Answer:
Explanation:
Use the trigonometric ratio definition of the tangent function and the quotient rule.
Quotient rule: the derivative of a quotient is:
- [the denominator × the derivative of the numerator less the numerator × the derivative of the denominator] / [denominator]²
- (f/g)' = [ g×f' - f×g'] / g²
So,
- tan(x)' = [ sin(x) / cos(x)]'
- [ sin(x) / cos(x)]' = [ cos(x) sin(x)' - sin(x) cos(x)' ] / [cos(x)]²
= [ cos(x)cos(x) + sin(x) sin(x) ] / [ cos(x)]²
= [ cos²(x) + sin²(x) ] / cos²(x)
= 1 / cos² (x)
= sec² (x)
The result is that the derivative of tan(x) is sec² (x)
Equation for Half life :
A = a(0.5)^(t/h)
A is current amount, "a" is initial amount, h is halflife, t is time
5 = 40(0.5)^(t/1.3x10^9)
5/40 = (0.5)^(t/1.3x10^9)
take the log of both sides , power rule
Log(5/40) = (t/1.3x10^9) * Log(0.5)
(1.3x10^9) * Log(5/40) / Log(0.5) = t
3.9x10^9 years = t
And if you think about what a half life is, the time it take for the amount to reduce to half.
40/2 = 20
20/2 = 10
10/2 = 5
It went through 3 half-lifes
3 * 1.3x10^9 = 3.9x10^9 years
Answer:
A hole
Explanation:
put a hole in the barrel and let some water out
Answer: True
Explanation: For example, changing direction can change velocity
Explanation:
a. 
→ ?
Removing common ions from both sides, we get the net ionic equation:
b. 
→
No precipitation is occuring.
c. 
→
Removing common ions from both sides, we get the net ionic equation:
d.
→
Removing common ions from both sides, we get the net ionic equation:
