I think your answer is going to be 23
Answer:
Possible values of dimensions are (24,16,2) or (24,8,4)
Step-by-step explanation:
We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.
Let us say that the width is x and height is y
Length = 24
Volume of a cuboid = length * width * height
Volume = 768
768=24*x*y

xy=32
Now the possible factors of 32
32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can not be more length)
32=2*16
32=4*8
Hence the possible values width are 8, 16 and that of height 4 and 2
Hence the possible values of dimensions are (24,16,2) or (24,8,4)
Answer:
8z+15
Step-by-step explanation:
We have to present the number 41 as the sum of two squares of consecutive positive integers.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
16 + 25 = 41
<h3>Answer: 4 and 5</h3>
Other method:
n, n + 1 - two consecutive positive integers
The equation:
n² + (n + 1)² = 41 <em>use (a + b)² = a² + 2ab + b²</em>
n² + n² + 2(n)(1) + 1² = 41
2n² + 2n + 1 = 41 <em>subtract 41 from both sides</em>
2n² + 2n - 40 = 0 <em>divide both sides by 2</em>
n² + n - 20 = 0
n² + 5n - 4n - 20= 0
n(n + 5) - 4(n + 5) = 0
(n + 5)(n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 =0
n = -5 < 0 ∨ n = 4 >0
n = 4
n + 1 = 4 + 1 = 5
<h3>Answer: 4 and 5.</h3>