Find the function J(t) that satisfies dJ(t)/dt = 4J(t) J(t) = ∫4J(t) dt J(t) = e4t + C where C is a constant. J(t=0) = 5 = e4*0 + C = 1 + C ...
Find the function J(t) that satisfies dJ(t)/dt = 4J(t) J(t) = ∫4J(t) dt J(t) = e4t + C where C is a constant. J(t=0) = 5 = e4*0 + C = 1 + C ...
(10x2 + 5x)/5x = 10x2/5x + 5x/5x = 2x + 1
If you had a 10 m piece of wire and cut out a 3 m piece, how much would you have left? You'd have 10 m - 3 m = 7 m left. Works the same in your problem: (10x-3) - (3x+5) = 10x - 3x - 3 - 5 = 7x-8 m
2/(x+1) + 4/(x2-1) = 1 2(x2-1)/(x+1) + 4 = x2 - 1 2(x+1)(x-1)/(x+1) + 4 = x2 - 1 2x - 2 + 4 = x2 - 1 0 = x2 - 2x - 3 Factors...
√(xy3) / xy = (xy3)1/2 / xy = x1/2y3/2 / xy = x1/2-1y3/2-1 = x-1/2y1/2 The answer is B)
In the real number set, you can't take the square root of a negative number. Therefore, the expression under the radical (known as the radicand) must be greater than or equal to zero: x+3 ≥ 0 or ...
4x+2 = 32 Now 4 = 22; so 4x+2 = (22)x+2 = 22x+4 = 22x*24 = 16*22x 16*22x = 32 22x = 21 2x = 1
30 + 15x = 90 Subtract 30 from both sides: 30 + 15x = 90 -30 -30 ------------------- 15x = 60 Divide both...
(−8a2 b3)/(−2a5 b−4 ) = (-8a2-5 b3-(-4))/(-2) = 4a-3b7 = 4b7/a3
Let x and y be the two unknowns positive integers the difference between 2 positive integers is 3: x - y = 3 If the smaller is added to the square of the larger, the sum is 339: x2 + y = 339 Since x-y = 3, then x = y+3. Substitute y+3 in...
Let: J = the number of diamonds that John has K = the number of diamonds that Kayla has If John gives Kayla a diamond, she will have twice as many as him: J-1 = (1/2)(K+1) If Kayla gives one to John,...
From a 30-60-90o right triangle, we know that sin(60o) = √3/2. Hence sin-1(√3/2) = 60o. To convert to radians: 60o/180o = x radians/pi radians pi/3 radians = x
Let x = the unknown number. Six hundred minus three fourths of a number (600 - (3/4)x) is (=) three times the number (3x) 600 - 3x/4 = 3x 600 = 15x/4 600*(4/15) = x ...
The variable Z is directly proportional to X z α x and inversely proportional to Y: z α 1/y So the equation of variation is z = k(x/y) where k is the constant of proportionality. ...
Follow this link to a picture of a 30-60-90o right triangle: http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphics/trig_30_60_90.gif From the picture, you can see that sin(30o) = 1/2. Therefore, sin-1(1/2) = 30o. Hence tan(sin-1(1/2)) = tan(30o)...
a + 2b = 1.25*4b a + 2b = 5b a = 3b a/b = 3
The general formula for this type of problem is: Population at time t = (Initial Population)*(Growth or Decay Rate)time In your case: Initial Population = 10,000 Growth Rate = 1.08 per year time = 20 years So...
There are 8 major planets in our solar system, in the order from closest to furthest from the sun: Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto used to be considered a 9th planet, but its status was downgraded in 2006 to a dwarf planet. ...
R = log(I/I0) where: R = magnitude of the quake on the Richter Scale I = the quake's intensity = 106.5*I0 I0 = minimum intensity quake R = log(106.5*I0/I0) R = log(106.5) R = 6.5
Let x be the unknown number Eight added (8+) to twice a number (2x) is 42 (=42) 8 + 2x = 42