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zhuklara [117]
3 years ago
14

A rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet. Describe the possible lengths o

f the garden. Round your answers to the nearest foot.
Mathematics
1 answer:
kipiarov [429]3 years ago
4 0

Answer: 51.86 and 23.14

Step-by-step explanation:

The rectangular garden must have a perimeter of 150 feet

Perimeter of rectangular garden =

2l + 2w=150 -----------1

The rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet.

Area of rectangular garden =

l×w= 1200 feet^2 -----------2

From equation 2, l=1200/w

Put l=1200/w in equation 1

2× 1200/w + 2w = 150

(2400/w) +2w = 150

(2400+2w^2)/w =150

2400+2w^2= 150w

2w^2- 150w+2400=0

Using the general formula

w = [-b+-√(b^2-4ac)]/2a

a = 2, b =-150, c=2400

w =[--150+/-√(-150^2-4×2×2400)]/2×2

=[150+/-√(22500-19200)]/4

=[150+/-√3300)]/4

=(150+57.45)/4 or (150-57.45)/4

w= 207.45/4 or 92.55/4

w= 51.86 or w= 23.14

l = 1200/51.86 or l= 1200/23.14

l = 23.14. or l= 51.86

For an area of at least 1200ft^2

The dimensions are 51.86 and 23.14

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Answer:

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Step-by-step explanation:

The given geometric sequence is

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The general form of a geometric sequence is given by

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Where n is the nth term that we want to find out.

a₁ is the first term in the geometric sequence that is 2

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Substitute the value of a₁ and r into the above general equation

a_{n} = 2\cdot 4^{n-1}

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Therefore, the correct option is B

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Verification:

a_{n} = 2\cdot 4^{n-1}

Lets find out the 2nd term

Substitute n = 2

a_{2} = 2\cdot 4^{2-1} = 2\cdot 4^{1} = 2\cdot 4 = 8

Lets find out the 3rd term

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a_{3} = 2\cdot 4^{3-1} = 2\cdot 4^{2} = 2\cdot 16 = 32

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Lets find out the 5th term

Substitute n = 5

a_{5} = 2\cdot 4^{5-1} = 2\cdot 4^{4} = 2\cdot 256 = 512

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