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Mathematics

1 answer:

Mars2501 [29]3 years ago

3 0

Answer:

Solve the rational equation by combining expressions and isolating the variable

All real numbers

Interval Notation:

−∞,∞)

Step-by-step explanation:

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

Tanzania [10]

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

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

4 0

3 years ago

rachel jogged along a trail that was 1/4 of a mile long. She jogged along the trail 8 times. how many miles did rachel jog?

____ [38]

To solve for how many miles Rachel jogged if she jogged a 1/4 mile trail 8 times, we simply need to multiply the distance she ran each time by the amount of times she ran it.

1/4 * 8 = 2

Rachel jogged 2 miles.
Hope that helped =)

4 0

3 years ago

PLEASE HELP ASAP

Tpy6a [65]

The area of the polygon with vertices W (1, 1), X (4, 4), Y (7, 1), and S (4, −8) is 36.
Have a great day! :D

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3 years ago

In which set do all of the values make the inequality 2x-1 <10 true?

Andrews [41]

Anything in the negatives like -2*2=-4-1 = -5

Or positive values up to 5

2*5=10-1=9

4 0

3 years ago