Answer:

Step-by-step explanation:
Let x be the distance from the foot of the ladder to the base of the building.
We have a right triangle, so we can use Pythagoras' Theorem.

three, twelve, five, and six
Answer:
A. -2sin(x)sin(0.4x)
Step-by-step explanation:
At x=0, the given expression evaluates to zero.
For x near zero, the given expression is slightly negative. You know this because cos(1.4x) decreases faster than cos(0.6x), so their difference will be negative.
Of the answer choices, you can eliminate C and D because they are not zero at x=0. You can eliminate choice B, because it is positive for values of x near zero. The only viable choice is A:
-2sin(x)sin(0.4x)
___
Of course, a graphing calculator can help you figure this out. See the attachment. The given expression is plotted using a solid red line; the answer choice A is plotted using blue dots.
Answer:
67,500 m²
Step-by-step explanation:
ASSUMING the fields look like this __________________
| | |
| | | W
|_________|_________|
L
Let L be the length of the combined field and W be the width
2L + 3W = 1800
2L = 1800 - 3W
L = 900 - 1.5W
A = LW
A = (900 - 1.5W)W
A = 900W - 1.5W²
Area will be maximized when the derivative equals zero.
dA/dW = 900 - 3W
0 = 900 - 3W
3W = 900
W = 300 m
L = 900 - 1.5(300)
L = 450 m
A = LW = 450(300) = 135,000 m²
so each sub field is 135000/2 = 67,500 m²
Step-by-step explanation:
2 × 10⁸ - 7 × 10⁷
= 200,000,000 - 70,000,000
=130,000,000
= 1.3 × 10⁸