The shortest distance on the surface will be along the shortest dimension and then the diagonal of the rectangle
replacing 10 12 20 with 12 16 36 respectively travel from A along 12cm edge then diagonal of 16 x 36 =4 sqrt97
4 sqrt 97 + 12 cm
The ENTIRE line is a common point....it is one line on top of the other, so there is no 'point' of intersection....all of the points on the lines are called 'collinear' rather than intersection.
Yikes....that is a bit garbled...I'm going to say the area is 15 sq ft and the width is 3
Area = w x h find h to see if it will fit
15 = 3 x h
h = 5 it will just fit !
Recognize that the sqrt function is the same as raising something to the 1/2 power
1st one sqrt( 50r^2s^4) = (50r^ s^4)^1/2 = r^(2*1/2) s^(4*1/2) 50^(1/2) = r s^2 sqrt(50) = r s^2 sqrt(25*2) = 5 r s^2 sqrt (2)
DO you see? Try the next one...
x^(3*1/2) realize = x^3/2 = x sqrt(x)
1 -x^2 + 4x = 13
-x^2+4x-13 = 0 simplify things by multiplying by -1 (not NECCESSARY) and use Quadratic Formula
x^2-4x+13 = 0
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) a = 1 b = -4 c = 13
results in x = 2+-3i
You can try the second one...
7x^2-2x+4 = 0 Quadratic formula a = 7 b = -2 c = 4
X intercept occurs when y = 0 sub in y=0 to find x intercept
5x -2(0) = 10 x intercept = 2 (2,0)
Y intercept occurs when x= 0 sub in x = 0 to find y-intercept
5(0) - 2y = 10 y intercept = - 5 (0, -5)
Sorry...CPhill.... I read this as two separate Q's....added a note to my answer....
For the second graph....the points of intersection are where f(x) = g(x) (whatever f(x) and g(x) are)
theis occurs at x = -2 and x = +2
3(4x+4)+15x=120 Use distrib property to expand left side
12x + 12 + 15x = 120 Collect the 'x' terms
27x + 12 = 120 subtract 12 from both sides
27x = 108 divide both sides by 27
x = 4
Well....we'll say she works 18 days and then gets a paid day off....
She works 9 x 18 = 162 hours
She gets paid for 171 hours (because of the day off) 171 hr x $36/hr / 162 hr = $38.00/hr
