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3 years ago

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9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa use

d to draw her circle? Use 3.14 for pi.
A 6
B 15.7
C 3
D 9.42

1 answer:

Sonbull [250]3 years ago

3 0

A. 6

The circumference can be found just by multiplying the diameter by pi.

So all you need to do is 18.84/3.14 which is 6.

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

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1 year ago

it cost $20 per hour to bowl and $3 for shoe rental. write a verbal model and algebraic expressions to represent the cost for n

tatyana61 [14]

20n+3
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20 per hour
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2 years ago

What is the slope of a line perpendicular to the line with equation y = 5x – 2?

LekaFEV [45]

Answer:

- $\frac{1}{5}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x - 2 ← is in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{5}$

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3 years ago

PLEASE HELP ASAP!! THANKS SO MUCH

Wittaler [7]

Answer:

The relationship shows a direct linear variation with a constant of variation of 1.

Step-by-step explanation:

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3 years ago

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Find the radius of a sphere with a volume of 972π cubic millimeters.

sesenic [268]

Answer:

The radius is 9 mm

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3 where r is the radius

972 pi = 4/3 pi r^3

Divide each side by pi

972 = 4/3 r^3

Multiply each side by 3/4 to isolate r^3

3/4 * 972 = 4/3 * 3/4 r^3

729 = r^3

Take the cube root of each side

(729) ^ (1/3) = (r^3) ^ (1/3)

9 = r

The radius is 9 mm

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2 years ago

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