Asmall resort is situated on an island that lies exactly 5 miles from p, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from p is the closest source of fresh water. if it costs 1.8 times as much money to lay pipe in the water as it does on land, how far down the shoreline from p should the pipe from the island reach land in order to minimize the total construction costs?

Distance of the pipeline down the shoreline should be = 3.34 miles

In the question,

Distance of the Resort, R, from the point, P = 5 miles

Distance of the Fresh Source of water, X, from P = 10 miles

Also, if,

Cost of laying pipeline on land = 1

then,

Cost of laying pipeline in water = 1.8

So,

Using Pythagoras theorem in triangle PRX, we get,

Length of pipe in water, LR is,

So,

Total cost, C, of laying the pipeline is,

On differentiating it w.r.t x, we get,

Therefore, the distance of the pipeline down the shoreline should be,

x = 3.34 miles to minimize the construction cost.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation: