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Find (x̅, y̅): R = {(x, y): 0 ≤ y ≤ √x^2 + 1 , 0 ≤ x ≤ 1} about the x-axis.
Find the center of mass of the solid generated by the area bounded by x = 1, x = 3, y = 0
and y = x^2 by revolving about the x-axis.
How many milliliters of a 6.75 M NaOH solution would be needed to prepare 575 mL of a 3.01 M solution?
2. Don, a canteen owner claims that the average meal cost of his usual costumers
is 190 pesos. In order to test his claim, Don took a random sample of 25
costumers and found out that the meal cost is 210 with a standard deviation of
30 pesos. Test the hypothesis at 0.01 level of significance.
Using shell method, find the volume of R, when it is bounded by √x + √y = √a , x =
0 , y = 0 about the line x = a.
Differentiate:
f(x)= (2x⁴+5x+2)
g(x)= 3x²√6x³+5x²+1
h(x)= 4x²/√x+7
find the surface area of the portion of the curve x^2+y^2=4 from x=0 to x=2 when it is revolved about the y-axis
- An underwater swimmer looks up toward the surface of the water on a line of sight that makes an angle of 25˚ with a normal to the surface of the water. What is the angle of incidence in air for the light rays that enter the swimmer’s eye?
2. In each of the following questions, the second medium is air.
a) What is the critical angle if the index of refraction for a medium is 1.68?
b) What is the index of refraction of a medium if the critical angle is 40˚?
- Light travels from air into water. If the angle of refraction is 30˚, what is the angle of incidence?
2. A ray of light in air strikes a block of quartz at an angle of incidence of 30˚. The angle of refraction is 20˚. What is the index of refraction in quartz?
1. Using Snell’s law, determine the constant when the angle of incidence and the angle of refraction are: a) 50˚ and 30˚ b) 30˚ and 18˚ c) 60˚ and 38˚
2. a) What is the angle of refraction in a medium if the angle of incidence in air is 48˚ and the index of refraction of the medium is 1.58? b) What is the angle of incidence in a medium in the case where the angle of refraction in air is 40˚ and the index of refraction of the medium is 1.58?
3. A ray of light passes from air into water at an angle of incidence of 50˚. What is the angle of refraction? (HINT: You will need to use the sin1 function on your calculator).
#339914 on Dec 2023