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2.A quantity with an initial value of 2300 decays exponentially at a rate of 0.9% every minute. What is the value of the quantity after 441 seconds, to the nearest hundredth?
1.A town has a population of 12000 and grows at 3.5% every year. What will be the population after 7 years, to the nearest whole number?
Show complete solution on the upper half of the graphing paper and the graph on the lower half portion. One function is the one graphing paper.
1.f(x)=2 sin (x-π/4)
2.f(x)=sin (x+π/3)
3.f(x)=3 cos (x+π/6)
4.f(x)=2 cos (x-2π)
5.f(x)=tan x
A cylindrical frame consisting of 2 circles and 4 vertical support bars are built from a piece of wire 180cm long, cut into 6 sections: 2 circles of one length and 4 straight pieces of another length. Find the lengths of the sections that will maximize the volume of the cylinder. [Vcylinder = πr^2h]
X^3+3X^2+X+9
/ / / dx
(X^2+1)(X^2+3)
Integration[-2xy/(x²+y²)²] with respect to y
The normal at P on the hyperbola meets the x - axis at Q and the tangent at P meets the y - axis at R. Show that the locus of the midpoint of QR, as P varies, is
2c^2*xy + y^4 = c^4
A(at1^2 , 2at1) and B(at2^2 , 2at2) are points on this parabola. The equation of the chord AB is 2x - (t1 + t2)y + 2at1at2 = 0
The tangents A and B meet at the point P. Find the coordinates of P.
The line through P parallel to the axis of the parabola meets the chord AB at M. Find the coordinates of M. Prove that M is the midpoint of AB.
A(at1^2 , 2at1) and B(at2^2 , 2at2) are points on this parabola. The equation of the chord AB is 2x - (t1 + t2)y + 2at1at2 = 0
The tangents A and B meet at the point P. Find the coordinates of P.
The line through P parallel to the axis of the parabola meets the chord AB at M. Find the coordinates of M.
#339914 on Dec 2023