Sep 8, 2017 · D: All real x R: y<=9 y = 9 - x^2 is an upside down parabola that has been shifted up 9 units. If it helps, you can rewrite the equation to make y = -x^2 + 9. The domain of any parabola is all real x, or x in RR. This does not change when shifting the parabola. The range of a normal parabola (y = x^2) is y>=0. The range of an upside-down parabola (y = -x^2) is y<=0. Shifting the parabola up by ...

Aug 21, 2015 · Domain: [-3, 3] Range: [-3, 0] In order to find the function's domain, you need to take into account the fact that, for real numbers, you can only take the square root of a positive number. In other words, in oerder for the function to be defined, you need the expression that's under the square root to be positive. 9 - x^2 >= 0 x^2 <= 9 implies |x| <= 3 This means that you have x >= -3" " and ...

The solutions are S={-3,3} The equation is |x^2-9|=x^2-9 Therefore, {(x^2-9=x^2-9),(x^2-9=-x^2+9):} <=>, {(O/),(2x^2-18=0):} <=>, {(O/),(x^2-9 =0):} <=>, {(O/),((x+3 ...

Dec 20, 2014 · Whenever I see these kind of functions, I recognize (by practicing a lot) that you should use a special substitution here: int sqrt(9-x^2)dx x = 3sin(u) This might look like a weird substitution, but you're going to see why we're doing this. dx = 3cos(u)du Replace everyhting in the integral: int sqrt(9-(3sin(u))^2)*3cos(u)du We can bring the 3 out of the integral: 3*int sqrt(9-(3sin(u))^2)*cos ...

Mar 20, 2018 · (x-3)(x+3) >x^2-9" is a "color(blue)"difference of squares" "and in general factorises as" •color(white)(x)a^2-b^2=(a-b)(a+b) "here "a=x" and "b=3 rArrx^2-9=(x-3)(x+3)

Aug 17, 2015 · int sqrt(9-x^2)dx = 9/2(sin^(-1) (x/3) + x/3sqrt(1-(x/3)^2)) + C sin^2 A + cos^2 A = 1 cos 2A = 2cos^2 A - 1 sin 2A = 2sin Acos A Use substitution.

Nov 1, 2016 · x = +3, x = -3 In x^2 =9 , you need to get rid of the power of 2 in order to isolate just x This involves finding the square root. sqrtx^2 = x However there are 2 possible answers to a square root, a positive or a negative answer. x = +-sqrt9 x = +-3

May 20, 2018 · What are the units used for the ideal gas law?

Jun 28, 2015 · x^2+9 has no (Real) factors (Unlike x^2-9) The most you could do with this is use the quadratic formula on ...

Feb 7, 2018 · A_max = 12sqrt3 For reasons of symmetry, the rectangle will be symmetric with respect to the y axis and thus the two vertices lying on the x axis have coordinates (-x,0) and (x,0) and the ones lying on the parabola have coordinates (-x, 9-x^2) and (x,9-x^2), and because they must lie above the x axis we can consider only x in [0,3). We have to maximize the area: A(x) = 2x(9-x^2) for x in [0,3 ...