solve this problem!!?
5. ### Calculus

Find the extreme value(s) of the function f(x)=1/(1-x^2). I tried, and for the first derivative I got -1/(2*sqrt((1-x^2)^3)). I then found critical values of the function to be -1 and 1. However, the textbook says that the minimum …
6. ### Calculus

Evaluate the integral of 4x^2(2+x^3)^9 dx. I'm supposed to use the substitution rule but I have absolutely no idea where to start with this problem.
7. ### ap calc

For the curve f(x)=xln(x)+ (1-x)ln(1-x), find the value of x in the interval 0<x<1 where f(x) has a minimum. Please help I have no idea how to solve.
8. ### AP CALC

Find the POSITIVE value of x that satisfies the mean value theorem for f(x)=sin(x) on the closed interval [-3pi/2, 3pi/2]. please help I have no idea how to solve this problem
9. ### Trigonometry

Find exact value of each expression sec^-1 (2root3) / 5 I have no idea what to do to make that into a value. I know that sec^-1 is in quadrants one and two, but I'm not sure how to use that to solve the problem. Thank you!
10. ### math

Find the value(s) of x for the following. (Enter your answers as a comma-separated list.) f(x) = 6 sin^2 x − 6 cos x, and the interval is 0 is less than or equal to x and x is less than or equal to pi. (a) f(x) has a local maximum …

More Similar Questions