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Solve using basic differentiation rule
y = 2/(x ^ (1/2)) + 6/(x ^ (1/3)) - 2/(x ^ (3/2)) + 4/(x ^ (3/4))
Solve using differentiation rule
y = 2x ^ 2 * sqrt(2 - x)
Solve using basic differentiation rule
𝑠 = (𝑡^2 − 3)^4
Solve using basic differentiation rule
𝑔(𝑥) =3−2𝑥/3+2𝑥
Consider the real space R3
The following vectors form a basis S of R3:
u1 = (1, −1, 0), u2 = (1, 1, 0), u3 = (0, 1, 1)
Find the coordinate vector [v] of v = (5, 3, 4) relative to the basis S .
Let
L(x,y
) be the statement “xl loves y,” where the universe of discourse for both x and y consist of all people in the world. Express each of these quantifications in English. (a)
Every body loves somebody.
(b)
There is somebody whom everybody loves.
(c) There is somebody whom Lynn does not love.
A 3.0-L bulb containing He at 145 mm Hg is connected by a valve to a 2.0-L bulb containing Ar at 355 mm Hg (see figure below). Calculate the partial pressure of each gas and the total pressure after the valve between the flasks is opened. [PHe = 87 mm Hg; PAr = 140 mm Hg]
A flat, circular metal disk of uniform thickness has a radius of 3.20 cm. A hole is drilled in the disk that is 1.60 cm in radius. The hole is tangent to one side of the disk. Where r = 3.20.Where is the x-component of the CM of the disk now that the hole has been drilled?
An organic compound contains carbon(71,17%),hydrogen(5.12%) with the remainder nitrogen.Dissolving 0.177 g of the compound in 10 g of benzene gives a solution with a vapour pressure of 94.16 mmHg at 25°C .(The vapor pressure of pure benzene at this temperature is 95.26 mmHg.)What is the molecular formula for the compound?
A mathematics teacher in senior high school developed a problem-solving test to randomly selected 40 grade 11 students. These students had an average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.
