The Gateway Arch in St. Louis was constructed using the equation

$$y = 211.49 - 20.96 cosh 0.03291765x$$

for the central curve of the arch, where x and y are measured in meters and |x| ≤ 91.20. Set up an integral for the length of the arch and use your calculator to estimate the length correct to the nearest meter.

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation

$$y=211.49-20.96 \cosh 0.03291765 x$$

for the central curve of the arch, where $x$ and $y$ are measured in meters and $|x| \leqslant 91.20$.

Graph the central curve.

The St. Louis Gateway Arch in St. Louis, Missouri, was built in 1965 and was designed as a catenary, which is a curve that approximates a parabola. The arch is 192 m wide and 192 m tall. a) Sketch a graph of the arch that is symmetrical about the y-axis. b) Label the x-intercepts and the vertex. c) Determine an equation to model the arch.

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation

$$y=211.49-20.96 \cosh 0.03291765 x$$

for the central curve of the arch, where $x$ and $y$ are measured in meters and $|x| \leqslant 91.20$.

What is the height of the arch at its center?

A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 22 ft/s^2 . What is the distance traveled before the car comes to a stop?

The design of the Gateway Arch in St. Louis, Missouri, by architect Eero Saarinan was implemented using equations provided by Dr. Hannskarl Badel. The equation used for the centerline of the arch was

$$y = 693.8597 - 68.7672 \cosh ( 0.010333 x ) \text { ft }$$

for x between -299.2239 and 299.2239. Use a graphing utility to graph the centerline of the arch.

Find the arc length of the following curves. $\mathbf { r } ( t ) = \left\langle t ^ { 2 } , \frac { 4 \sqrt { 2 } } { 3 } t ^ { 3 / 2 } , 2 t \right\rangle$, for $1 \leq t \leq 3$

Prove that the centroid of any triangle is located at the point of intersection of the medians. [Hints: Place the axes so that the vertices are (a, 0), (0, b), and (c, 0). Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall also that the medians intersect at a point twothirds of the way from each vertex (along the median) to the opposite side.]

Find the arc length function for the curve y = ln(sin x), 0 < x < π, with starting point (π/2, 0)

Find the exact length of the curve. y = x3 / 3 + 1 / 4x, 1 ≤ x ≤ 2

Two trains on parallel tracks are traveling in the same direction. One train starts 10 km behind the other. It overtakes the first train in 2 hours . What is the relative speed of the second train with respect to the first train?

How will the total distance traveled by a car in 2 hours be affected if the average speed is doubled?

Use the numerical integration capability of your calculator to evaluate the surface areas correct to four decimal places. y = e^-x^2, -1 ≤ x ≤ 1

Find the centroid of the region bounded by the curves $y=2^{x}$ and $y=x^{2}, 0 \leqslant x \leqslant 2,$ to three decimal places. Sketch the region and plot the centroid to see if your answer is reasonable.