The answer to this is 2.
There are a number of proofs to this. Here, we use Euclidean geometry with trigonometry. If we let the center of the circle to be O.
Then, we have the following equations for the angles
CEO = OED = 90
Since, CO = OD because they're radii of the circle, then
ΔCOD is an isosceles triangle and
OCE = ODE
CE + DE = CD
dividing the whole equation by DE
CE/DE + 1 = CD/DE
Using trigonometric functions:
CE = OC cos OCE and
DE = OD cos ODE
Substituting.
OC cos OCE / OD cos ODE + 1 = CD/DE
Since, OCE = ODE,
cos OCE = cos ODE
The equation would be reduced to:
1 + 1 = CD/DE
CD/DE =2
Answer:
im not positive but i think theres only 1
Step-by-step explanation:
its been a long time since i learned this
Dy/dx = (dy/dt) / (dx/dt)
dy/dt = 2cos(2t)
dx/dt = -2sin(2t)
dy/dx = 2cos(2t)/-2sin(2t) = -cot(2t)
d^y/dx^2 = d(-1/tan(2t))/dx = (tan(2t) * 0 - (-1)*2sec^2(2t))/tan^2(2t) = 2sec^2(2t)/tan^2(2t) = 2csc^2 (2t)
The answer should be D. 10.
Substitute x for the number 3 in the first equation.
f(x)=2(3)+1, then solve to get x=7
Substitute 7 for x in the second equation
g(x)=(3(7)-1)/2
g=(21-1)/2
g=(20)/2
g=10
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<span>1) 2p = -2.
<span> 4p [ y - k ] = [ x - h) ]² --- > - 4 [ y + 5 ] = [ x + 5 ]²
2) </span></span><span>4p * (y - k) = (x - h)^2 </span>
<span>(h , k) is the vertex </span>
<span>The vertex is halfway between the focus and the directrix (when they're at their closest) </span>
<span>p is that distance </span>
<span>2 - 1 = 1 </span>
<span>4p = 1 </span>
<span>p = 1/4 </span>
<span>(1/4) * (y - k) = (x - h)^2 </span>
<span>y - k = 4 * (x - h)^2 </span>
<span>The vertex is at (6 , 3/2), since that's midway between (6 , 1) and (6 , 2) </span>
<span>y - 3/2 = 4 * (x - 6)^2 </span>
<span>y = (3/2) + 4 * (x - 6)^2
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4) </span><span>f(x) = (-1/16)*(x²)
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5) </span><span>f(x) = −1/4 x2 − x + 5</span><span>
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