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finlep [7]
3 years ago
8

) the top and bottom margins of a poster are 4 cm and the side margins are each 5 cm. if the area of printed material on the pos

ter is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.
Mathematics
1 answer:
grin007 [14]3 years ago
8 0
If x represents the width of the poster (including borders), the area of the finished poster can be written as
.. a = x*(390/(x -10) +8)
.. = 8x +390 +3900/(x -10)

Then the derivative with respect to x is
.. da/dx = 8 -3900/(x -10)^2
This is zero at the minimum area, where
.. x = √(3900/8) +10 ≈ 32.08 . . . . cm
The height is then
.. 390/(x -10) +8 = 8 +2√78 ≈ 25.66 . . . . cm

The poster with the smallest area is 32.08 cm wide by 25.66 cm tall.

_____
In these "border" problems, the smallest area will have the same overall dimension ratio that the borders have. Here, the poster is 10/8 = 1.25 times as wide as it is high.
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Approximately 920.324 p/m

Step-by-step explanation:

so to figure this out, we need to simply divide 6,688 people by 7.267 square miles. 6,688/7.267=920.324.... So we have approximately 920.324 people per square mile

5 0
3 years ago
How do u write 32/100 in expanded form
laiz [17]
In expanded form or decimal form 32/100 is equal to 0.32 or 32% or if simplified the fraction is 8/25
3 0
3 years ago
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Ms. Hernandez gave her students a math test
emmainna [20.7K]

Answer:

85-86%

Step-by-step explanation:

Make it an equation

You want to find the percent out of a hundred, so 42 is 100 since it is all of the questions and 36 is the unknown percent X

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Cross multiply

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2 years ago
I have 1,141 point i thought i might share them you here you go
zaharov [31]

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Thank you, person.

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7 0
3 years ago
You are on the south side of a river and you need to cross the river in order to get to a campsite. Not
Doss [256]

Answer:

Width of river = 0.25 mile

As length of river is not given , but it is given that  campsite is located 1 mile east upstream, So length of river = 1 mile

Speed of mine in river while going upstream = 3 miles per hour

Speed of current as going Upstream = 1 miles per hour

Now Reduced speed of mine = Speed of mine in river while going upstream - Speed of current as going Upstream

                                              = 3 - 1

                                              = 2 miles per hour

1. There are two ways to reach campsite

(a) either walk 1 mile from starting point in east direction and then swim 0.25 mile in North direction to reach campsite.

Or

(b) From the starting point Considering a right triangle having, base=1 mile and altitude = 0.25 mile, then finding the length of hypotenuse using formula = \sqrt{(altitude)^2 + (Base)^2

=\sqrt{.25^2+1^2}

=√1.0625

=1.03078(approx)

⇒ you must walk a distance of 1 mile in the east direction and then swim 0.25 mile north direction to reach directly at campsite.[shown in the diagram]



7 0
3 years ago
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