Verify that the given equation is an identity.coth2x = 1 + csch2x

What will be an ideal response?

1 + csch2x = 1 + 2
 = 1 + 
 = 
 = 
 = 
 =  Divide top and bottom by 4 
 = 
 = coth2x

Mathematics

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Solve the application.To obtain a certain shade of paint, Peter mixed 2 gallons of white paint with 6 gallons of brown and 2 gallons of blue paint. How much paint did he have?

A. 3 gallons
B.  gallon
C.  gallon
D. 10 gallons

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Mathematics

Solve the problem.According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 28 volts are applied, the current is 2 amperes. What is the current when 7 volts are applied?

A. 37 amperes B. 98 amperes C. 0.5 amperes D. 14 amperes

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Mathematics

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. -  = 1

A. center at (2, 3)
transverse axis is parallel to x-axis
vertices at (-2, 3) and (6, 3)
foci at (2 - , 3) and (2 + , 3)
asymptotes of y - 3 = - (x - 2) and y - 3 = (x - 2)
B. center at (3, 2)
transverse axis is parallel to x-axis
 vertices at (-1, 2) and (7, 2)
foci at (3 - , 2) and (3 + , 2)
asymptotes of y - 2 = - (x - 3) and y - 2 = (x - 3)
C. center at (3, 2)
transverse axis is parallel to y-axis
vertices at (3, -2) and (3, 6)
foci at (3, 2 - ) and (3, 2 + )
asymptotes of y + 2 = - (x + 3) and y + 2 = (x + 3)
D. center at (3, 2)
transverse axis is parallel to x-axis
vertices at (-2, 2) and (8, 2)
foci at (3 - , 2) and (3 + , 2)
asymptotes of y - 2 = - (x - 3) and y - 2 = (x - 3)

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Mathematics

Find the domain of the variable in the equation. Write the answer in interval notation. = 2 + 

A. (-?, 2) ? (2, ?) B. (0, ?) C. (-?, 0) ? (0, ?) D. (1, ?)

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Mathematics