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2 years ago

Write down the negation of each statement

Mathematics

1 answer:

prohojiy [21]2 years ago

6 0

Answer:

1. ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y)

2. ∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Step-by-step explanation:

If we negate a quantified statement, first we negate all the quantifiers in the statement from left to right, ( keeping the same order ) then we negative the statement,

Here, the given statement,

1. ∃y ∈Z such that ∀x ∈Z, R (x + y)

By the above definition,

Negation of this statement is ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y),

2. Similarly,

The negation of statement ∀x ∈Z, ∃y∈Z such that R(x + y),

∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

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a football is kicked into the air. The height of the football can be modeled by h=-16x^2 +32x, where h is the height reached by

Andrej [43]

Your question is incomplete, here is the complete question;

A football is kicked into the air and follows the path defined by h=-2x^2+16x, where x is the time in seconds and h is the height in meters. What is the maximum height reached by the football?

Answer:

maximum height=h=32 meters

Step-by-step explanation:

The given equation is the equation of the parabola or quadratic equation.

The maximum height of the ball will occur at the axis of symmetry.

For the axis of symmetry let h=0,

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$-2x^2+16x=0$

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a= -2, b=16 and c=0

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put x=4 to get maximum height as;

$h=-2(4)^2+16(4)$

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