Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.
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c) The derivative of the area with respect to x is ...
When this is zero, area is at an extreme.
![0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583](https://tex.z-dn.net/?f=0%3D2x%20-%5Cdfrac%7B492%7D%7Bx%5E2%7D%5C%5C%5C%5C0%3Dx%5E3-246%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B246%7D%5Capprox%206.26583)
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d) The second derivative is ...
This is positive, so the value of x found represents a minimum of the area function.
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e) The minimum area is ...
The minimum area of metal used is about 117.78 m².
Answer:
X = 5 unit
Step-by-step explanation:
Given as , ABC is a Triangle ,
AC extended to through C to D
∠BAC = 6x + 10
∠ABC = 6x - 10
∠BCD = ∠ 8x + 20
When c extended to D then , ∠BCD is an external angle
∵ <u>External angle = Sum of opposite internal angles</u>
Or ,∠BCD = ∠BAC + ∠ABC
Or, ∠ 8x + 20 = 6x + 10 + 6x - 10
Or, ∠ 8x + 20 = 12x
Or, 12x - 8x = 20
∴ 4x = 20
So, x = 
= 5
Hence the value of X = 5 unit Answer
Here here here here here here here
Answer:12
Step-by-step explanation:
Let the numbers be a and b
a-3b=5 ........equation (1)
There product is :
ab=68 ..........equation (2)
From equation (1)
a-3b=5
Make a the subject of the formula
a=5+3b. ........equation (3)
Substitute equation (3) into equation (2)
(5+3b)b=68
3(b^2)+3b-68=0
The product is -204b^2(17 and -12)
(b+17)(b-12)=0
b=-17 or b=12
So the number is 12
Y = -41.
EXPLANATION.
if -5 is the midpoint, it must be -5 + 36.
Because there is 36 numbers between 31 and -5.
So -5 + 36 = -41.
