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3 years ago

13

What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is a perfect squa

re?

1 answer:

Zigmanuir [339]3 years ago

6 0

Answer:

two real solutions

Step-by-step explanation:

You might be interested in

Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

3 years ago

Suma de fraccion 1/5 + 5/8

lbvjy [14]

Answer:

33/40

Step-by-step explanation:

1/5x8= 8/40

5/8x5=25/40

add them

reduce answer:

33/40

3 0

2 years ago

Read 2 more answers

The point (-1,4)is translated five units right and three units down.which rule describes the translation

xz_007 [3.2K]

Answer:

(x, y ) → (x + 5, y - 3 )

Step-by-step explanation:

5 units right means add 5 to the x- coordinate

3 units down means subtract 3 from the y- coordinate

the translation rule is

(x, y ) → (x + 5, y - 3 )

5 0

2 years ago

To find the surface area of the pyramid, in square inches, Vikram wrote (33.2) (34.2) + 4 (one-half (34.2) (28.4)). What error d

madam [21]

Answer:

B. He used the wrong expression to represent the area of the base of the pyramid.

Step-by-step explanation:

Given

See attachment for pyramid

$Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4$

Required

Vikram's error

The surface area of a square pyramid is:

$Area = Base\ Area + 4 * Area \triangle$

Where

$Base\ Area = Length * Length$

$Base\ Area = 34.2 * 34.2$

$4 * Area \triangle = 4 * \frac{1}{2} * Base * Height$

$4 * Area \triangle = 4 * \frac{1}{2} * 34.2 * 28.4$

So:

$Area = Base\ Area + 4 * Area \triangle$

$Area = 34.2 * 34.2 + 4 * \frac{1}{2} * 34.2 * 28.4$

By comparing the calculated expression with

$Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4$

Option (b) is correct

3 0

3 years ago

Write y= - 4x on a graph

ELEN [110]

If u put in a graphing calculator and look at the table you can plot the points given

8 0

2 years ago