Answer:
Step-by-step explanation:
the answer is c because that is what i get
Answer:
Area: 16π-32
Perimeter: 4π + 8sqrt(2)
Step-by-step explanation:
Area:
The shaded part plus the right triangle BCD makes a quarter circle, so you can find the area of the quarter circle minus the triangle.
For the quarter circle, the radius is 8, so the entire circle area is 64π, making the quarter circle 16π.
The triangle is 8*8/2 = 32.
So, the quarter circle minus the triangle, or the area, is 16π-32.
Perimeter:
Again, this is a quarter circle. So, you can add the lengths of arc BD and the line segment BD.
The radius is 8, so the entire circumference is 16π, making the quarter circle 4π.
The hypotenuse of the right triangle will be sqrt(8*8+8*8), or 8sqrt(2).
Add and get 4π + 8sqrt(2) as your perimeter.
1) A, 1:2
Because the ratio of the points is 7:14
2) C, 3:5
Because there are 9:15 boys, so divide by 3
3) C, 33 yards
Convert 1200 inches into yards, it makes 33.3
Answer:
Let x represent the edge dimension of the square base in feet. Then the area of the base or lid is x², and the height of the box is 5/x². Total cost is then ...
... cost = cost of lid + 4×(cost of one side) + cost of bottom
... cost = 0.2x² + 4×(0.2x(5/x²)) + 0.5x²
... cost = 0.7x² + 4/x
We can differentiate this with respect to x and set that derivative to zero. This will give us the x-value at which the cost is a minimum.
... d(cost)/dx = 1.4x -4/x² = 0
... x³ = 4/1.4
... x = ∛(20/7) ≈ 1.419
Then the height of the box is
... height = 5/x² ≈ 5/2.01351 ≈ 2.483
The box is 1.491 ft square and 2.483 ft high.
______
The average cost of the top and bottom is (0.2 +0.5)/2 = 0.35 per square foot. The overall cost will be minimized when the average cost of each face is the same. That is, the areas of the lateral faces will be equal and must be 0.35/0.2 = 1.75 times the area of the top or bottom to make the average cost of a lateral face equal to that of the top or bottom. Hence, the base will be square, and the box will be 1.75 times as high as it is wide or deep. The base edge dimension is then ∛(5/1.75) ≈ 1.419 ft.
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
All triangles = 180 degrees
65 + 4x + x = 180
65 + 5x = 180
- 65 - 65
----------------------
5x = 115
--- = ----
5 = 5
x = 23
4(23) = 92
F = x = 23
B> 65
92 + 23 + 65 = 180
x = 23
F> = B>