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2 years ago

Let z be the product of any 5 consecutive three digit odd natural numbers. When you multiply

Mathematics

1 answer:

Charra [1.4K]2 years ago

4 0

Answer:

Step-by-step explanation:

If x is the middle number of the 5 consecutive odd numbers, their product is ...

x(x -2)(x +2)(x -4)(x +4) = x(x² -4)(x² -16) = x⁵ -20x³ +64x

The first 3-digit prime is 101, so the product of that with this is ...

101(x⁵ -20x³ +64x) = 101x⁵ -2020x³ +6464x

Since we're only interested in the units digit, we can find the mod 10 value of this to be ...

(x⁵ +4x) mod 10

Possible units digits of x are 1, 3, 5, 7, 9, so possible units digits of this product are ...

x(x⁴ +4) = 1(1⁴ +4) = 5

3(3⁴ +4) = 3(1 +4) = 5 . . . . mod 10

5(5⁴ +4) = 5(5 +4) = 5 . . . . mod 10

7(7⁴ +4) = 7(1 +4) = 5 . . . . mod 10

9(9⁴ +4) = 9(1 +4) = 5 . . . . mod 10

In every case, the units digit of 101z will be 5.

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Answer:

C. The zeros are -1 and 5/2, because f(x) = (x + 1)(2x-5).

Step-by-step explanation:

The zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

The sign of the constant (-5) tells you the product of the constants in the factors must be -5. That is only true for choices B and C.

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The factors of C are zero when x=-1, x=5/2.

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So, to calculate electric fields, we need to find the proper equation to do so: $E=k\frac{q}{r^{2} }$ ; as you can see, first we need to find the charges.

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