A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 62 feet less than the height of the pole. If the wire is to be 36 feet longer than the height of the pole, what is the height of the pole?

14 feet or 182 feet

Step-by-step explanation:

Let the height of the pole be x

Distance from the bottom of the pole to the anchor point = (x - 62)

Length of the wire = (36 + x)

From Pythagoras theorem;

(36 + x)2 =  + (x - 62) 2

1296 + 72x +  x2 = x2 + x2 - 124x + 3844

collecting like terms;

72x + 124x  + x2 - 2x2 + 1296 - 3844 = 0

196x - x2 - 2548  = 0

Rearranging the quadratic equation;

x2 - 196x + 2548 =0

(x−14)(x−182)=0

x = 14 feet or 182 feet

Hence, the height of the pole is 14 feet or 182 feet

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: