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2 years ago

Please help if u can your a life saver!

Mathematics

1 answer:

Rom4ik [11]2 years ago

7 0

Answer:

189.25in^2

Step-by-step explanation:

$\pi$ r^2

a*b

3.14 * 5^2 = 78.5

78.5/2 = 39.25

10 * 15 = 150

39.25+150=189.25

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Add the following fractions. 3/8 + 5/12 = a 8/20 b 19/24 c 8/24 d 1/3

loris [4]

3/8 + 5/12 =

B. 19/24

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3 years ago

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The population of a city grows exponentially at rate of 8% per year.Find the number of years it takes for the population to be d

Ilya [14]

Answer:

It will take 9 years for the population to double

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.

Substituting in the equation:

$2P_o=P_o(1+0.08)^t$

Simplifying:

$2=(1.08)^t$

Taking logarithms:

$\log 2=\log (1.08)^t$

Applying the exponent property of logs:

$\log 2=t\log (1.08)$

Solving for t:

$\displaystyle t=\frac{\log 2}{\log (1.08)}$

Calculating:

$t\approx 9$

It will take 9 years for the population to double

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2 years ago

2+2+6+6+6+6+66+66666

alexira [117]

2+2=4
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3 years ago

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

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so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

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3 years ago

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Step-by-step explanation: I took the test and got it wrong, but they told me the correct answers after I took the test. (I got to K-12) Proof:

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2 years ago