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3 years ago

What is the approximate circumference of a circle with a radius of 8.5 meters? Use π ≈ 3.14.

Mathematics

1 answer:

vovangra [49]3 years ago

4 0

Circumference = 2 pi r
Circumference = 2 x 3.15 x 8.5 m
Circumference = 53.4 metres

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Kamila [148]

Answer Interest rate = 12.3%

The compound interest formula is given by:

Where

A = Future amount

P = Present amount (Principal amount)

r = Interest rate in decimal form

n = No. of times compounded per year

t = time in years.

We can say that if:

Present amount = P

Future amount = 3P

r = 12.3/100 = 0.123

n = 1

t = ?

Substitute the values in the formula of compound interest:

Taking log on both sides.

Round off to nearest option

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3 years ago

A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and

nasty-shy [4]

Answer:

correct option is C) 2.8

Step-by-step explanation:

given data

string vibrates form = 8 loops

in water loop formed = 10 loops

solution

we consider mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = $\rho$

case (1)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

so here

$l = \frac{8 \lambda _1}{2}$ ..............1

$l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}$

and we know velocity is express as

velocity = frequency × wavelength .....................2

$\sqrt{\frac{Tension}{mass\ per\ unit \length }}$ = f × $\lambda_1$

here tension = mg

$\sqrt{\frac{mg}{\mu}}$ = f × $\lambda_1$ ..........................3

and

case (2)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

$l = \frac{10 \lambda _1}{2}$ ..............4

$l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}$

when block is immersed

equilibrium eq will be

Tenion + force of buoyancy = mg

T + v × $\rho$ × g = mg

and

T = v × $\rho$ - v × $\rho$ × g

from equation 2

f × $\lambda_2$ = f × $\frac{1}{5}$

$\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}$ .......................5

now we divide eq 5 by the eq 3

$\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}$

solve irt we get

$1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}$

relative density $\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}$

relative density = 2.78 ≈ 2.8

so correct option is C) 2.8

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3 years ago

20. Factor the expression. ^2 + 7 + 12

neonofarm [45]

Answer: x^2 + 19

Step-by-step explanation: Cancel out x^2 and add 7 and 12 together. 7 + 12 = 19. Next plug in x^2. So, its now x^2 + 19.

Hope this help!

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3 years ago

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