Answer:
x = 8 ft
h = 1/2 ft
Step-by-step explanation:
Let x be side of the base then area of the base is x²
Let h be the height of the tank
Tank volume is 32 ft³ and is 32 = x²*h then h = 32 /x²
Area of base + lateral area = total area (A)
A = x² + 4*x*h ⇒ A = x² + 4*x*(32/x²) A = x² + 128/x
A(x) = x² + 128/x (1)
Taking derivatives on both sides of the equation
A´(x) = 2x - 128/x² A´(x) = 0 2x - 128/x² = 0
(2x² -128) / x² = 0
2x² - 128 = 0
x² =√64
x = 8 ft
The result is minimum since replacing in equation (1) x = 8 we get
A(x) > 0
And
h = 32/x²
h = 1/2 ft
It is actually both the M and the X, they both represent the slope. I guess in terms of this question literally, no, it is false, M does not represent the slope alone, but if you would've said MX, then it would be true.
68 will be the measure of the other angle.
I have no idea, sorry
DONT REPORT OR ILL MAKE UR LIFE A MOUSECAT!!!
<span>x = 4
Given the description of the triangles, you have 2 similar right triangles. The smaller triangle has a height of 20 and a base of 3x, while the larger has a height of (20+8) = 28 and a base of 4x + 2. We wish to determine the value of x. Since the triangles are similar, the ratio of corresponding sides will be a constant. So:
20/28 = (3x)/(4x+2)
(4x+2)20/28 = (3x)
(20/28)*4x+(20/28)*2 = (3x)
(80/28)*x+(40/28) = (3x)
(20/7)*x + 4/7 = 3x
4/7 = 3x - (20/7)*x
4/7 = (21/7)x - (20/7)*x
4/7 = x/7
4 = x
So the value of x is 4.</span>