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Leto [7]
3 years ago
4

The length of a rectangular shaped park is (3x+5) miles. The width is (2x+8) miles. The area of the park is 360 square miles. Wh

at are the dimensions of the park?
Mathematics
1 answer:
AnnyKZ [126]3 years ago
8 0
Area (rectangle)=length x width
length=(3x+5)
width=(2x+8)

therefore:
(3x+5)(2x+8)=360
6x²+24x+10x+40=360
6x²+34x-320=0

We solve this square equation:
x=[-34⁺₋√(1156+7680)]/12=(-34⁺₋94) / 12
We have two solutions:
x₁=(-34-94)/12=-10.666  this solution is not valid.
x₂=(-34+94)/12=5

length=(3x+5)=3*5+5=20
width=(2x+8)=2*5+8=18

answer: the dimensions of the park is : length=20 miles, and width=18 miles.
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Answer:

56 days

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Here given:

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final amount: 3.125 millicuries

half life: 8 days

time taken: ?

Hence solve for time taken:

\sf \rightarrow A  = A_O   \ x \ (\dfrac{1}{2} )^{\dfrac{t}{h} }

<u>insert values given</u>

\sf \rightarrow 3.125  = 400  \ x \ (\dfrac{1}{2} )^{\dfrac{t}{8} }

<u>divide both sides by 400</u>

\sf \rightarrow (\dfrac{1}{2})^{\dfrac{t}{8}}=0.0078125

<u>apply exponent rule</u>

<u />\sf \rightarrow {\dfrac{t}{8}}=\dfrac{ln(0.0078125)}{ln(1/2)}

<u>simplify</u>

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<u>multiply both sides by 8</u>

\rightarrow \sf t = 56

4 0
2 years ago
Given n objects arranged in a row, a subset of these objects is called unfriendly if no two of its elements are consecutive. Sho
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Complete question is;

Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )

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Answer:

I've been able to prove that the number of unfriendly subsets of a k-element set is;

( n−k+1 )

( k )

Step-by-step explanation:

I've attached the proof that the number of unfriendly subsets of a k-element set is;

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4 years ago
find the lenght of the poster board is 2 feet and the width is 1 whats the serea of the board of the poster
rusak2 [61]
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3 years ago
B: 6 Point: (-4, 2)<br> Solve for y=mx+b<br> Please help
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<em>Answer:</em>

y=-4x+2

<em>Step-by-step explanation:</em>

<em>B is the y-intercept and M is the sope, or x, knowing this now we slove:</em>

<em>(-4, 2)</em>

<em>m    b</em>

<em>y=mx+b</em>

y=-4x+2

<em>Have a beautiful day!</em> v(⌒o⌒)v♪

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4 0
3 years ago
Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calcul
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Answer:

5536 calculators

Step-by-step explanation:

We integrate the function dx/dt to obtain the number of new calculators between beginning of the 3rd week  and end of week 4. Note that beginning of 3rd week is the same as end of 2nd week. So, \int\limits^4_2 {\frac{dx}{dt} } \, dx=  \int\limits^4_2 {5000 (1 - \frac{100}{(t +12)^{2} }) } \, dx

Let u = t + 12, then \frac{du}{dt}= 1. So, du = dt. We also change the limits of our integration. So, when t = 2, u = 2 + 12 = 14 and when t = 4, u = 4 + 12 = 16

Then  \int\limits^4_2 {5000(1 -\frac{100}{(t+12)^{2} } )} \, dx = ∫₁₄¹⁶ {5000(1 -\frac{100}{u^{2} } )} \, du = 5000[ u + \frac{100}{u} ]₁₄¹⁶ = 5000[16 + \frac{100}{16} - (14 + \frac{100}{14} )] = 5000 [16 - 14 + \frac{100}{16} - \frac{100}{14}  ] = 5000 [2 + \frac{100}{16} - \frac{100}{14}  ] = 5535.7

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