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4 years ago

13

A drop of oil of volume

- 10} " alt=" {10}^{ - 10} " align="absmiddle" class="latex-formula">

1 answer:

Monica [59]4 years ago

8 0

Answer:

$\frac{1}{10^{10}}\\$

Explanation:

$10^{-10}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\\10^{-10}=\\\frac{1}{10^{10}}\\\\\left(\mathrm{Decimal:\quad }\:0.0000000001\right)$

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slab of ice floats on water with a large portion submerged beneath the water surface. The slab is in the shape of a rectangular

n200080 [17]

Answer:

a) $\%V = 87.36\,\%$ , b) $x = 1.248\,m$ , c) $F_{B} = 176488.341\,N$ , d) Six polar bears.

Explanation:

a) The slab of ice is modelled by the Archimedes' Principles and the Newton's Laws, whose equation of equilibrium is:

$\Sigma F =\rho_{w}\cdot g \cdot A \cdot x-\rho_{i}\cdot g\cdot V = 0$

The height of the ice submerged is:

$\rho_{w}\cdot A \cdot x = \rho_{i}\cdot V$

$x = \frac{\rho_{i}\cdot V}{\rho_{w}\cdot A}$

$x = \frac{\left(900\,\frac{kg}{m^{3}}\right)\cdot (20\,m^{3})}{\left(1030\,\frac{kg}{m^{3}} \right)\cdot (14\,m^{2})}$

$x = 1.248\,m$

The percentage of the volume of the ice that is submerged is:

$\%V = \frac{(1.248\,m)\cdot (14\,m^{2})}{20\,m^{3}} \times 100\,\%$

$\%V = 87.36\,\%$

b) The height of the portion of the ice that is submerged is:

$x = 1.248\,m$

c) The buoyant force acting on the ice is:

$F_{B} = \left(1030\,\frac{kg}{m^{3}} \right)\cdot (1.248\,m)\cdot (14\,m^{2})\cdot \left(9.807\,\frac{m}{s^{2}} \right)$

$F_{B} = 176488.341\,N$

d) The new system is modelled after the Archimedes' Principle and Newton's Laws:

$\Sigma F = -n\cdot m_{bear}\cdot g-\rho_{i}\cdot V \cdot g + \rho_{w}\cdot V\cdot g = 0$

The number of polar bear is cleared in the equation:

$n\cdot m_{bear} = (\rho_{w} - \rho_{i})\cdot V$

$n = \frac{(\rho_{w}-\rho_{i})\cdot V}{m_{bear}}$

$n = \frac{\left(1030\,\frac{kg}{m^{3}} - 900\,\frac{kg}{m^{3}} \right)\cdot (20\,m^{3})}{400\,kg}$

$n = 6.5$

The maximum number of polar bears that slab could support is 6.

8 0

3 years ago

Read the question below.

Oxana [17]

Answer:

Experimental

Explanation:

Here the dependency of pressure on the temperature is to be determined. For finding this factor we need to calculate the pressure of the object at different temperature.

The process of calculating pressure for different temperature is experimental investigation because we need to perform this experiment for finding these value. On the basis of observed values the we can conclude the dependency.

Thus, this investigation is experimental.

8 0

3 years ago

Read 2 more answers

GIVING BRAINLIEST PLS HELP!!!

MA_775_DIABLO [31]

Answer:

it's the first one

Explanation:

Have a great day hope it helps

3 0

3 years ago

Dimensional formula of frequency with explation

____ [38]

Frequency:

Frequency is defined as number of events occurring per second.

Mathematically written as

$f=\frac{no. of events}{time}$

The dimensions $f$ are

$[f]=\frac{1}{[T]}$

as

$[T]=[S]$

so,

$[f]=[S^{-1}]$

5 0

3 years ago

Find the coefficient of x3 y4 in the expansion of ( x+2y )^7.

yKpoI14uk [10]

Answer:

The coefficient of x³y⁴ in the expansion of ( x+2y)⁷ is 560.

Explanation:

The given expression is

$(x+2y)^7$

According to binomial expansion,

$(a+b)^n=^nC_0a^nb^0+^nC_1a^{n-1}b^1+...+^nC_{n-1}a^1b^{n-1}+^nC_0a^0b^n$

The r+1th term of the expansion is

$^nC_rx^{n-r}(2y)^r=^nC_r(2^r)x^{n-r}(y)^r$ ... (1)

In the term x³y⁴ the power of x is 3 and the power of y is 4. It means the value of r is 4 and the value n-r is 3.

$n-r=3$

$n-4=3\Rightarrow n=7$

Put n=7 and r=4 in equation (1)

$^7C_4(2^4)x^{7-4}(y)^4$

$\frac{7!}{4!(7-4)!}(16)x^3y^4$

$\frac{7\times 6\times 5\times 4!}{4!(3)!}(16)x^3y^4$

$560x^3y^4$

Therefore the coefficient of x³y⁴ in the expansion of ( x+2y)⁷ is 560.

5 0

4 years ago