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aleksandrvk [35]
3 years ago
6

What are the x- and y-intercepts of f(x)=x^2-49?

Mathematics
1 answer:
svlad2 [7]3 years ago
7 0
X-intercept(s):
(7,0),(−7,0)(7,0),(-7,0)
y-intercept(s):
(0,−49)
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How does the degree relate to the extrema?
Alex_Xolod [135]
I'm assuming this is for apolynomial function. The question of whether a degreee is odd or even changes the look of a graph. An even-numbered degree forms a parabola, where (in the most basic form), the one minimum point (extrema) just touches the origin. An odd-numbered degree, in its most basic form, doesn't touch a point, it crosses it. It expands infinitely without extrema.

Let's assume you're just talking about quadratic functions (or [even] parabolic functions, to be more general), in which case something like x^2 (the simplest quadratic equation) and x^50 would have the same extreme minimum point.
5 0
3 years ago
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
3 years ago
What are the roots of the quadratic function f(b)=b^2-75
Ivahew [28]
Set f(b) = b^2 - 75 = to 0 and solve for b:

b^2 = 75
b^2 = 25(3)
b = plus or minus sqrt(25[3]) = plus or minus sqrt(25)*sqrt(3) = plus or minus 5 sqrt(3).
5 0
3 years ago
What is the result when 3x3 – 7x2 – 17x - 12 is divided by 2 – 4?
lisabon 2012 [21]
It is that’s wat I got 1028
8 0
3 years ago
Find the minimum value of the parabola y = x2 + 10.
natulia [17]

Answer:

(0,10)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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