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2 years ago

How many positive 3-digit numbers are divisible by 11?

Mathematics

1 answer:

enyata [817]2 years ago

4 0

Answer:

Step-by-step explanation:

If a number is divisible by 11, then you can make those numbers by multiplying 11 by any number. Like 33 is divisible by 11 because 3×11 is 33.

Of course, 33 is too small, we are looking for 3-digit numbers...

see image.

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natta225 [31]

Answer:

(a) at t=2, the particle is moving toward the origin

(b) a(t) = 70(8 -9t^2)/(3t^2 +8)^3; a(2) = -0.245

Step-by-step explanation:

(a) The function x(t) is negative for -3 < t < 3, so at t = 2, the particle is to the left of the origin.

The velocity of the particle is given by the derivative of the position function:

$x'(t)=\dfrac{(3t^2+8)(2t)-(t^2-9)(6t)}{(3t^2+8)^2}=\dfrac{70t}{(3t^2+8)^2}$

Then, at t=2, the expression is positive, indicating the particle is moving toward the origin.

(b) The acceleration is the derivative of the velocity, so is ...

$a(t)=\dfrac{70(3t^2+8)^2-(70t)(12t)(3t^2+8)}{(3t^2+8)^4}=\dfrac{70(3t^2+8-12t^2)}{(3t^2+8)^3}\\\\\boxed{a(t)=\dfrac{70(8-9t^2)}{(3t^2+8)^3}}$

Then at t=2, the acceleration is ...

a(2) = 70(8 -9·4)/(3·4+8)^3 = 70(-28)/8000

a(2) = -0.245

(c) As t gets large, the value of x(t) approaches t^2/(3t^2) = 1/3.

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