Answer:
C. Graph C
Explanation:
We have a mixture of water and ice.
At 0 °C they are at equilibrium.
water-to-ice rate = ice-to-water rate
Next, we lower the temperature to -3 °C — just slightly below freezing.
The water will slowly turn to ice.
The water-to-ice rate will be slightly faster than the ice-to-water rate.
The purple bar will be slightly higher than the blue bar.
Graph C best represents the relative rates
A. is wrong. The ice-to-water rate is faster, so the water is melting. The temperature is slightly above freezing (say, 3 °C).
B. is wrong. The two rates are equal, so the temperature is 0 °C.
D. is wrong. The water-to-ice rate (freezing) is much greater than the ice-to-water rate, so the temperature is well below freezing( say, -10 °C).
58.5 is the final mass of the compound as long as any gases the reaction causes to be
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)
