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Topic: Implicit Differentiation
1. Find y’ in 𝑥3 + 2𝑦3 = 3𝑥2𝑦.
2. Find the derivative of 𝑦 = √𝑠𝑖𝑛𝑥𝑦
Topic: Optimization
1. A close right circular cylinder is to be constructed to hold a 1 liter oil can shape.
What dimensions will minimize the amount of material, assuming that the
thickness of the material is uniform?
2. Find two positive numbers whose sum is 9 and whose product is a maximum.
A radio transmission tower is 150 feet tall. How long should a wire be if it is to be attached 5 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.
explain clearly.
∫(7𝑐𝑠𝑐2𝑥 + 2 sec 𝑥 tan 𝑥)𝑑𝑥
. One of the undersecretaries of the Department of Labor and Employment (DOLE) claims that the average salary of civil engineers is 18,000php. A sample of 19 civil engineers' salaries has a mean of 17,350php and a standard deviation of 1,230php. Is there enough evidence to reject the undersecretary's claim at a 0.01 level of significance?
In a biology class, a group of students brought 9 mice for their experiment. They measured the weight and the length of the body of each mouse from the tail to the nose. The findings are recorded below:
Length in cm
13
14
14
11
12
13
12
14
14
Weight in kg
10
10
12
11
16
14
14
17
17
What is the slope of the regression equation? Round your answers to the nearest hundredths.
A study was conducted to investigate the relationship between roadway surface temperature (x) and pavement deflection (y). The data are as follows:
x
65.3
66.4
70.8
70.7
69.8
71.6
72.1
72.4
73.5
y
0.6144
0.6273
0.6668
0.6781
0.6497
0.6678
0.6783
0.6755
0.6873
Calculate the Pearson correlation coefficient. Round your answers to the nearest hundredths.
In a biology class, a group of students brought 9 mice for their experiment. They measured the weight and the length of the body of each mouse from the tail to the nose. The findings are recorded below:
Length in cm
4
5
5
5
7
8
9
9
10
Weight in kg
6
7
8
10
10
11
12
12
13
Calculate the Pearson correlation coefficient. Round your answers to the nearest hundredths.
For a certain process at 127°C, ΔG = -16.20 kJ and ΔH = -17.0 kJ. What is the entropy change for this process at this temperature? Express your answer in the form, ΔS = ____________________ J/K.
Calculate ΔG0 at 298 K for the reaction below.
Fe2O3(s) + 13CO(g) > 2Fe(CO)5(g) + 3CO2(g)
ΔH0f (kJ/mol) -824.2 -110.5 -733.8 -393.5
S0 (J/mol•K) 87.4 197.6 445.2 213.6
