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

the answer is: -(x^3)

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

7a^2 + 50a + 7 = (7a + 1)(a + 7)

7b^2 + 22b + 3 = (7b + 1)(b + 3)

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...