The equation is the form:
Height = Constant / Width

There are several points that can be used to determine the constant. Picking out one which is (4,20)
20 = Constant / 4
Constant = 4(20)
Constant = 80

The constant is 80.

3 0

3 years ago

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What are all of the real roots of the following polynomial? f(x) x^4-24x^2-25

Greeley [361]

Answer:

x = ±5

Step-by-step explanation:

We are given the following polynomial function and we are to find all of its real roots:

$x^4-24x^2-25$

Let $y=x^2$ so we can now write it as:

$y^2-24y-25$

Factorizing it to get:

$(y^2+y)+(-25y-25)$

$y\left(y+1\right)-25\left(y+1\right)$

$\left ( y + 1 \right ) \left ( y - 2 5 \right)$

Substitute back $y=x^2$ to get:

$\left ( x^2 + 1 \right ) \left ( x^2 - 25 \right )$

$\left ( x^2 + 1 \right ) \left ( x + 5 \right ) \left ( x - 5 \right )$

The quadratic factor has only complex roots. Therefore, the real roots are x = ±5.

3 0

4 years ago

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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros for

timama [110]

The general form of a polynomial is: x² + bx + c = 0. Substituting the roots,

3² + b(3) + c = 0
3b + c = -9 --> eqn 1

(5 + √5)² + (5 +√5)(b) + c = 0
(5+√5)b + c = -30-10√5 --> eqn 2

Solving both equations simultaneously by subtracting eqn 2 from eqn 1,
(-2 - √5)b = 21 + 10√5
b = -8 - √5

Using eqn 1,
3(-8 - √5) + c = -9
-24 - 3√5 + c = -9
c = -9 + 24 + 3√5
c = 15 + 3√5

Hence, the polynomial is: f(x) = x² + (-8 - √5)x + (15 + 3√5).

7 0

4 years ago