:<span> </span><span>You need to know the derivative of the sqrt function. Remember that sqrt(x) = x^(1/2), and that (d x^a)/(dx) = a x^(a-1). So (d sqrt(x))/(dx) = (d x^(1/2))/(dx) = (1/2) x^((1/2)-1) = (1/2) x^(-1/2) = 1/(2 x^(1/2)) = 1/(2 sqrt(x)).
There is a subtle shift in meaning in the use of t. If you say "after t seconds", t is a dimensionless quantity, such as 169. Also in the formula V = 4 sqrt(t) cm3, t is apparently dimensionless. But if you say "t = 169 seconds", t has dimension time, measured in the unit of seconds, and also expressing speed of change of V as (dV)/(dt) presupposes that t has dimension time. But you can't mix formulas in which t is dimensionless with formulas in which t is dimensioned.
Below I treat t as being dimensionless. So where t is supposed to stand for time I write "t seconds" instead of just "t".
Then (dV)/(d(t seconds)) = (d 4 sqrt(t))/(dt) cm3/s = 4 (d sqrt(t))/(dt) cm3/s = 4 / (2 sqrt(t)) cm3/s = 2 / (sqrt(t)) cm3/s.
Plugging in t = 169 gives 2/13 cm3/s.</span>
Answer:
23
Step-by-step explanation:
This equation can be derived from the question
let a represent the initial number Gus started with
{[(a x 8) - 12] / 4 } + 7 = 50
subtract 7 from both sides of the equation
[(a x 8) - 12] / 4 } = 43
Multiply both sides of the equation by 4
(a x 8) - 12] = 172
Add 12 to both sides
8a =184
Divide both sides by 8
a = 23.
Answer:
1. 11/12
2. 1/2
3. 2/3
4. 3/4
5. 1
6. 4/5
7. 9/10
8. 3/5
Step-by-step explanation:
1. 11/12
2. 5/10= 1/2
3. 4/6=2/3
4. 6/8=3/4
5. 3/3=1
6. 4/5
7. 9/10
8. 3/5
Answer: 1/10
Step-by-step explanation:
given:
numbers contained in the i.d
1,4,3,7,6
1. permutations of 5 possible outcome
T = 5
= 5 * 4 * 3 * 2 *1
= 120 times.
2. permutations of 3 odd numbers
( 1,3 and 7 )
T = 3
= 3 * 2 * 1 * 2 * 1
= 12
probability of of first three digits being odd numbers
P = 12 / 120
= 1 / 10
Answer:
weight of 25 students
25 × 58 = 1450kg
weight of 29 students
29 × 62 = 1798kg
total students = 25 + 29 = 54
total weight of students = 1450 + 1798 = 3248
mean weight of all students = 3248/54 = 60.19kg
