The final result is: 20x^3 + 62x^2 + 8x - 64.
A poster is to have an area of 240 in^2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exa
ct dimensions that will give the largest printed area.
1 answer:
Answer:
4√10 inches wide by 6√10 inches tall
Step-by-step explanation:
"Poster area" problems have an interesting general solution. The "printed area" is maximized, or the "poster area" is minimized, when the ratio of poster dimensions is equal to the ratio of margin dimensions.
Here, the top/bottom margins total 3 inches, and the side/side margins total 2 inches. That is, the printed area will be maximized when the poster has a width : height aspect ratio of 2 : 3. If w represents the width, then the total area is ...
(w)(3/2w) = 240 . . . . square inches
w^2 = 160
w = √160 = 4√10 . . . . width in inches
Then the height is ...
height = (3/2)w = (3/2)(4√10) = 6√10 . . . . height, inches
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<em>Graphical solution</em>
A graphing calculator gives the same result for x=width. Poster width is about 12.649 inches (=4√10), and printed area is a maximum of about 170.1 square inches.
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<em>Calculus solution</em>
Let x represent the width of the poster. Then x-2 is the width of the printed area. The height of the poster will be 240/x, and the height of the printed area will be (240/x)-3. We want to maximize the printed area ...
a = (x -2)(240/x -3)
which means we want to find the value of x where the area derivative is zero.
a = 240 -480/x -3x +6
da/dx = 0 = 480/x^2 -3
Solving for x, we get ...
x^2 = 480/3 = 160
x = √160 = 4√10 . . . . . poster width, as above
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The final result is: 20x^3 + 62x^2 + 8x - 64.
Answer:
10. 285
11.
16.a. Stiles Family
<u>Reason</u>-The Styles family uses twice as much as the other two, because the electric consumption per person (which is =745 KWh) is much higher than the other two.
16.b. Mendelez family
Reason-The Mendelez family uses the least amount of water, because the water usage per person (which is =875 gallons) is much lower than the other two.
Step-by-step explanation:
10. In 6 mins, no. of machine parts produced = 114
in 1 min, no. of machine parts produced = 114/6
in 15 min, no. of machine parts produces
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11. To make 8 jumbo muffins take, amount of baking powder used =
To make 1 jumbo muffin, amount of baking powder used = =3/16
To make 3 dozens = (3 * 12 )= 36 muffins, amount of baking powder used = 36 *3/16
=
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16. a. Electricity consumed by 1 person in the Mendelez family :
=1560/4
=390 KWh
Electricity consumed by 1 person in the Barton family:
=2130/6
=355 KWh
Electricity consumed by 1 person in the Styles Family:
=1490/2
=745 KWh
The Styles family uses twice as much as the other two, because the electric consumption by 1 person is much higher than the other two.
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16.b. Water consumed by 1 person in the Mendelez family = 3500/4=875 gallons
Water consumed by 1 person in the Barton family = 6400/6=1050 gallons
Water consumed by 1 person in the Styles family =2500/2=1250 gallons