Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent an
d opposite θ. Suppose also that x and y vary with time.
a.	How are dθ/dt, dx/dt and dy/dt related?
Please give steps and explain!
       
      
                
     
    
    
    
    
    2 answers:
            
              
              
                
                
Explanation is given step by step just below:
tan(theta(t))=y(t)/x(t)
differentiate
sec^2(theta(t))*theta'(t)=y'(t)x(t)-y(t)x'(t)/x^2(t)
thus
theta'(t)=(y'(t)x(t)-y(t)x'(t))
divided by (x^2(t)*sec^2(θ(t))
                                
             
                    
              
              
                
                
Answer:
dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)
Step-by-step explanation:
Given that x and y are the lengths of the sides adjacent and opposite θ, then they are related by:
tan θ = y/x
Differentiating respect to t, we get:
sec^2 θ * dθ/dt = (dy/dt * x - y * dx/dt)/(x^2)
dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)
 
                                
             
         	    You might be interested in
    
        
        
Answer:
13 cm
Step-by-step explanation:
AC=BD=13 cm
 
        
             
        
        
        
Answer:
WOMP WOMP WOMP!!!
Step-by-step explanation:
 
        
             
        
        
        
✧・゚: *✧・゚:*    *:・゚✧*:・゚✧
                   Hello!
✧・゚: *✧・゚:*    *:・゚✧*:・゚✧
❖ She has 173 pages left to read.
73 + 68 = 141
314 - 141 = 173
~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡
~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ 
 
        
             
        
        
        
It’s tc ccgvchvg gyvCyzbzugs if htkgin to be even
        
             
        
        
        
X + 4y = 3 x = -4y + 3
2x - 3y = 17
2(-4y + 3) - 3y = 17
-8y + 6 - 3y = 17
-11y + 6 = 17
-11y = 11
y = -1
x = -4(-1) + 3
x = 4 + 3
x = 7
(7, -1) is your answer