What is the simplest form of√1,764? A. 32(72) B. 22(32)(72) C. 21 D. 42
2 answers:
Answer:
The simplest form of√1,764 is 42.
Step-by-step explanation:
We have to write in simplest form. It can be simplified by taking its square root. If a number is multiplied with itself such that we get a original number, then that number is called square root.
For example, 3 and -3 are square roots of 9. In this case, the square root of 1764 can be determined using factorization method also.
Factors of 1764 are : 2 × 2 × 3 × 3 × 7 × 7. So, in simplest form 1764 is equal to 42.
Hence, the correct option is (d) " 42 ".
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Answer:
0.0313
Step-by-step explanation:
Given that in the shipment of 71 vials, only 13 do not have hairline cracks
Probability of not having a hairline cracks =
If you randomly select 2 vials from the shipment
(Probability of not having a hairline cracks)' = =
what is the probability that none of the 2 vials have hairline cracks.
i.e
= 0.183 × 0.171
= 0.0313
Hence, the probability that none of the 2 vials have hairline cracks = 0.0313
The cost of the least expensive fence is $3200
Step-by-step explanation:
The given is:
- A fence must be built to enclose a rectangular area of 20,000 ft²
- Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides
We need to find the cost of the least expensive fence
Assume that the length of each side opposite to North or South is x feet and the length of each other sides is y feet
∵ The length of the rectangle = x feet
∵ The width of the rectangle = y feet
∵ The rectangular area is 20,000 ft²
- Area of a rectangle = length × width
∴ x × y = 20,000
- Divide both sides by x to find y in terms of x
∴
The fence's length is equal to the perimeter of the rectangular area
∵ Perimeter of the rectangle = 2 length + 2 width
∴ Perimeter of the rectangle = 2x + 2y
∵ Fencing material costs $4 per foot for the two sides facing
North and South
∴ x costs $4 per foot
∵ The cost of the other two sides is $8 per foot
∴ y costs $8 per feet
The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y
∵ The cost of the fence (C) = 4(2x) + 8(2y)
∴ C = 8x + 16y
- Substitute y by its value above
∴
∴
To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x
∵ can be written as
∴
∵
∴
- Equate by zero
∴
∵
∴
- Subtract 8 from both sides
∴
- Multiply both sides by x²
∴ - 320,000 = - 8x²
- Divide both sides by -8
∴ 40,000 = x²
- Take √ for both sides
∴ 200 = x
Substitute x in the equation of C to find the least cost of fence
∵
∴ C = 1600 + 1600
∴ C = 3200
The cost of the least expensive fence is $3200
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