Answer:
25/4 square inches
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = (1/2)r²θ
where r is the radius and θ is the central angle in radians.
For your sector, the area is ...
A = (1/2)(5 in)²(1/2) = 25/4 in²
5. Given the equation y = (1/4) cos[(2pi/3)*theta]:
5a. For the general equation y = a cos(bx), the period is given by 2pi/b. In this equation, b = 2pi/3, so this means that 2pi/b = 2pi/(2pi/3) = 3. Therefore, the period of this equation is 3, and the cosine wave repeats itself every 3 x-units.
5b. For the general equation y = a cos(bx), the amplitude is given by a. Therefore the amplitude is a = 1/4, and this means that the cosine wave's range is from -1/4 to 1/4 for all values of x.
5c. The equation of the midline is y = 0. This represents the average value over the wave. This is determined by adding the highest and lowest values of the range and taking the average, in this case, 1/4 + (-1/4) = 0, and 0 / 2 = 0. Another way to do this is using the general equation y = a cos(bx) + c, where the midline's equation is y = c. In this case, there is no value of c in the given, implying that c = 0, and the midline is y = 0.
6. Let the horizontal distance be x. Then tan42 = h/x, and h = x tan42. Then using the Pythagorean theorem: 3280^2 = h^2 + x^2
3280^2 = x^2 (tan42)^2 + x^2
3280^2 = x^2 [(tan42)^2 + 1]
x = 2437.52
Therefore, h = x tan42 = 2,194.75 ft.
Answer:
61
Step-by-step explanation:
79 + 40 = 119
180 - 119 = 61
The answer is true, and let me explain this to you like this:
<span>F(x) = 4x - 6
when x = 1, F(x) = 4 * 1 - 6 = -2
when x = 2, F(x) = 4 * 2 - 6 = 2
when x = 3, F(x) = 4 * 3 - 6 = 6
when x = 4, F(x) = 4 * 4 - 6 = 10
</span><span>second row is: -2, 2, 6, 10
</span><span>differences are: 2 - (-2) = 4; 6 - 2 = 4; 10 - 6 = 4
</span>So, the <span>second row is in arithmetic progression.
Hope this is what you were looking for</span>
Answer:
Step-by-step explanation:
1) First, find the slope of the line. Take two points the line intersects and use them for the slope formula, 
. We already know the line intersects (-4, -2). Just choose any one of the points you can see the line intersecting (in this case, I chose (0,3)) and plug in its values, too. Then solve:
So, the slope is 
.
2) Now that you have the slope, plug in values for the point-slope formula, 
. In order to write a linear equation with it, the 
, 
, and 
have to be substituted for with real values. The represents the slope - which means that we should place there. The and represent the x and y values of a point - and the questions wants us to use (-4, -2), so substitute -4 for and -2 for :
Thus, the answer is .
