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...
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)
I am retired, so increasing my income is ok, but I find that as I interview my students, many of them have difficulty understanding what the teacher is trying to convey. I love math and hope that I can help the students I work with to enjoy math as much as I do. Kevin Caughlan
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...
The segments that join the sides are ½ of the opposite sides. So: AB = ½GJ => 3x + 8 = ½(2x + 24) => 3x + 8= x + 12 => 2x = 4 => x = 2. So AB = 3(2) + 8 = 14. AC = ½HJ and AC = HB. Draw the triangle...
What are the two earthquakes numbers?
If the two nun=mbers are x and x+1, the reciprocals of these are 1/x and 1/(x+1) Therefore the equation is 1/x + 1/(x + 1) = 9/20. Multiply this equation by the Least Common denominator 20(x)(x+1). This becomes 20(x)(x+1)/x +...
s = rθ where s = arc length, r = radius, and θ = angle in radians. θ = 45π/180 = π/4. A = πr2 x (θ/360°)
Remember the formulas: degrees = (radianx180)/π radians = (degreesxπ)/180. This...
Remember that lnA + lnB = ln(AB), and 2lnA = ln(A2) So ln|1+cosθ|+ln|1-cosθ| = 2ln|sinθ| = ln|(1 - cos2θ)| = ln|sin2θ| Therefore, 1 - cos2θ = sin2θ. This is an identity. sin2θ + cos2θ = 1. And can be proved using the...
Let x = the second number, and x-1 = the first number. That means 2x = 4x - 12. x = 6. So the numbers are 5, and 6 2(6) = 12, and 4(6) - 12 = 24 - 12 = 12. I hope this helps.
What this means is that the equation has two solutions, each the same. x = 5, and x = 5, so the equation is y = (x - 5)(x - 5) = (x - 5)2. So, the domain is (-∞, ∞) or all real numbers and the range is [0, ∞), or y≥0. The graph is a parabola resting on...
OK. This is using the basic slope y-intercept equation of old. Let f(x) = lnx. Then f(1) = 0, f'(x) = 1/x and f'(1) = 1 In other words, let your point be (a, f(a)) instead of (x1, f(x1)) and m = f'(a) Since x = 1, let x1 = a = 1. Then...
The equation for continually compounded interest is: A = Pert, where A = final amount, P = principal invested, r = rate in decimal, and e is the constant. Since you want to double your investment, let A = 2p. Thus makes the equation 2P = P e.08t So:...
So, V = (1/3)πr2h, and h = 14 m., when d = 6.5 m. = 13/2 m., which means r = ½d = 13/4 m. dV/dt = (-0.008 + k) m3/min (leaking 0.008 and increasing by a constant,m k) at the time when h = 2.5 m. and dh/dt = +.28 m/min. I would stat by finding...