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Algebra

A parachutist's rate during a free fall reaches 165

feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 15 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.

Algebra

- Shea is walking on a circular path. The path has a diameter of 8 miles. If

Shea walks about 4 miles an hour, how many hours will it take him to

complete the path? Round your answer to the nearest hour.

Simplify (45x^{6}y^{2})/(5x^{4}y^{9})

Convert 1.5555.....to a fraction

Algebra

We consider the sequence of real numbers (Un) defined on N by Uo = -1, U1 = 1/2 and for every n E N, U(n+2) = U(n+1) - 1/4 Un. Where N reprents the set of natural numbers. Vn = U(n+1) - (1/2)Un.

We define the sequence (Wn) by for every n E N, (Wn) = Un / Vn.

(i) Deduce an expression for Un in terms of n.

(ii) For every natural number n, we set Sn = Uo + U1 + U2 + ...+ Un. Show by induction that for every n E N, Sn = 2 - (2n + 3)/ 2^n.

We define the sequence (Wn) by for every n E N, (Wn) = Un / Vn.

(i) Deduce an expression for Un in terms of n.

(ii) For every natural number n, we set Sn = Uo + U1 + U2 + ...+ Un. Show by induction that for every n E N, Sn = 2 - (2n + 3)/ 2^n.

Algebra

A particle P, of mass m, is projected vertically upwards from a point O with speed 2g/k m/s in a medium whose resistance to motion is of magnitude kv per unit mass, where v is the speed of P and k a positive contant.

(i) Show that v(dv/dx) = -g - kv

The particle P attains the highest point H of its path.

(ii) Show further that OH = g/k^2 (2 - In3)metres

Given that P reaches another point M with speed g/2k m/s as it traces its path back to O, the point of projection,

(iii) Prove that HM = g/k^2 ( In2 - 1/2)

(i) Show that v(dv/dx) = -g - kv

The particle P attains the highest point H of its path.

(ii) Show further that OH = g/k^2 (2 - In3)metres

Given that P reaches another point M with speed g/2k m/s as it traces its path back to O, the point of projection,

(iii) Prove that HM = g/k^2 ( In2 - 1/2)

Algebra

Three vectors a = (3i 4j), b = (-4i + 3j), c = (-3i + 4j) lie on a horizontal plane, pie(ll).

(i) Determine which of the vectors b or a is perpendicular to a.

Two smooth spheres, S and T, each of mass m lie on the plane ll. Sphere S is projected along the plane towards sphere T with velocity 5x(i + 2j) so that it collides obliquely with T. At the instant of collision, the line of impact is parallel to the vector a. Given that the coefficient of restitution between the two spheres is 1/2,

Show that

(ii) the component of the initial velocity of S parallel to a is 11x.

(iii) the component of the final velocity os S parallel to a is (11/4)x.

(iv) the magnitude of the impulse exerted by sphere T on sphere S is (33/4)mx.

(i) Determine which of the vectors b or a is perpendicular to a.

Two smooth spheres, S and T, each of mass m lie on the plane ll. Sphere S is projected along the plane towards sphere T with velocity 5x(i + 2j) so that it collides obliquely with T. At the instant of collision, the line of impact is parallel to the vector a. Given that the coefficient of restitution between the two spheres is 1/2,

Show that

(ii) the component of the initial velocity of S parallel to a is 11x.

(iii) the component of the final velocity os S parallel to a is (11/4)x.

(iv) the magnitude of the impulse exerted by sphere T on sphere S is (33/4)mx.

Algebra

Aaron saw it was 86° Fahrenheit,*F*, in Australia in January. Aaron used the formula C=59(F−32)

C=59(F−32)to find the temperature in degrees Celsius,*C*. What temperature, in degrees Celsius, did Aaron find?

Use the on-screen keyboard to type your answer in the box below.

Algebra

What is 2p(x)+m(x)