Answer:
They can sit next to each other in 24 different ways.
Step-by-step explanation:
In order to solve this problem, use the factorial function (!).
4! = 4 * 3 * 2 * 1 = 24
The total surface area would be 370.58 square units.
Answer:
Roots are not real
Step-by-step explanation:
To prove : The roots of x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0 are real for all real values of k ?
Solution :
The roots are real when discriminant is greater than equal to zero.
i.e. b^2-4ac\geq 0b
2
−4ac≥0
The quadratic equation x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0
Here, a=1, b=1-k and c=k-3
Substitute the values,
We find the discriminant,
D=(1-k)^2-4(1)(k-3)D=(1−k)
2
−4(1)(k−3)
D=1+k^2-2k-4k+12D=1+k
2
−2k−4k+12
D=k^2-6k+13D=k
2
−6k+13
D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))
For roots to be real, D ≥ 0
But the roots are imaginary therefore the roots of the given equation are not real for any value of k.
Answer:16 hours
Step-by-step explanation:
Answer:
for x = 14, the given ABCD is a RECTANGLE.
Step-by-step explanation:
Given : ABCD is a quadrilateral.
E is the intersection points of the diagonal AC and BD.
AE = x+10, and BE= 3x -18
Now, as we know:
IN A RECTANGLES , DIAGONALS BISECT EACH OTHER.
⇒ E is the mid point of AC and BD respectively.
⇒ AE = BE
⇒ x+10 = 3 x - 18
or, 10 + 18 = 3 x - x
or, 2 x = 28
or, x = 28/2 = 14 ⇒ x = 14
Hence, for x = 14, the given ABCD is a RECTANGLE.
