When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)
Therefore Option C and D is the correct answer.
<h3>What is a Quadratic Function?</h3>
The equation for a quadratic function is given by
y = a(x-h)² +k²
where (h,k) is the extreme value(vertex).
Here the equation given is
y = x²-4x +8
y = x²-4x+4+4
y = (x-2)² +4
Here the value of a = 1 , h = 2 and k = 4
The extreme value is at (2,4)
Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)
Therefore Option C and D is the correct answer.
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The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
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A line being rotated in such a way I would think would be A
Answer:
Answer choice A) About 38.47 square units
Step-by-step explanation:
Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:
Since the area of a circle is , the area of this circle is:
Hope this helps!