Answer:
option C is the correct answer
Step-by-step explanation:
The trigonometric equation you are using has a general form
y = A* tan w*(x - r)
Where
A is the amplitude of the function
w is the frequency rad/s
r is the phase shift
In your case
A = -2
The frequency is
w = (2*pi)/period
period = pi/4
w = 8
r = -pi/2
y = -2* cos 8*(x + pi/2)
Complete the square fr x and y's sepreatly to get into form
(x-h)²+(y-k)²=r²
the center is (h,k) and radius is r
so
group x's and y's seperatly
(4x²-10x)+(4y²+24y)+133/4=0
undistribute leading confident from each
4(x²-2.5x)+4(y²+6y)+133/4=0
take 1/2 of each linear confident and square it and add negative and positive inside the parenthasees
-2.5/2=-1.25 (-1.25)²=1.5625
6/2=3, 3²=9
4(x²-2.5x+1.5625-1.5625)+4(y²+6y+9-9)+133/4=0
factor perfect squares
4((x-1.25)²-1.5625)+4((y+3)²-9)+133/4=0
expand
4(x-1.25)²-6.25+4(y+3)²-36+133/4=0
4(x-1.25)²+4(y+3)²-9=0
add 9 to both sides
4(x-1.25)²+4(y+3)²=9
divide both sides by 4
(x-1.25)²+(y+3)²=9/4
(x-1.25)²+(y+3)²=(3/2)²
the center is (1.25,-3) and the radius is 1.5
-4^2 is the same as -4*-4
-4*-4=16
-4^2= 16
-4^2 is the exponent.
I hope this helps!
~kaikers
9514 1404 393
Answer:
20 square units
Step-by-step explanation:
The area is given by the formula ...
A = bh
where b is the base of the parallelogram, and h is the perpendicular distance between the parallel bases. Using the numbers from the figure, we have ...
A = 5·4 = 20 . . . . square units
_____
<em>Additional comment</em>
You will notice this is the same formula as is used for a rectangle. You can consider the parallelogram to have the same area as a rectangle of these dimensions if you look at what happens when you cut the right triangle from the right end and add it to the left end. The result is a rectangle 5 units wide and 4 units high.
The same formula applies even if the skew is so great that the bases do not overlap. (That much skew would not result in a triangle of the kind shown in this diagram.)
Answer:
33.2%
Step-by-step explanation:
Calculate the z-scores.
z = (x − μ) / σ
z₁ = (82 − 100) / 15
z₁ = -1.2
z₂ = (98 − 100) / 15
z₂ = -0.133
Use a chart or calculate to find the probability.
P(-1.2 < Z < -0.133) = P(Z < -0.133) − P(Z < -1.2)
P(-1.2 < Z < -0.133) = 0.4470 − 0.1151
P(-1.2 < Z < -0.133) = 0.3319
Rounded to the nearest tenth, the percentage is 33.2%.
