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bazaltina [42]
3 years ago
15

16. Garrett can complete four laps around the

Mathematics
1 answer:
SashulF [63]3 years ago
3 0

Answer:

Step-by-step explanation:

45 seconds = 45/60 = 0.75 minutes

7 minutes 45 seconds = 7.75 minutes

One hour = 60 minutes

Number of full laps = 60/ 7.75 = 6000/775 = 7.74

He can make 7 full laps in one hour

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Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

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-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

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P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

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LHS = RHS; So, the sum of the zeros and the coefficients are the same

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2(-1) + (-1)(½) + (½)(2) = -3/2

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LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

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2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

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