Write 12,430,000 in expanded form

An arch in the shape of a parabola has a height of 50 feet at the center and a span of 120 feet across. Find the height of the a

Feliz [49]

Check the picture below.

so, we know the parabola has a vertex at (0 , 50), we also know it passes through (60 , 0), so then

$~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\stackrel{vertex}{(0~~,~~50)}\implies y=a(x-0)^2+50\implies y = ax^2+50 \\\\\\ \begin{cases} x =60\\ y = 0 \end{cases}\implies 0=a6^2+50\implies -50=3600a\implies -\cfrac{50}{3600}=a \\\\\\ -\cfrac{1}{72}=a~\hfill therefore~\hfill \boxed{y=-\cfrac{1}{72}x^2+50}$

so then, what's "y" when x = 25?

$y=-\cfrac{1}{72}25^2+50\implies y = -\cfrac{625}{72}+50\implies y = \cfrac{2975}{72}\implies y\approx 41.32$

8 0

3 years ago

The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −2, −1, 1 and 3.

Sergio [31]

Answer:

f(x) = x^4 - x^3 - 7x^2 + x + 6

Step-by-step explanation:

Please, always share the instructions with every question you post. I am assuming that you are to write out the factors corresponding to the given roots, thus constructing a 4th degree polynomial, and then performng the multiplication necesssary to produce that polynomial with terms in descending order by power of x. Note that there must be 5 such terms.

f(x) = (x + 2)(x + 1)(x - 1)(x - 3)

Multiplying this out, we get:

f(x) = (x + 2)(x^2 - 1)(x - 3), or

f(x) = (x^3 - x + 2x^2 - 2)(x - 3), or:

f(x) = (x^3 + 2x^2 - x - 2)(x - 3), or:

f(x) = x^4 + 2x^3 - x^2 - 2x - 3x^3 - 6x^2 + 3x + 6

Combining like terms, we get:

f(x) = x^4 - x^3 - 7x^2 + x + 6

Note that because this is a 4th degree polynomial, the end behavior resembles that of the graph of y = x^4. As x increases, y initially decreases in Quadrant II, passes through the y-intercept (0, 6), and then increases without bound in Quadrant I.

5 0

4 years ago

Clarify the below Question

zavuch27 [327]

Yes I do clarify the answer

8 0

2 years ago

What is the coefficient of 5x4

tatiyna

5

option A

hope it helps...!!!

5 0

2 years ago

Use the information in the diagram to determine the height of the tree to the nearest foot.

algol13

Answer:

The correct option is A. The height of tree is 60 ft.

Step-by-step explanation:

From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.

According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.

Using midpoint theorem of triangle, we can say that the length of tree is half of the building.

$Tree=\frac{1}{2}\times Building$

$Tree=\frac{1}{2}\times 120$

$Tree=60$

Therefore correct option is A. The height of tree is 60 ft.

5 0

3 years ago