Answer:
x = (1/2) (-9 ± √73)
Step-by-step explanation:
Using completing the square method
x²+9x+2=0
x²+9x = -2 (complete the square by adding (9/2)² to both sides)
x²+9x + (9/2)² = -2 + (9/2)²
( x + (9/2) )² = -2+ (9/2)²
( x + (9/2) )² = -2+ (81/4)
( x + (9/2) )² = 73/4
x + (9/2) = ± √(73/4)
x + (9/2) = ± √(73) / 2
x = -(9/2) ± √(73) / 2 (factorize out (1/2) )
x = (1/2) (-9 ± √73)
Answer:



Step-by-step explanation:
<u>Given:</u>



<u>Solve for </u>
<u> in the 1st equation:</u>



<u>Substitute the value of </u>
<u> into the 2nd equation and solve for </u>
<u>:</u>






<u>Substitute the value of </u>
<u> into the 3rd equation and solve for </u>
<u>:</u>






<u>Plug </u>
<u> into the solved expression for </u>
<u> and evaluate to solve for </u>
<u>:</u>



<u>Plug </u>
<u> into the solved expression for </u>
<u> and evaluate to solve for </u>
<u>:</u>




Therefore:



X = 1/2 =0.500
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Answer:
3.04m
Step-by-step explanation:
Time taken to swing the rope = 3.5s
Length of the rope = L
T = 2π√(L / 9.8)
3.5 = 2π√(L / 9.8)
take the square of both sides
(3.5)² =[2π√(L/9.8)]²
12.25 = 39.48 × (L / 9.8)
12.25 = 39.48L / 9.8
39.48L = 12.25 × 9.8
39.48L = 120.05
L = 120.05 / 39.48
L = 3.04m
The length of the rope is 3.04m
Answer:
base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)
Step-by-step explanation:
<u>3 x 3</u> = 9 x <u>3</u> = 27 x <u>3</u> = 81 = 3^4
You multiply 3 by itself 4 times.
<u>9 x 9</u> = 81 = 9^2
You multiply 9 by itself 2 times.