As an odometer check, a special counter measures the miles a car travels modulo 7. explain how this counter can be used to determine whether the car has been driven 49,335; 149,335; or 249,335 miles when the odometer reads 49,335 and works modulo 100,000.

249335 miles

Step-by-step explanation:

Let x be the number of miles the car has travelled.

The odometer can only tell us that x≡49335(mod 100000).

If we also know the value of c where x≡c(mod 7)and 0≤c<7 by the Chinese remainder theorem we know the congruence satisfied by x modulo 100000•7 = 700000.

As long as the car has been driven less that 700000 this uniquely determines the number of miles driven.

In particular, we easily see that if x≡6 (mod 7)then the car was driven 49335 miles, if x≡4 (mod 7)then the car was driven 149335 miles, and if x≡2 (mod 7)then the car was driven 249335 miles

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

u rich

step-by-step explanation: