Answer:
f(x)=11+7√x
f'(x)=7/(2x^(1/2))
putting x=1
f'(1) = 7/(2×1^(1/2))
= 7/2 = 3.5
putting x=2
f'(2) = 7/(2×2^(1/2))
= 7/(2×√2)
= 7√2/4
= 2.47 (rounded to the nearest hundredth)
f'(3) = 7/(2×3^(1/2))
= 7/(2×√3)
= 7√3/6
= 2.02 (rounded to the nearest hundredth)
Answer:
Each side of the hexagon is a rectangle of height 4ft and width 11ft.
The area of each one of these rectangles is:
A = 4ft*11ft = 44ft^2
And a hexagon has 6 faces, so the fish tank will have 6 of these rectangles, then the total area is:
area = 6*44ft^2 = 264 ft^2
We know that the base of the hexagon is not made of glass, but we do not know if the top is made of glass or not.
In the case that the top is not made of glass, the amount of glass needed is 264 ft^2
If the top is made of glass, then we need to add the area of a hexagon of side 11 ft, which is:
a = (3*√3)*(11ft)^2/2 = 314.4ft^2
Then the total area in this case is:
264 ft^2 + 314.4ft^2 = 578.4 ft^2
This is the total amount of glass needed to construct the tank if the top of the tank is made of glass.
Answer:
2x + 30° = 40°
4x + 30° = 50°
Step-by-step explanation:
2x + 30° and 4x + 30° are complementary angles.
Complementary angles sum up to give 90°.
Therefore,
2x + 30° + 4x + 30° = 90°
Add like terms
6x + 60 = 90
6x = 90 - 60
6x = 30
6x/6 = 30/6
x = 5
✔️2x + 30°
Plug in the value of x
2(5) + 30
10 + 30
= 40°
✔️4x + 30°
4(5) + 30°
20 + 30
= 50°
1. For y, I think that refers to the first picture attached. As you can see, each side of the triangle have the same short line drawn across it. It means that they are equal in length. That means the triangle is equilateral, which means each interior angle is 60°. Thus,
60 = 5y + 10
5y = 60 - 10
5y = 50
y = 50/5 =<em> 10</em>
2. As you can see in the second picture attached, Angles B and C are equal. That also means that their respective opposite sides are equal. So,
8x - 4 = 5x + 11
8x - 5x = 11 + 4
3x = 15
x = 15/3 = 5
Consequently,
BC = 4x - 2
BC = 4(5) - 2 = <em>18</em>
She was able to find the point on the line that intersected at 5 and 75
