Answer:
central angle=18
arc length=2.5 π feet
area of a sector=31.25π square feet
Step-by-step explanation:
Given
wheel radius=25 feet
attached cars=20
Space between cars along the circumference of wheel= 360/20
=18
Finding arc length:
arc length= radius x angle(in radians)
angle in radian = 18 x π/180 = 0.1π radians
arc length = 25 x 0.1π
=2.5π feet
Area of the circle = πr^2
Area of the circle = π(25)^2
Area of the circle = 625π square feet.
As the ratio of the central angle to the full circle angle is proportional to the area of the sector to the complete circle:
central angle/360=area of sector/area of circle
Area of sector= area of circle x 18/360
= 625π(1/20)
=31.25π !
<h3>
Answer:</h3>
none of the above
(the <em>first choice</em> will probably be marked correct, though it is not)
<h3>
Step-by-step explanation:</h3>
You can find the inverse function by solving for y:
x = f(y)
x = √(y -5)
x² = y -5
x² + 5 = y
Then ...
f^-1(x) = x² + 5 . . . . . matches the equation in the first selection
We note that the original function f(x) is a function by virtue of the fact that only the positive square root is of interest. That is, the <em>range</em> of the function f(x) is y ≥ 0. Then the inverse function will have the <em>domain</em> x ≥ 0.
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The offered choices seem to put restrictions on the <em>range</em> (y-values) of the inverse function. There is no need. The range is automatically restricted by the values the inverse function can generate (y ≥ 5). What is needed is a restriction on the <em>domain</em>, which must be x ≥ 0.
_____
<em>Comment on the graph</em>
The inverse of a function is the mirror image of that function reflected across the line y=x. That line is shown in dashed orange. The original function f(x) is shown in red.
The offered choice #1 for the inverse function f^-1(x) is shown in blue. As you can see, for negative values of x, there is no corresponding branch of the square root function f(x). In order to properly define the inverse function, we must make it look like the portion of the blue curve that is overlaid with purple dots. That is, we must restrict the domain of the inverse function to x ≥ 0. (The values of the inverse function will always satisfy y ≥ 5, whether we have properly restricted its domain or not.)
Answer: 23
Step-by-step explanation:
Step 1. 30-6=24
Step 2. 24-3=21
Step 3. 21+2=23
The object's maximum height is the same as the y-coordinate of the vertex.To find that, first, finds the x- coordinate(t).You can find it by:
first identifying a,b and c.Multiply the b by negative 1 or simply change its sign and divide it by 2a.Afterward, plug the answer in the equation to find y, your answer.
(ax+bx²+c=-16t²+64t+80). Therefore, a=-6, b= 64 and c=80
-64/2(-16)=-64/-32=2
-16(2)²+64(2)+80=144 ft
So the maximum height of the object, when launched 64ft/sec from a platform that is 80 ft high, is 144 ft
Hope this helps(there are other methods)
Answer:
The value of cos Ф is ±
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
∵ sin Ф =
∴ sin²Ф =
∴ sin²Ф =
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 -
∴ cos²Ф =
→ Take square root for both sides
∴ cos Ф = ±
∴ The value of cos Ф is ±