Question

1. an engineer needs to run a cable from (0, 0, 0) to (10, 8, 15). what is the cable length?

a. 15.36
b. 17.32
c. 19.72
d. 18.24

Explanation:

Step1: Use the distance formula in 3 - D

The distance formula between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}\). Here, \((x_1,y_1,z_1)=(0,0,0)\) and \((x_2,y_2,z_2)=(10,8,15)\).

Step2: Substitute the values

Substitute \(x_2 = 10\), \(x_1=0\), \(y_2 = 8\), \(y_1 = 0\), \(z_2=15\), \(z_1 = 0\) into the formula: \(d=\sqrt{(10 - 0)^2+(8 - 0)^2+(15 - 0)^2}=\sqrt{100 + 64+225}\).

Step3: Calculate the sum inside the square root

\(100+64 + 225=389\).

Step4: Find the square root

\(\sqrt{389}\approx18.24\).

Answer:

D. 18.24