In right trapezoid MNPQ
1 answer:
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)
__
PQ = 60tan(α)
area MPQ = (1/2)(MP)(PQ) = 1800tan(α)
__
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)
__
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.
_____
With perhaps a little more trouble, you can find the exact value to be ...
perimeter = (6√10)(7+√6+√15)
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Answer:
Josh's total bill is $ 27.825
Step-by-step explanation:
Given:
The subtotal of the Josh Bill = $21.00
<u>Finding the usual amount Josh gave as Tip To his sever:</u>
Usually josh tips 20% to all servers
So Tip = 20% of his subtotal
=>
=>
=>
=>4.2
So Josh usually tips $4.2 to his server
<u>Finding the amount Josh gave 25%</u><u> </u><u>as Tip To his sever:</u>
But now he tips 25% which is
=> 25% of 21
=>
=>
=> 5.25
Thus the tip amount will be $5.25
So he will be giving (5.25 - 4.2) = $1.05 more than the usual tip
<u>Finding the total bill</u>
The total bill = subtotal+ 7.5% sales tax + 25% tip
=> 21 + 7.5 % of 21 + 25% of 21
=>
=>
=> 21 +1.575 +5.25
=>27.825