1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s whilethe height, h, is increasing at a rate of 0.15 cm/s. Find the rate at whichthe volume, V, is changing when d-4 cm and h=30 cm.azb. If z=x³+2xy² and x = rcose, y = rsine, find andsimplest form.in theirде2. Using the appropriate method taught in class solve the following questions.a) i. Find the general solution of x2 = y2-xy dydydxii. Given that y = 1 when x = 1, show that the particular solution of theequation above isy=exb) Solve the following first order differential equation2x+y=y³ (x-1)

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1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while the height, h, is increasing at a rate of 0.15 cm/s. Find the rate at which the volume, V, is changing when d-4 cm and h=30 cm. b. If z=x³+2xy² and x = rcose, y = rsine, find and in their simplest form.

1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while the height, h, is increasing at a rate of 0.15 cm/s. Find the rate at which the volume, V, is changing when d-4 cm and h=30 cm. b. If z=x³+2xy² and x = rcose, y = rsine, find and in their simplest form.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 67E

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Question

1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while
the height, h, is increasing at a rate of 0.15 cm/s. Find the rate at which
the volume, V, is changing when d-4 cm and h=30 cm.
az
b. If z=x³+2xy² and x = rcose, y = rsine, find and
simplest form.
in their
де
2. Using the appropriate method taught in class solve the following questions.
a) i. Find the general solution of x2 = y2-xy dy
dy
dx
ii. Given that y = 1 when x = 1, show that the particular solution of the
equation above is
y=ex
b) Solve the following first order differential equation
2x+y=y³ (x-1)

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Step 2: Find rate of change of volume

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Step 3: Find partial derivative of r w.r.t. r and theta

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