Your first derivative didn't use a correct form of differentiation. f(t) = t(4-t2) = 4t - t3 f'(t) = 4 - 3t2 We set the derivative equal to zero 4 - 3t2 = 0 4 = 3t2 4/3 = t2 t = +/- 2√3/3 When...
Your first derivative didn't use a correct form of differentiation. f(t) = t(4-t2) = 4t - t3 f'(t) = 4 - 3t2 We set the derivative equal to zero 4 - 3t2 = 0 4 = 3t2 4/3 = t2 t = +/- 2√3/3 When...
This is a parabolic function. Therefore, the minimum or maximum will occur at the point where t = -b/2a. b = 63 a = -16 t = -63/-32 = 63/32 The height at t=63/32 would be: h(63/32) = -16(63/32)2 + 63(63/32) + 4 = -3969/64 +...
To differentiate this function, we must use the product rule of differentiation: y = f(x) * g(x) * h(x) y' = f'(x)*g(x)*h(x) + f(x)*g'(x)*h(x) + f(x)*g(x)*h'(x) = ex(csc x) + xex(csc x) - xex(csc x)(cot x)
C = present amount of chlorine C0 = initial amount of chlorine k = decay constant t = time C = C0ekt at t=0, C = 2.5. At t=1, C = 2.2 2.2 = 2.5ek ek = .88 k = ln .88 = -.1278 C(t) = 2...
A. The cost of producing widget number 31 should be the cost of producing 31 widgets minus the cost of producing 30 widgets which is: C(31) - C(30) = (5000 + 40*31 - 0.02*312) - (5000 + 40*30 - 0.02*302) = 6220.78 - 6182 = 38.78 B. Marginal Cost is defined...
The molar mass of an element or compound is equal to the atomic mass of the element or compound except that is measured in grams. For example, an atom of helium has a mass of 4 amu. Therefore one mole of helium would have a mass of 4 grams. Phosphorous has an atomic mass of 31 amu...
A 200 kilogram chocolate with 13% fat content would have 200 * .13 = 26 kilograms of fat let x = mass of chocolate with 10% fat content let y = mass of chocolate with 40% fat content x + y = 200 .1x + .4y = 26 Multiply the second equation...
Let x = quantity of 10% fat-content chocolate in kilograms Let y = quantity of 60% fat-content chocolate in kilograms The two must add up to 100 kilograms of chocolate. The fat content of the two must add up to 55 kilograms x + y = 100 .10x +...
This is the same truth value as p V s because the negation of a negation always means the original statement much like -(-8) is the same as 8.
let x = calories burned by running per hour let x - 230 = calories burned by riding a bike per hour Joe's two hour run plus warm up = 2x + 150 Tommy's 4 hour bike ride = 4(x - 230) 2x + 150 = 4x - 920 -2x ...
9x4 - 28x2 + 3 = 0 Since the c value is positive, the sign of both factors must be the same. Since there is a minus sign in front of the b value, both factors must have a minus sign. (9x2 - 1)(x2 - 3) = 0 9x2 - 1 = 0 (3x+1)(3x-1)...
Since water slows down the boat going upstream & speeds up the boat going downstream by the same speed of 3 mph, the average speed of the boat relative to the water would be the same as the average speed of the boat without the water current. That would (72 miles + 72 miles)/18 hours which...
Sodium Phosphate: Na3PO4 Zinc Nitrate: Zn(No3)2 Barium Bromate: Ba(BrO3)2 Iron (II) perchlorate: Fe(ClO4)2 cobalt (II) hydrogen carbonate: Co(HCO3)2 -----------this should be called cobalt bicarbonate Chromium (III)...
Hydroiodic acid: HI Chloric Acid: HClO3 Nitrous Acid: HNO2 H2CO3: Carbonic acid HClO4: Perchloric acid CH3COOH: acetic acid
F = Five dollar bills T = Ten dollar bills F = 3T 5F + 10T = 675 5(3T) + 10T = 675 15T + 10T = 675 25T = 675 T = 27 F = 3* 27 = 81 There are 27 ten dollar bills
M stands for moles/liter. 1) The atomic mass of sucrose is 342 daltons. This means the mass of one mole of sucrose is 342 grams. To make a 2 molar solution of sucrose, you must have 2 moles of sucrose in 1 liter of solution. 2 moles of sucrose would have a mass of 684 grams...
500 gallons that have 3% particulate contamination would have: 500 * 3% = 15 gallons of contaminants For that oil to have only 1% contamination, there would have to be a volume to all of the oil 100 times that of the contaminants. That would be: 15...
If the two planes are traveling in opposite directions, then they are traveling on a straight line with respect to each other. Therefore, their distance apart will be equal to their composite speed times the time aka: distance = (total speed) * (time) 2250 km = (470...
The equation of a circle at the origin is x2 + y2 = r2 where r represents the radius of the circle. In the case of a circle with radius 1 centered at the origin, the equation would be: x2 + y2 = 1 Points in the first quadrant that satisfy this equation...
From what I can surmise from the tracking stations and the weather balloon, we have a triangulation going on. A triangle has formed between the two tracking stations & the weather balloon with angles of 38º, 14º, and lastly 128º. To find the distance between the weather balloon & the western...