if tan(theta) = -15/8 = y/x, with theta in fourth quadrant, then with y  =15, and x = 8, we have sin(theta) = y/r, where r = square_root(x^2+y^2) = square_root(8^2 + 15^2) = square_root(64 + 225) = square_root(289); so that, sin(theta) = -15/square_root(289) = -15/17 = -0.88

E(x) = (3x  + 1) - ( x + 12) = 2x - 11; E(8) = 2(8) - 11 = 16 - 11 = 5

from equations of Kinematics: v^2 = vo^2 - 2gy; v = vo - gt;  at top of flight path, v = 0;   then: 0 = vo^2 - 2gH, where H = peak height of soccer ball, and 0 = v0 - gT, where T = time to reach top of flight path, and where vo = initial speed = 15 m/s, and g = acceleration...

from Empirical Rule, approximately 98% of the scores (98% of 40 = 39.2 ---> 39) lie within 2 standard deviations of the Mean

H/36 = 6/4 = 3/2;  H = 3(36)/2 = 3(18) = 54 inches

weight of 15 cases of oranges = 15m kg

use AC Method:  compute 3(49) = 3(7)(7)   form the following products and sums:            -1      -3(49)     -[1 + 3(49)]       -3      -49         -(3...

from x = 0.5(a)(t^2),  we have 18 = 0.5(a)(5^2) = 0.5(25)a, or a = 2(18)/25 = 36/25 m/s^2;  then, if T = tension in rope attached to block A, then T = 15(a) = 15(36)/25 = 108/5 Newtons = 21.6 Newtons;  if F denotes the applied force (applied to block B), then:  F - T...

let A = Alvin's age; and let E = Elga's age; then:  A = E + 11, and A + E = 103; then (substituting):  (E + 11) + E = 103;  or 2E + 11 = 103;  or  2E = 103 - 11 = 92;  or E = 46;  A = 46 + 11 = 57

let area of rectangular field be A = xy, where x = length, y = width;  then: A = 3,000,000 = xy ---> y = 3,000,000/x = 3,000,000 x^(-1); ---> L = length of fencing = 2x + 2y + y = 2x + 3y = 2x + 3(3,000,000)[x^(-1)] = 2x + (9,000,000)[x^(-1)];   compute...

x - y^2 = 0 ---> x = y^2 ( parabola opening to the right, vertex at  (0,0)) ;  let point on parabola that minimizes distance from (0,3) be (a,b); then, slope of line joining (0,3) and (a,b) = m =  -(3 - b)/a = (b - 3)/a;  using a = b^2, we have the following:  m = (b...

I agree with Kenneth S. that since the integrand is an odd function of x, and the integral, call it I, is between symmetrically placed limits, -a and a, the result should be, even without any detailed calculations, I = 0.

perhaps the two curves were f(x) = 2sin((π/2)x), and g(x) = cos((π/2)x);  if so, then that would seem to imply that the area in question is:                         b             ∫ [(f(x) -...

Answer:  9 < A < 11;  note that exact answer (area of trapezoid) is:  A = 10   details of the above answer, with f(x) = 2x + 3:   using inscribed rectangles:  A1 = 0.5[f(0) + f(0.5) + f(1) + f(1.5)] = 0.5[3 + 4 + 5 +...

what's the question?

note the following:   n        2n          2n-1   0          0            -1 1          2             1 2  ...

actually, the work done on a body, W = (component of force in direction of motion)(distance)                                                       = increase...