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
__
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.
__
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)
__
d) The second derivative is ...
This is positive, so the value of x found represents a minimum of the area function.
__
e) The minimum area is ...
The minimum area of metal used is about 117.78 m².
Answer:
y= -x+7, b= sqrt(2P/a), c=3P^2-b
Step-by-step explanation:
First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.
Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).
Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.
Hey there! I'm happy to help!
To find the distance between two points, you find the difference between the x values, square that, find the difference between the y values, square that, add the two numbers you got, and then find the square root.
We find the difference between the x values.
-7-2=-9
Square it.
-9²=81
We find the difference between the y-values.
5--3
5+3=8
We square it.
8²=64
We add the numbers we got.
81+64=145
We square root.
√145≈12.04
This formula comes from the Pythagorean Theorem! Now you can find the distance between any two points! Have a wonderful day! :D
Answer:
6 and 9
Step-by-step explanation:
set up an equation and solve for x
(x+3) * x = 54
easiest way to to try some numbers.
if you know your multiplication tables...
what two number multiplied together are 54
be sure the numbers you are thinking of meet the rules
is one 3 more than the other
do they multiply together to get 54
The answer is c , between 52.43 and 64.20
