The discriminant formula is used to determine the nature of the roots of a quadratic equation. The discriminant of a quadratic equation $ax^{2} +bx+c=0$ is D = $b^{2} -4ac$

If D > 0, then the equation has two real distinct roots.

If D = 0, then the equation has only one real root.

Given that: $Area\; of \;walkway,\; a(w)\;= 4w^{2} + 100 w$

also, area of walkaway = 464 square feet.

So, $4w^{2} + 100 w =464$

$4w^{2} + 100 w -464=0$

Using Discriminant method,

a=4, b=100, c=-464

$w= \frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

w= $\frac{-100\pm\sqrt{(100)^{2}-4*4*(-464)} }{2*4}$

w= $\frac{-100\pm\sqrt{17424} }{8}$

So, $w_1= \frac{-100+\sqrt{17424} }{8} \;\;\;\; w_2= \frac{-100-\sqrt{17424} }{8}$

$w_1= \frac{-100+132 }{8} \;\;\;\; w_2= \frac{-100-132}{8}$

$w_1 = 4 \;\;\;\; and \;\;\; w_2= -29$

Hence the width of the walkaway be 4 feet.

Learn more about discriminant formula here:

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8 0

1 year ago

99 POINTS

inysia [295]

Answer:

Part a) The exact area of the sidewalk is $80\pi\ m^{2}$

Part b) The approximate area of the sidewalk is $251.2\ m^{2}$

Step-by-step explanation:

we know that

The area of the sidewalk is equal to the area of the outer circle minus the area of the inner circle

Part a) Find the exact area of the sidewalk

$A=\pi (12)^{2} -\pi (8)^{2}$

$A=\pi [144-64]$

$A=80\pi\ m^{2}$

Part b) Find the approximate area of the sidewalk

assume $\pi=3.14$

substitute

$A=80(3.14)=251.2\ m^{2}$

5 0

2 years ago

5×6 ÷ (9-4)= use PEMDAS FORGOT HOW TO DO THIS

Morgarella [4.7K]

PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction

This is the order of how to solve the problems. For this problem, we can start with parentheses since it has that in this equation.

5 x 6 ÷ (5)

The next step is to do Multiplication.

30 ÷ 5

Finally Division.

This is your final answer.

Hope that helps!

5 0

3 years ago

Read 2 more answers