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pratice final A, TI-89 titatnium calculator may be used if needed. whichever is easier for me. please help

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asked Dec 11, 2014 in PRECALCULUS by Baruchqa Pupil

4 Answers

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(30)

The radius of the circle is 10 mts.

Rate of change in radius of the circle (dr/dt) is 0.2 mts.

We know that

Area of the circle A is πr²

To calculate the rate of change in area, we differentiate above with respect to time t.

(dA/dt) = π (d(r²)/dt)

(dA/dt) = π(2r * dr/dt)

dA/dt = π * (2*10*0.2)

dA/dt = π (2 * 2)

dA/dt = 4π

Therefore rate of change in area of the circle is dA/dt = 4π m²/sec.

Option (c) is the correct answer.

answered Dec 11, 2014 by Lucy Mentor
0 votes

(31)

The function is f(x) = x^4+2x²

f'(x) = 1

Apply derivative to the function f(x) with respect to x on both sides.

f'(x) = 4x³+2(2x)

f'(x) = 4x³ + 4x

Given that f'(x) = 1

4x³ + 4x = 1

4x³ + 4x - 1 = 0

Roots of the qudratic polynomial are 0.2367, -0.11837+1.0208i and -0.11837 - 1.0208i.

As we do not consider the imaginary values, so x = 0.2367.

Substitute x = 0.2367 in f(x)

f(x) = (0.2367)^4 + 2(0.2367)²

f(x) = 0.1151

So the point is (0.2367, 0.1151)

The tangent line equation is in the form of y = mx + c

f'(x)  = 1 and (0.2367, 0.1151) passes through the line.

y = x + c

0.1151 = 0.2367 + c

c = -0.1216

c = -0.122

then line equation is y= x - 0.122

Therefore the tangent line equation is y= x - 0.122.

Option (d) is the correct answer.

answered Dec 11, 2014 by Lucy Mentor
edited Dec 11, 2014 by Lucy
0 votes

(32)

The cost price function is c(x) = 4x²+4x-80

Where x is the number of computers sold.

The Selling price of each computer is $1012

Total selling price = (Selling price of each computer )* (Number of computers sold ) = 1012x

Profit = selling price - cost price

Profit = 1012x - (4x²+4x-80)

P(x) = -4x² + 1008x + 80

Apply derivative with respect to x.

P'(x) = -8x + 1008

To find the maximum profit, P'(x) = 0

-8x + 1008 = 0

8x = 1008

x = 126

Therefore number of computers must be sold to obtain maximum profit is 126 units.

Option (b) is the correct answer.

answered Dec 11, 2014 by Lucy Mentor
edited Dec 11, 2014 by steve
0 votes

(29)

The system of equation are

x + z = 3

x+y-2z = 10

y-3z = 8

Let us write the equation in the form of matrix AX = B

image

Let us write the augmented matrix

image

Now apply image

image

Apply image

image

Here the rank of Augmented matrix [A|B] is 3

Rank of matrix A is 2

Rank of [A] < Rank of [A|B] then AX = B is inconsistent and No solutions exist.

Therefore the system has no solutions

Option (e) is the correct answer.

answered Dec 11, 2014 by Lucy Mentor
edited Dec 11, 2014 by Lucy

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