Answer/respuesta:x=6
Step-by-step explanation paso-por-paso explication: Move the constant to the right-hand side and change its sign Subtract the numbers Divide both sides of the equation /Mover la constante al lado derecho y cambiar su signo Restar los números Dividir ambos lados de la ecuación por
The first point will be (0,0), then (1,4), then (2,8)
You basically have to use the quadratic formula to solve this since there are no factors of - 9 which add to give 6.
Then you use
To find which numbers will go into what place inside the quadratic equation.
So a = 1 (because x is alone)
b = 6
c = -9
Then you solve it. I've included a picture of how I did it and I got the answer x=-3+-3sqrt2
To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4
Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2
antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x
* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2
To find integral from 1 to 4:
Find anti-derivative at x=4, and subtract from the anti-derivative at x=1
2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1
2/3 (8) + 8 - 2/3 - 2 Collect like terms
2/3 (7) + 6 Express 6 in terms of 2/3
2/3 (7) + 2/3 (9)
2/3 (16) = 32/3 = 10 2/3 Answer is B