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2 years ago

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Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

5 0

First expression: (-7)/(-4)

Divide. Note that two negative numbers divided will result in a positive answer

(-7)/(-4) = 7/4 = 1.75

First expression: Greater than 1.

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Second expression: -(3/2)

Simplify: 3/2 = 1.5

-(1.5) = -1.5

Second expression: Less than -1

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Third expression: (-8/5) x (-5/8)

Note that two negatives = one positive answer when multiplying

8/5 x 5/8 = 40/40 = 1

Third expression: Neither

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Fourth Expression: (-5)/(-3)

Divide: (-5)/(-3) = 5/3 = ~1.67

Fourth Expression: Greater than 1

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Fifth Expression: (-9)/6

Divide: (-9)/6 = -1.5

Fifth expression: Less than -1

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hope this helps

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Answer:

$f(x) = 63000(0.97)^x$

Step-by-step explanation:

Given

$f(0) = 63000$ ---x = 0, in 2012

$f(5) = 54100$ -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

$f(x) = ab^x$

Where

$b = rate$

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

$f(x) = 63000(0.97)^x$

Set x = 0

$f(0) = 63000(0.97)^0 = 63000*1=63000\\$

Set x = 5

$f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100$

This is true because the calculated values of f(0) and f(5) correspond to the given values

For option (d), we have:

$f(x) = 52477(0.97)^x$

Set x = 0

$f(0) = 52477(0.97)^0 - 52477* 1 = 52477$

This is false because the calculated value of f(0) does not correspond to the given value

For option (e), we have:

$f(x) = 63000(0.97)^\frac{1}{5x}$

Set x = 0

$f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =$ undefined

This is false because the f(x) is not undefined at x = 0

For option (f), we have:

$f(x) = 52477(0.97)^{5x$

Set x = 0

$f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477$

This is false because the calculated value of f(0) does not correspond to the given value

From the computations above, only (c) $f(x) = 63000(0.97)^x$ is true

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2 years ago

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rusak2 [61]

Answer:

The amount of water left in the tank is approximately 58.1 cubic meters

Step-by-step explanation:

step 1

Find the volume of the a cube shape tank

The volume is equal to

$V=b^{3}$

we have

$b=4.6\ m$

substitute

$V=4.6^{3}=97.336\ m^{3}$

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Find the volume of cone

The volume is equal to

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we have

$r=2.5\ m$

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$V=39.25\ m^{3}$

step 3

Find the difference of the volumes

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2 years ago

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Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

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Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

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