CITIES: The distance between New York City, New York, and Boston, Massachusetts, is 187 miles, and the distance between New York City and Hartford, Connecticut, is 97 miles. Hartford, Boston, and New York City form a triangle on a map. What must the distance between Boston and
Hartford be greater than?

Greater than 90 miles

Step-by-step explanation:

Use the triangle inequality theorem, since the cities form a triangle.

This theorem states that the sum of any 2 sides of a triangle has to be greater than the length of the third side.

We can find what the length of the third side has to be greater than by subtracting 97 from 187:

187 - 97

= 90

So, the distance has to be greater than 90 miles.

step-by-step explanation:

its 512 because parenthesis and to the 2nd power is 512 so it will be 512

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west