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the ratio of m∠pqr to m∠pqs is 3: 2. what is m∠rqs?

answers are
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36
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54

ANSWER



EXPLANATION

From the diagram, m∠PQR and m∠RQS are complementary.

This means that the two angles will add up to 90°.



Also, we were given that,





This implies that,



We put equation (2) into equation (1) to get,



Multiply through by 2 to get,





Divide through by 5.

a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

(c) d2y/dx2 = -64/243

Step-by-step explanation:

You have the following equation

  (1)

(a) You first derivative implicitly the equation (1) respect to x:

next, you solve the last result for dy/dx:

(2)

(b) The equation for the tangent line is given by:

   (3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m =

Hence, by replacing in the equation (3) you obtain:

hence, the equation for the tangent line is y = 4/9 x - 14/9

(c) To find d2y/dx2 you derivative the result obtain in the equation (2):

    (4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Step-by-step explanation: