Answer:
about 252.78 ft
Step-by-step explanation:
Define angle QMP as α. Then ...
MN = 60·sin(α)
NP = 60·cos(α)
area MPN = (1/2)(MN)(NP) = 1800sin(α)cos(α)
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PQ = 60tan(α)
area MPQ = (1/2)(MP)(PQ) = 1800tan(α)
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The ratio of areas is 2.5, so we have ...
1800tan(α) = 2.5·1800sin(α)cos(α)
1 = 2.5cos(α)² . . . . . . divide by 1800tan(α)
cos(α) = √0.4 . . . . . . solve for cos(α)
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Then the perimeter is ...
Perimeter = MN +NP +PQ +QM = 60sin(α) +60cos(α) +60tan(α) +60/cos(α)
= 60(sin(α) +cos(α) +tan(α) +sec(α))
= 60(0.774597 +0.632456 +1.224745 +1.581139)
= 60(4.212936) = 252.776
The perimeter of the trapezoid is about 252.776 feet.
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With perhaps a little more trouble, you can find the exact value to be ...
perimeter = (6√10)(7+√6+√15)
The number of bananas required to make the third scale balance is 3.
<h3>What is a scale?</h3>
A scale is a tool used for weighting objects. If the objects on each side weigh the same the scale is balanced. Based on this, let's determine the possible weight of each fruit to balance the last scale.
- Scale 1 (10 bananas/ 2 pineapples)
It is known 10 bananas weigh as much as 2 apples, but to solve this problem let's assume 10 bananas weigh a total of 1000 grams.
- 10 banans = 1000 grams = each banana weighs 100 grams
- 2 pineapples = 1000 grams = each pineapple weighs 500 grams
Scale 2 ( 1 pineapple / 2 bananas, 1 apple)
Using the same imaginary weights let's find the weight of the apple.
- 1 pineapple = 500 grams
- 2 bananas = 200 grams
- 1 apple = 300 grams (500 - 200 = 300)
Scale 3 (1 apple /x )
We know 1 apple is equal to 300 grams and 1 banana is equal to 100 grams. Based on this, the number of bananas to balance the scale is 3.
Learn more about balance in: brainly.com/question/7181548
70 x 9.50 = 665 so 1000 - 665 =335 and 335 / 9.50 = 35 so, it needs 35 more tickets to get 1000.
Answer:
A. Square
Explanation:
The square with sides: x+1
Has an area of: (x+1)^2
The rectangle with sides: x+2 and x
Has an area of: x(x+2)
So we simplify the square: (x+1).(x+1)= x^2+2x+1
Simplifying the rectangle: x^2+2x
Therefore the square area is larger by one unit.
Hope you get it!