Question 1

Find the numerical value of the expression.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

11ea8a3b_b6df_dfdb_9fff_23535c0d5c56_TB6897_11

Question 2

A telephone line hangs between two poles at 12 m apart in the shape of the catenary   , where x and y are measured in meters.Find the slope of this curve where it meets the right pole.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

We can use the formula for the catenary curve:

y = a*cosh(x/a)

where a is a constant that depends on the weight of the cable and the distance between the poles.

To find the slope of the curve at the right pole (x=6), we need to take the derivative of y with respect to x and evaluate it at x=6:

dy/dx = sinh(x/a)

dy/dx @ x=6 = sinh(6/a)

Now we can use the fact that the curve passes through the two poles at the same height, which is given as 11 in the equation:

11 = a*cosh(0)
cosh(0) = 1

Therefore, a = 11.

Substituting into the derivative:

dy/dx @ x=6 = sinh(6/11)

Using a calculator, we get approximately 0.524, which corresponds to choice C.

Question 3

Find the derivative.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

11ea8a3b_b6e0_2e06_9fff_f9745000bda8_TB6897_11

Question 4

Find the numerical value of the expression.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Find the numerical value of the expression....

Question 5

Find the value of the expression accurate to four decimal places. sinh 4&#10;A) 29.3082&#10;B) 55.5798&#10;C) 15.145&#10;D) 27.2899

Accepted Answer

Using a calculator, we get sinh 4 = 27.2899. Rounded to four decimal places, the answer is D, 27.2899.

Deck 3: Extension F: Differentiation Rules