A person stands 151515 meters east of an intersection and watches a car driving towards the intersection from the north at 111 meter per second. At a certain instant, the car is 888 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)

dL/dt = 110,98 m/s

Step-by-step explanation:

Let´s call A the point where a person is, the intersection (o) and the car from the north form a right triangle. According to Pythagoras Theorem

L²  =  x²  +  y²      where L is the distance between the person and the car ( x is constant since the person does not move)

Tacking derivatives with respect to time we have:

2*L*dL/dt  =   2*y*dy/dt     (1)

x  =  15 mts         y  = 888    and  dy/dt  = 111 m/s

L² =  x²  +  y²

L  = √ (15)² + (888)²      ⇒     L = √ 225  + 788544

L = 888,13 m

2*L* dL/dt  = 2* (888)*111

dL/dt  = (888)*111/888,13

dL/dt  =0,99*111

dL/dt = 110,98 m/s

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.