Kiley would need glass of area between 3.14 and 12.56 square feet
Step-by-step explanation:
The Circumference of the circle is given by 2πr where “r” is the radius
Range of the circle’s circumference- 6.28 feet to 12.56 feet
Considering lowest radius as r₁ and the largest as r₂
2πr₁= 6.28
∴r₁= 6.28/(3.14*2) = 1 feet
Similarly
⇒2πr₂=12.56/(3.14*2)=2 feet
We know that area of the circle is given by πr
²
Area of the circle= 3.14*(1)² = 3.14 square feet
Area of the largest radius= 3.14*(2)²= 12.56 square feet
Hence Kiley would need glass of area between 3.14 and 12.56 square feet
Answer:
16
x
^4 − 96
x^
3 + 216
x
^2 − 216
x + 81
Step-by-step explanation:
Use the binomial expansion theorem to find each term. ∑
∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k
Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4
Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4
Simplify each term.
= 16
x
^4 − 96
x^
3 + 216
x
^2 − 216
x + 81
Answer:
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Step-by-step explanation:
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Answer:
3.8E-6
Step-by-step explanation: