Use the double angle formula: cos2x = 1 - 2sin2x. Therefore, if sinx = -3/5, and sin2x = 9/25, cos2x = 1 - 2(9/25) = 1 - 18/25 = 25/25 - 18/25 = 7/25. BUT: Since the angle lies in quadrant 3, (π < x < 3π/2), the double angle, 2x lies between...
Use the double angle formula: cos2x = 1 - 2sin2x. Therefore, if sinx = -3/5, and sin2x = 9/25, cos2x = 1 - 2(9/25) = 1 - 18/25 = 25/25 - 18/25 = 7/25. BUT: Since the angle lies in quadrant 3, (π < x < 3π/2), the double angle, 2x lies between...
... or using de Moivre's Theorem: wk = z1/n = (rcisθ)1/n = r1/n (cis(θ+360k)/n), where k = 0 and 1, and n = 2, z = 0 + 2i, so r = 2, and θ = 90°. we get w0 = √2 (cis(90/2)), and w1 = √2 (cis(90 + 360)/2); So, w0 = √2 cos 45 + √2 i sin...
Hi, David. The half angle formula: cos(θ/2) = ±√((1 + cosθ)/2). Since sinθ = 3/5, cosθ = 4/5. Therefore, (1+cosθ)/2 = 9/10, and cos(θ/2) = ±√.9. Since 0 < θ < π, we know that 0 < θ/2 < π/2, and cos(θ/2)...
Hi, David. The half angle formula: sin(θ/2) =± √((1-cosθ)/2). Therefore, (1-cosθ)/2 = (1+.6)/2 = .8. sin(θ/2) = ±√(.8) and since π/2 < θ < 3π/2, Π/4 < θ/2 < 3π/4, sin(θ/2) is ±√(.8). I hope...
The arithmetic mean is the average of 2 or more numbers. The arithmetic mean of x and y is: (x + y)/2. The geometric mean is the square root of the product of two numbers. For example: the geometric mean of 4 and 9 is 6, the square root...
y = cos-1(1/2) = π/3 and, since the cos is also positive for (3π/2, 2π), the answer needs to include 5π/3. The value of arccos0 has two values: at π/2, and 3π/2. Arccos(-15/17): x = -15, r = 17, and y = 8. Therefore, the cot must = x/y, or -15/8. If...
Hi, Ehsan. Using the product formula, taking the derivative of: x cos y = 2, We get: 1 cos y + x (-sin y) dy/dx = 0 So -x sin y (dy/dx) = -cos y, Divide by -xsiny, dy/dx = (cos y)/(x sin y) = (cot y)/x. Since...
First: multiply all equations by 10. 5a + 3b = 22 12c + 85b = -244 33c + 13a = 290 Eliminate b from the first 2 equations, getting an equation in a and c. Use that and the 3rd equation to solve for a and c. Finally,...
Zakiya. Bus: r = 45 m/h, t = 2 h, d = rt, therefore, the bus travels 90 miles in 2 hours. Car: let its rate = r, time = 2 h, d = 20 miles more than bus (90 miles + 20 miles) = 110 miles. So: r = 110/2 = 55 mph. I...
Q1. Do you mean hextagon or hexagon? The last three are parallelograms, and therefore, by definition, are polygons with parallel sides. Also, all hexagons don't have any parallel sides unless they are regular or they may have only 2 parallel sides.
Hi, Matia. If you take the equation and square both sides, here is what happens: (√x - √5)2 = (√x-5)2 becomes: x -2√(5x) + 5 = x-5 So, subtract x and subtract 5: -2√(5x) = -10 Square both sides: 4(5x) = 100, ...
Let x = the angle. So: x + 3(90 - x) = (180 - x) + 55 x + 270 - 3x = 235 - x -2x + 270 = 235 - x ...
f(x) = x3 -12x2 + 12x + 80 OK, Katheryn. There are 2 or 0 positive real zeros, and 1 negative real zeros, according to Descartes' Rule of Sign. Also, the possible rational zeros are ±{1, 2, 4, 5, 8, 10, 16, 20, 40, 80} Try ±1 and 2, these 3 won't...
Hi, Lisa. Remember that the point-slope form of a linear equation with point (x1, y1) and slope m: y - y1 = m(x - x1) and the slope-intercept form: y = mx + b. Therefore, using the points (-5, -10), and (-9, 8), we find the slope: (8 - (-10))/(-9...
2x2 + 1 = 6x First, put this in standard form: 2x2 - 6x + 1 = 0 Using a = 2, b = -6, and c = 1, the quadratic formula gives: x = (6 ±√(36 - 4(2)(1)))/4 So x = (6 ± √(36 - 8)/3 = (6 ± √28)/4 = (6 ± 2√7)/4 = (3 ± √7)/2 ...
Hint: divide 98 by 49 (which is 72)
Using the formula A = P(1 + r/n)^(nt) where P = principal, r = rate, n = number of times per year, and t = number of years. we get A = 6300(1 + .06/2)^(2*2) = 7090.71 I hope this helps.
Set equal to 0: 9x5 + 42x4 + 49x3 = 0 Factor: x3(9x2 + 42x + 49) = 0 => x3(3x + 7)2 = 0. Now: Set each factor equal to 0. The exponents will tell you the multiplicity of each zero.
By elimination, I get {24/11, -5/11, -15/11} (The "{}" symbols are shift [, right below Backspace)
How far from the ground is the ball when it hits the ground? So h(t) = 0 ft. So: -16t2 - 10t + 150 = 0 To make the math easier, divide by -2. So: 8t2 + 5t - 75 = 0 Solve this and there's your answer...