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a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950 m, find d for h = 5250 m.
b) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V = 250 cm3 when T = 200° C and P = 130 kPa, what is the volume when T = 170°C and P = 130 kPa?
c) The acceleration of gravity g on a satellite in orbit around the earth varies inversely as the square of its distance r from the center of the earth.
If g = 8.7 m/s2 for a satellite at an altitude of 400 km above the surface of the earth, find g if it is 1000 km above the surface.
The radius of the earth is 6 6.4×10 m.
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
x=±4, if -2 = y =0 x=±2, if -2 = y = 0
Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form
from 0->1: Int sqrt(1-x^2) Solution) I=∫sqrt(1-x 2 )dx = sqrt(1-x 2 )∫dx - ∫{(-2x)/2sqrt(1-x 2 )}∫dx ---->(INTEGRATION BY PARTS) = x√(1-x 2 ) - ∫-x 2 /√(1-x 2 ) Let
Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
Some interpretations of the derivative Example Is f ( x ) = 2 x 3 + 300 +4 increasing, decreasing or not changing at x = -2 ? Solution: We already know that the rate
If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have among 2 and 6 of them left. Which of the subsequent represents how many gumdrops, x, were originally in his b
what is the meaning of statistics
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