A police car is approaching a right-angled intersection from the north at 35 mph, and a speeding car is heading east at 30 mph. When the police car is 0.75 miles north of the intersection and the speeding car is 1 mile to the east, what is the rate that the distance between the police car and car is changing?

The rate that the distance between the police car and car is changing = 3 m/s

Step-by-step explanation:

The given speed of the police car = 35 mph

The speed of the speeding car = 30 mph

The position of the police car = 0.75 miles north

The position of the speeding car = 1 miles east

The distance of the police car from the speeding car, d = √(0.75² + 1²) = 1.25

d² = x² + y²

2d·dd/dt = 2x·dx/dt + 2·y·dy/dt

Where;

dx/dt = 30 mph

dy/dt = -35 mph

x = 1

y = 0.75

Substituting gives;

2×1.25 ×dd/dt = 2×1×30 - 2×0.75×35

2×1.25 ×dd/dt = 7.5

dd/dt = 7.5/2.5 = 3

dd/dt = 3 m/s

The rate that the distance between the police car and car is changing = dd/dt = 3 m/s

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

answer: its the third option.

step-by-step explanation:

i just took the test.