Let the numbers be x, x + 1 and x + 2.
From the information given:-
x(x + 1)(x + 2) = x^3 + 85
Solving for x:-
x(x^2 + 3x + 2) = x^3 + 85
x^3 + 3x^2 + 2x = x^3 + 85
3x^2 + 2x - 85 = 0
3x^2 - 15x + 17x - 85 = 0
3x(x - 5) + 17(x - 5) = 0
(3x + 17)(x - 5) = 0
x = -17/3 , 5
We take x = 5 because x is an integer.
Answer:- the 3 integers are 5, 6 and 7.
Answer:
Total paper required to wrap the gift without any overlaps: ![2700\ cm^{2}](https://tex.z-dn.net/?f=2700%5C%20cm%5E%7B2%7D)
Step-by-step explanation:
Here, we need to find the total paper required without any sides overlapping to wrap the gift.
The gift is of <em>cuboid </em>type.
Given the following:
<em>Length </em>= 15 cm
<em>Width </em>= 30 cm
<em>Height </em>= 20 cm
Please refer to the attached figure.
We can infer that to find the paper required, we actually need to the find the<em> total surface area of the cuboid</em>.
Because the gift wrap will be done <em>on the faces of gift</em> (which is of cuboid shape).
Formula for Surface Area of <em>Cuboid:</em>
![\text {Area = } 2 \times (\text{Length}\times \text{Width} + \text{Width}\times \text{Height} + \text{Length}\times \text{Height} )\\\\\Rightarrow 2 \times (15 \times 30 + 30 \times 20 + 15 \times 20)\\\Rightarrow 2 \times (450 + 600 + 300)\\\Rightarrow 2 \times (1350)\\\Rightarrow 2700 cm^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7BArea%20%3D%20%7D%202%20%5Ctimes%20%28%5Ctext%7BLength%7D%5Ctimes%20%5Ctext%7BWidth%7D%20%2B%20%5Ctext%7BWidth%7D%5Ctimes%20%5Ctext%7BHeight%7D%20%2B%20%5Ctext%7BLength%7D%5Ctimes%20%5Ctext%7BHeight%7D%20%29%5C%5C%5C%5C%5CRightarrow%202%20%5Ctimes%20%2815%20%5Ctimes%2030%20%2B%2030%20%5Ctimes%2020%20%2B%2015%20%5Ctimes%20%2020%29%5C%5C%5CRightarrow%202%20%5Ctimes%20%28450%20%2B%20600%20%2B%20300%29%5C%5C%5CRightarrow%202%20%5Ctimes%20%281350%29%5C%5C%5CRightarrow%202700%20cm%5E%7B2%7D)
Hence, total paper required to wrap the gift without any overlaps: ![2700 cm^{2}](https://tex.z-dn.net/?f=2700%20cm%5E%7B2%7D)
Answer:
$4,508.64
Step-by-step explanation:
The compound interest formula can answer this for you.
A = P(1 +r/n)^(nt)
where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Putting the given values into the formula, doing the arithmetic tells us ...
A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64
There will be $4,508.64 in the account at the end of 6 years.
I’m not going to give you the exact answers because I believe you can do it :)))
So what you should do is 180 divided by 1/5
When people write a slash (/) it means divide
And a fraction is the same as saying 1 divided by 5
180 divided by 3/10
180 divided by 1/10
180 divided by 2/5
The biggest it can be is 110 by 110, and the area would be 2,100 ft.
Hope this helps!