Hillass22

course Mth 152

Rݜԫioȁ͵{χassignment #022

022. `query 22

Liberal Arts Mathematics II

11-17-2008

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18:23:07

**** query 9.3.12 area of parallelogram **** What is the area of the given parallelogram and how did you obtain it?

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RESPONSE -->

A=hb

A= 2.5 x 4

A=10

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18:23:13

The formula for the area of a parallelogram is

A = bh ( area = base times height)

From the figure the base is 4 and the altitude is 2.5 so we have

A = 4 * 2.5 = 10.

The area is 10 in.

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RESPONSE -->

o.k.

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18:26:52

**** query 9.3.18 area of trapezoid **** What is the area of the given trapezoid and how did you obtain it?

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RESPONSE -->

A=1/2h(b1 + b2)

A = 1/2(3) x (4+5)=

A = 1/2(3) x 9

A = 1/2 x 27

A = 13.5

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18:27:01

The formula for finding the area of a trapezoid is A = 1/2h ( b + B )

h = 3, b = 4, B = 5

A = 1/2 (3) (4 + 5)

A = 1/2 (3) (9)

A = 1/2 (27)

A = 13.5

The area is 13.5

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RESPONSE -->

o.k.

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18:37:48

**** query 9.3.24 dim of rect with lgth 20 more than wdth and perimeter 176 **** What are the dimensions of the rectangle?

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RESPONSE -->

P = 2l +2w

176 = 2l + 2w

176 = l+l+10+10+w+w

176 = 2l +20+ 2w

l=24 w=34

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18:38:42

** The perimeter of a rectangle is P = 2l + 2w, where l and w are length and width.

From the given information

Length = 20 + w

Perimeter = 176

This gives us the equation

176 = 2 (20 + w) + 2w

which we proceed to solve for w:

176 = 40 + 2w + 2w by the Distributive Law. Simplifying we get

176 = 40 + 4w

Subtract 40 from both sides to get

136 = 4w

Divide both sides by 4 to get

w = 34

l = w + 20 so

l = 34 + 20 = 54

We have

Length = 54 and

Width = 34

Checking, we have perimeter = 2 * length + 2 * width so we should have

176 = 2(54) + 2(34).

The right-hand side does give us 176 so the solution checks out. **

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RESPONSE -->

o.k.

I messed up on the formula, but figured out the answer

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18:52:18

**** query 9.3.48 trap bases x, x+4 alt 3 area 30 **** What is the value of x?

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RESPONSE -->

A = 1/2 h(b1 + b2)

30 = 1/2 3(x+4 + x)

30 = 1/2 3(2x + 4)

30 = 1/2 6x + 12

30 = 3x + 6

30 - 6 = 24

3x =24

x = 8

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18:52:25

The formula for finding the area of a trapezoid is A = 1/2h ( b + B). We have

A = 30

h = 3

B = x + 4

b = x

30 = 1/2(3) ( x + x+4)

30 = 1.5 ( x+x+4)

30 = 1.5x + 1.5x + 6

30 = 3x + 6 Subtract 6 from both sides

24 = 3x Divide both sides by 3

x = 8

The answer is 8.

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RESPONSE -->

o.k.

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18:54:59

**** query 9.3.54 $60 to paint ceiling of 9 x 15 rm, how much to paint if dimensions 18 x 30 **** What is the cost for the second ceiling? **** How did you use the results of exercise 53 to obtain your result?

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RESPONSE -->

$60 9 x 15

18 x 30

60 x 4 =$240

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18:55:08

The sides doubled from 9 ft. to 18 ft. and from 15 ft. to 30 ft. When the sides are doubled the area increases by a factor of 4. So the cost is

$60 * 4 = $240

The cost for the second ceiling is $240

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RESPONSE -->

o.k.

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19:01:41

**** query 9.3.60 triangle alt 9 on top of 10 x 4 rect; parallelogram alt 3 under **** What is the area of the given figure and how did you obtain your result?

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RESPONSE -->

A=Triangle 1/2bh = 45

A = Rectangle hb = 40

A = parallelogram hb = 12

45 +40 + 12 =97

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19:02:38

** Here's a solution by a student from a previous semester:

I found the area of each figure and then added those three results together.

Area of Triangle = 1/2bh

A = 1/2 (10) (9)

A = 1/2 (90)

A = 45

Area of Rectangle = lw

A = (10) (4)

A = 40

Area of Parallelogram = bh

A = (10) (3)

A = 30

45 + 40 + 30 = 115

Area = 115 **

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RESPONSE -->

o.k. I misjudged the measurment for the parallelogram

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19:07:56

**** query 9.3.67 26 m diam circle inscribed in sq; area outside circle **** What is the area of the shaded region and how did you obtain it?

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RESPONSE -->

A circle = pi r ^2

A = 3.14 x 13^2

A = 3.14 x 13 x 13 =

A = 530.66

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19:09:01

** The circle has diameter 26 m so its radius is 13 m and its area is

A = pi r^2 = pi * (13 m)^2 = 169 pi m^2 = 531 m^2.

The area of the square is the square of its side

A = (26 m)^2 = 676 m^2.

The area of the shaded region is the difference

}

676 m^2 - 531 m^2 = 145 m^2. **

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RESPONSE -->

o.k.

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19:20:26

**** query 9.3.72 10, 12, 14 in pizzas for 11.99, 13.99, 14.99 **** Which pizza is the best buy and how did you

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RESPONSE -->

Area for a 10 in. pizza = 3.14 x 5^2 = 78.5

12 in. pizza = 3.14 x 6^2 =113.04

14 in. pizza = 3.14 x 7^2 = 154.86

10 in. = 11.99 / 78.5 = .152

12 in. = 13.99 / 113.04 = .123

14 in. = 14.99 / 154.86 = .096

14 in. pizza is the best buy

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19:20:31

obtain your result?

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RESPONSE -->

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19:20:40

Student Solution: The thickness is about the same for all three pizzas so the amount of pizza can be measured by its area. I therefore found the area of each.

A = 3.14 * r^2 and radius is 1/2 the circumference. So we get areas

A = 3.14 (5)^2 = 78.5

A = 3.14 (6)^2 = 113.04

A = 3.14 (7)^2 = 153.86

I then divide the prices and these answers to get the price per square inch.

$11.99 / 78.5 = 15.3

$13.99 / 113.04 = 12.4

$14.99 / 153.86 = 9.7

Since 9.7 is the least, and since this is the result for the 14 inch pizza, the 14 in. pizza for $14.99 is the best buy.

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RESPONSE -->

o.k.

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19:20:47

**** Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

no surprises

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19:20:52

There weren't any big surprises.

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RESPONSE -->

o.k.

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&#Your work looks good. Let me know if you have any questions. &#