Answer:
The ideal size will be a 45cmx45cm square, giving you a perimeter of 180cm.
Step-by-step explanation:
The shortcut answer here is that the square will always be the most efficient rectangle for border to area, so the sides should be the square root of 2025 cm, or 45 cm each, giving you a total of 180 minimum perimeter.
The full solution is to express the perimeter as a function of the length and width, define either length or width as a function of the other, take the entire expression's derivative and solve for zero. Let's do it:
So first the area:
2025 = wl
l = 2025 / w
Now the sides:
Then we can take its derivative with respect to w
Now we can set the derivative to zero, and solve for w:
So the width being 45, we can get the length by dividing the area by that amount, which of course is also 45.
Answer: false
Step-by-step explanation:
Since it is a circle, when you draw the line it will meet at two points which fails the vertical line test. In order to pass the vertical line test it must only meet at one point.
Answer: 0.17 or not rounded, 0.17175572519.
Step-by-step explanation: 6 x 3 x 2.5 = 45, now we just need to divide 45 by 262, so 45/262 = 0.17175572519, or rounded, 0.17.
Hope this helps! :)
140° + ∠5 = 180° <em>same side interior angles </em>⇒ ∠5 = 40°
∠2 ≅ ∠5 <em>vertical angles ⇒ </em>∠2 = 40°
∠8 = 53° <em>alternate interior angles</em>
∠3 ≅ ∠8 <em>vertical angles ⇒ </em>∠3 = 53°
x + ∠2 + ∠3 = 180° <em>triangle sum theorem</em>
x + 40° + 53° = 180°
x + 93° = 180°
x = 87°
Answer: 87°
Note: I just realized that there is an easier way to solve this:
∠9 + 53° + x = 180° <em>triangle sum theorem</em>
140° + ∠9 = 180° <em>supplementary angles </em>⇒ ∠9 = 40°
40° + 53° + x = 180°
x + 93° = 180°
x = 87°
Use whichever solutions makes sense to you.
