We use
trigonometry for this problem. You might have learned about SOH CAH TOA. In right triangles, when given an angle, you can name the three sides of the triangle a certain part:
Opposite,
Adjacent, and
Hypotenuse.
For this problem, we are given the angle and the ADJACENT length (73). We want to find the OPPOSITE side's length.
TOA
We must use the tangent function.
TOA helps us remember this relationship:
tan( theta ) = opposite / adjacent.
Plug in our values:
tan(29 degrees) = opposite / 73
Multiply by 73 to isolate "opposite" and solve for it.
73 * tan(29) = opposite.
Using a calculator, the answer is approximately 40.46 ft.
Answer: 30 degrees
This is the minimum amount of rotation.
Why this value? Well because 360/12 = 30
Consider a triangle with 3 sides. Specifically I mean an equilateral triangle. We can rotate it 120 degrees to have it line up with itself. Now notice that 360/3 = 120.
For a square, we can rotate it 90 degrees and we can say 360/4 = 90
So the general rule is that the minimum angle of rotation is 360/n, where n is the number of sides. This rule only works for regular polygons. Regular polygons have the same side length and the same angle measure (the side and angle measure won't necessarily be equal).
So going back to this 12 sided dodecagon, we have n = 12 and 360/n = 360/12 = 30 as the minimum angle of rotation. Each 30 degree rotation will have the polygon match up perfectly with its old image. The preimage and image will be identical.
Answer:
do you have a pic you can put up if you can that would help
Step-by-step explanation:
Hello, I have done this same math question before.
1. 15 dollars
2. Deposit=15*month+105
3. Deposit=15*12+105=$285
4. 500=15*month+105
395=15*month
26.33=month
Round up to 27 for the nearest whole month, so month 27.
Hope this helps!
V=x(8-2x)(10-2x) or expanded
V=x(4x^2-36x+80)
V=4x^3-36x^2+80x
...
If you were to graph the above equation for V(x) you will see a maximum point where the "y" value is maximized, but be careful as V will increase without bound at values of x that are not part of the domain, ie, in this case x<8/2, x<4 to have any meaning...The proper domain of this function is:
x=(0,4), Mathematically finding this point quickly is by differentiating it with respect to x...
dV/dx=12x^2-72x+80, The maximum volume will occur when dV/dx=0 and the x value is within the correct domain...
12x^2-72x+80=0 (using the quadratic formula for ease)
x=(72±√1344)/24, and since x<4
x≈1.472in (to the nearest one thousandth of an inch)
