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.
The equation of the line which has a gradient of 2 and passes through the point (1,4) is y = 2x + 2.
We have given that,
A line that has a gradient of 2 and passes through the line (1, 4).
We have to determine the equation of the line,
<h3>What is the gradient?</h3>
The gradient also known as the slope is the defined as
Gradient (m) = change in y coordinate / change in x coordinate
The equation of a line passing through a given point is given by the following equation
y – y₁ = m(x – x₁)
How to determine the equation of the line passing through point (1,4)
x coordinate (x₁) = 1
y coordinate (y₁) = 4
Gradient (m) = 2
Equation =
y – y₁ = m(x – x₁)
y – 4 = 2(x – 1)
Clear bracket
y – 4 = 2x – 2
Make y the subject by adding 4 to both sides
y – 4 + 4 = 2x – 2 + 4
y = 2x + 2
The equation of the line which has a gradient of 2 and passes through the point (1,4) is y = 2x + 2.
To learn more about the line visit:
brainly.com/question/5396646
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Answer:
Acute angle
Step-by-step explanation:
170-100=70
An angle between 0 and 90 degrees is an acute angle.
