The height y (in feet) of a punted football is given by -16/2025x^2 + 9/5x + 2.5 where x is the horizontal distance (in feet) from the point at which the ball is punted. (a) How high is the ball when it is punted?
(b) What is the maximum height of the punt? (Round your answer to two decimal places.)
(c) How long is the punt? (Round your answer to two decimal places.)

Answers

Answer 1

Answer: a) The ball is 2.5 feet high when it is punted ( for: x=0 )
b) The maximum height ( formula for the parabola):Ymax= $(4ac-b^(2) )/(4a)= (4* (-16)/(2025)*25- (9)/(5)^(2) )/(4* (-16)/(2025) )$
Finally: Ymax= 105.02 feet.
c)We will find how long is the punt with the formula:
$- (16)/(2025) x^(2) + (9)/(5)x +2.5=0$
We will multiply it by 2025 to avoid the fractions:
$-16 x^(2) +3645x+5062.5=0$
And we will solve it:
$x_(12) = \frac{-b\pm \sqrt{b^(2) -4ac} }{2a}= (-3645\pm √(13286025+324000) )/(-32) x_(1)= (-3645-3689.1767)/(-32)$
x=229.19 feet.
We will except this answer because another one is negative.

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Does the following set of coordinates represent a function? *1 point
{(-2, 1), (3, 11), (-4,-3), (-2, 8), (0,5)}
Yes
No

Answers

Answer:

no because the x value -2 has two corasponding y values

Step-by-step explanation:

What are the possible number of positive, negative, and complex zeros of f(x) = x6 – x5– x4 + 4x3 – 12x2 + 12 ?

Answers

This is a polynomial with more than 2 as a degree. Using Descartes Rule of Signs:
f(x) = x⁶ + x⁵ + x⁴ + 4x³ − 12x² + 12
Signs: + + + + − + 2 sign changes ----> 2 or 0 positive roots
f(−x) = (−x)⁶ + (−x)⁵ + (−x)⁴ + 4(−x)³ − 12(−x)² + 12 f(−x) = x⁶ − x⁵ + x⁴ − 4x³ − 12x² + 12
Signs: + − + − − + 4 sign changes ----> 4 or 2 or 0 negative roots
Complex roots = 0, 2, 4, or 6

Descarte's Rule of Sign is useful for finding the zeroes of a polynomial. The rule will tell you how many roots you can expect and of which type not where the polynomial's zeroes are. This rule is given as follows:

$For \ a \ polynomial \ f(x)=a_(n)x^n+a_(n-1)x^(n-1)+ \ldots a_(2)x^2+a_(1)x+a_(0) \n \n with \ real \ coefficients \ and \ a_(0) \neq 0$

$\bullet \ The \ number \ of \ \mathbf{positive \ real \ zeros} \ of \ f \ is \ either \ equal \ to \n the \ number \ of \ variations \ in \ sign \ of \ f(x) \ or \ less \ than \ that \n number \ by \ an \ even \ integer. \n \n \bullet \ The \ number \ of \ \mathbf{negative \ real \ zeros} \ of \ f \ is \ either \ equal \ to \n the \ number \ of \ variations \ in \ signs \ of \ f(x) \ or \ less \ than \ that \n number \ by \ an \ even \ integer.$

That is, the function:

$f(x)=x^6-x^5-x^4+4x^3-12x^2+12 \n \n \n + \ - \ - \ + \ - \ + \n \n Has \ four \ changes \ in \ sign$

4, 2, or 0 positive roots

On the other hand, the function:

$f(-x)=(-x)^6-(-x)^5-(-x)^4+4(-x)^3-12(-x)^2+12 \n \n f(-x)=x^6+x^5-x^4-4x^3-12x^2+12 \n \n \n + \ + \ - \ - \ - \ + \n \n Has \ 2 \ changes \ in \ sign$

2, or 0 negative roots

Finally:

Complex roots: 0, 2, 4, or 6

the length of a rectangle is 3 more than the width. if the area is 40 square inches, what is an equation to find the area and what is the length of the rectangle

Answers

Answer:

5 x 8 = 40 square cm

Step-by-step explanation:

Ricardo read that it may be unhealthy to eat more than 5,500 mg of table salt (NaCl) in a day. He wants to see how much salt 5,500 mg is, but his scale only weighs in units of grams.How many grams of salt should he measure out on the scale?
0.055 g
55 g
550 g
5.5 g

Answers

Answer:

5.5 grams

Step-by-step explanation:

i did it on study island

sorry, we haven't studied that yet :(

How many triangles exist with the given side lengths?12 in, 15 in, 18 in
A) No triangle exists with the given side lengths.
B) Exactly one unique triangle exists with the given side lengths.
C) More than one triangle exists with the given side lengths.

Answers

According to triangle inequality theorem, “The sum of the length of two sides of a triangle should be greater than the third side”. In order to verify the mentioned theorem, some calculations are performed below.

12 + 15 > 18

15 + 18 > 12

12 + 18 > 15

As the triangle inequality theorem satisfied, so there is only one triangle possible with the given sides length. No more than one triangle is possible, because the angles are not given, and the sides length are fixed.

So option “B” is correct.

Answer:

it is b

Step-by-step explanation:

What is the sum of all the positive integers from square root 14 to square root 80