Asmall house was built on an island off a perfectly straight shoreline. the point b on the shoreline that is closest to the island is exactly 6 miles from the island. eight miles east of b is the closest source of fresh water to the island. a pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point q on the shoreline between b and the water source, and then laying pipe on land along the shoreline from q to the source. it costs 6000 dollars per mile to lay the pipe under the water and 3750 dollars per mile to lay pipe on land. how far east of b should q be located in order to minimize the total construction costs

Q should be 4.8 miles east of B.

Explanation:

As the diagram shows, we can simply express the construction cost as a function of angle θ (represented in the diagram).  

The length of the pipe in water (represented with blue) = 6/cos θ

The length of the pipe on land (represented with brown) = (8-6*tan θ)

Construction Cost = (6/cos θ) (6000) + (8-6*tan θ)(3750)

The above function represents the construction cost and is in terms of θ

The value of θ varies from 0 degrees to 53.13 degrees as per the diagram.

We can take the derivative of Construction Cost function with respect to θ and equate it to zero to find the angle θ at which the construction cost is minimum.

d(Construction Cost)/d θ = -4500(5*sec θ – 8*tan θ)(sec θ)

-4500(5*sec θ – 8*tan θ) (sec θ) = 0

θ = 38.68 degrees

Using the value of θ, we can find the distance of Q from B.

Distance of Q from B = 6*tan θ  

Distance of Q from B = 6*tan (38.68 degrees)

Distance of Q from B = 4.8 miles

This is what i found on google “what happens to the bond angle when you add or remove an electron domain? the bond angle decreases as you add domains 5. can you force the atoms into new configurations by pushing atoms around? note: we can think of a bond or a lone pair of electrons as a “domain” of electrons.” i hope this you

A., d., and f i think