Answer: x = ¹/₂ ± √⁸¹
------------
2
Step-by-step explanation:
First write out the equation
x² - x - 20
Now we now write the equation by equating to 0
x² - x - 20 = 0
We now move 20 to the other side of the equation. So
x² - x = 20,
We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes
x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²
x² - ( ¹/₂ )² = 20 + ¹/₄
( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction
( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4
Taking the square root of both side to remove the square,we now have
x - ¹/₂ = √⁸¹/₄
x - ¹/₂ = √⁸¹/₂
Therefore,
x = ¹/₂ ± √⁸¹
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2
9514 1404 393
Answer:
115.5 cubic yards
Step-by-step explanation:
The volume is given by the formula ...\
V = 1/3πr²h
Here the diameter is 7 yards, so the radius is 3.5 yards. The volume is then ...
V = (1/3)π(3.5 yd)²(9 yd) = 36.75π yd³ ≈ 115.454 yd³
The volume of the cone is about 115.5 cubic yards.
Answer:
Answer:
safe speed for the larger radius track u= √2 v
Explanation:
The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.
Also given that r_1= smaller radius
r_2= larger radius curve
r_2= 2r_1..............i
let u be the speed of larger radius curve
now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=
r
1
mv
2
=
r
2
mu
2
................ii
form i and ii we can write
v^2= \frac{1}{2} u^2v
2
=
2
1
u
2
⇒u= √2 v
therefore, safe speed for the larger radius track u= √2 v
Answer:
-2/3
Step-by-step explanation:
The slope of a line can be represented as 
where (x1, y1) and (x2, y2) are points on the line. We can substitute the points given, (-3, 5) and (6, -1), to calculate the slope:
