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jenyasd209 [6]
3 years ago
8

Prove whether the following are identities 2tanh 1/2x / 1−tanh^2 1/2 x = sinh x​

Mathematics
1 answer:
Tanzania [10]3 years ago
4 0

Recall that

\cosh^2(x) - \sinh^2(x) = 1

Dividing both sides by cosh²(x) gives

1 - \tanh^2(x) = \mathrm{sech}^2(x)

Also, recall the identity

\sinh(2x) = 2\sinh(x)\cosh(x)

Then

\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \dfrac{2\tanh\left(\frac x2\right)}{\mathrm{sech}^2\left(\frac x2\right)} \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\tanh\left(\dfrac x2\right)\cosh^2\left(\dfrac x2\right) \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\sinh\left(\dfrac x2\right)\cosh\left(\dfrac x2\right) \\\\\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \sinh(x)

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A rectangular prism is 12 inches long, 9 inches wide, and 6 inches high. What is the volume of the prism?
zmey [24]

Answer:

Volume = 12×9×6 = 648 inches^3

Step-by-step explanation:

Hope this helps! Have a nice day!

5 0
3 years ago
What is the solution to y-7>3+2y
Alex17521 [72]

Solving:

-7 + y = 3 + 2y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2y' to each side of the equation.

-7 + y + -2y = 3 + 2y + -2y

Combine like terms: y + -2y = -1y

-7 + -1y = 3 + 2y + -2y

Combine like terms: 2y + -2y = 0

-7 + -1y = 3 + 0

-7 + -1y = 3

Add '7' to each side of the equation.

-7 + 7 + -1y = 3 + 7

Combine like terms: -7 + 7 = 0

0 + -1y = 3 + 7

-1y = 3 + 7

Combine like terms: 3 + 7 = 10

-1y = 10

Divide each side by '-1'.

y = -10

Hope it helps. (:

6 0
3 years ago
Find the values of x and y using the given​ chord, secant, and tangent lengths.
inn [45]

Answer:

x = 15.65

y = 3.5

Step-by-step explanation:

Step 1

Find the equation for x and y

Equation for x is given as

x² = 7( 7+28) ..........Equation 1

14(14 + y) = x²........ Equation 2

Solving for Equation 1

x² = 7( 7+28)

x² = 7(35)

x² = 245

x = √245

x = 15.65

From Equation 1 , x² has been determined to be 245

Therefore we substitute 245 for y in Equation 2

14(14 + y) = x²........ Equation 2

14(14 + y) = 245

196 + 14y = 245

14y = 245 - 196

14y = 49

y = 49 ÷ 14

y = 3.5

4 0
2 years ago
A bag contains eight red marbles three blue marbles and one green marble find P not blue
suter [353]
9 marbles are not blue
7 0
2 years ago
Help, Find value of x
Ahat [919]

Answer:

29

Step-by-step explanation:

4x+(x+35)=180

5x+35=180

5x=145

x=29

8 0
3 years ago
Read 2 more answers
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