1.

A rectangular coordinate system with coordinates in miles is placed with the origin at the center of los Angeles. The figure indicates that the University of Southern California is located 2.4 miles west and 2.7 miles south of central Los Angeles. A seismograph on the campus shows that a small earthquake occurred. The quake’s epicenter is estimated to b approximately 30 miles from the university. Write the standard form of the equation for the set of points that could be the epicenter of the quake.

 

Answer-(x+2.4)^2+(y+2.7)^2=900

 

https://www.chegg.com/homework-help/rectangular-coordinate-system-coordinates-miles-placed-origi-chapter-2.8-problem-73e-solution-9780321879103-exc

 

 

2.

Will a truck that is 8 feet wide carrying a load that reaches 7 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure?

https://www.chegg.com/homework-help/truck-8-feet-wide-carrying-load-reaches-7-feet-ground-clear-chapter-9.1-problem-65e-solution-9780321837349-exc?trackid=5dfa3047&strackid=4410e6cd&ii=1

 

ans=yes, height = 9.64 ft

 

3.

The elliptical ceiling in Statuary Hall in the US capital building is 96 feet long and 23 feet tall.

https://www.chegg.com/homework-help/elliptical-ceiling-statuary-hall-us-capitol-building-96-feet-chapter-9.1-problem-67e-solution-9780321837349-exc?trackid=120e7802&strackid=4866d937&ii=1

 

ans=

a. x^2 / 48^2+y^2 / 23^2 =1

b. 42 feet

 

4.

an architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 6225y^2-400x^2=250,000, where x and y are in yards. How far apart are the houses at their closest point?

https://www.chegg.com/homework-help/architect-designs-two-houses-shaped-positioned-like-part-bra-chapter-13.3-problem-33e-solution-9780321758941-exc?trackid=049e6838&strackid=1e12976f&ii=1

 

ans = 40yds

 

5.

The George Washington bridge spans the Hudson river from New York to New Jersey. (see link)

 

https://www.chegg.com/homework-help/george-washington-bridge-spans-hudson-river-new-york-new-jer-chapter-9-problem-37re-solution-9780321837349-exc?trackid=62391cad&strackid=639f06b6&ii=1

 

ans=

a. y=0.0001032x^2

b.58 ft

 

6.

A satellite dish is in the shape of a parabolic surface. Signals coming from the satellite strike the surface of the dish and are reflected to focus where the receiver is located.

https://www.chegg.com/homework-help/satellite-dish-like-one-shown-shape-parabolic-surface-signal-chapter-9.3-problem-63e-solution-9780321837349-exc?trackid=5df3b25e&strackid=4a00530b&ii=1

ans=

a.y=1/18^x^2

b.4.5ft

7.

A small television has a picture with a diameter measure of 10 inches and a viewing area of 48 square inches. Find the length and width of the screen.

 

https://www.chegg.com/homework-help/use-formula-area-rectangle-pythagorean-theorem-solve-exercis-chapter-7.4-problem-59e-solution-9780321837349-exc?trackid=12cfcdc1&strackid=6b1da273&ii=1

 

ans=

 

length = 8 in, width 6 inches