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3 years ago

6

The decay of 942 mg of an isotope is described by the function A(t)= 942e-0.012t, where t is time in years. Find the amount left

after 71 years. Round your answer to the nearest mg.

2 answers:

ad-work [718]3 years ago

6 0

That would be 942 e^(-0.012*71) = 401.82 mg (answer)

Katarina [22]3 years ago

4 0

$\bf A(t)=942e^{-0.012t}\qquad \boxed{\stackrel{\textit{after 71 years}}{t=71}}\qquad \qquad A(t)=942e^{-0.012(71)}
\\\\\\
A(t)\approx 401.82042087707606813879$

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prohojiy [21]

Answer:

20%

Step-by-step explanation:

$(200 000/ 250 000) = .8 = 80%, seguís pagando 80% entonces distes un descuento de 20% (100-80=20%)

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2. what is the area of the figure below?

Vera_Pavlovna [14]

For number two, to get the area, multiply 6 and 14 which is 84. C is the answer. I can’t see 3.

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The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?

andrew11 [14]

Answer:

Not a linear relationship

Step-by-step explanation:

Given

The attached table

Required

Linear or not

To do this, we simply calculate the slope of the table at different intervals.

Slope (m) is calculated as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (0.5,7.2)$

So, the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{7.2 - 0}{0.5-0}$

$m = \frac{7.2}{0.5}$

$m = 14.4$

Let:

Let:

$(x_1,y_1) = (1,10.7)$

$(x_2,y_2) = (2,12.2)$

So, the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{12.2 - 10.7}{2 - 1}$

$m = \frac{1.5}{1}$

$m = 1.5\\$

See that the calculated slopes are not equal.

Hence, it is not linear

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3 years ago

If I add the square of a number<br> to the number itself, I get 30.<br> What could the number be?

Wittaler [7]

Answer:

I know you could easily solve this just looking at it.

But if you want the algebraic solution:

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x^2 + x -30 = 0

a = 1

b = 1

c = -30

Using the quadratic formula:

x = [ -b +- sqr root (b^2 - 4ac) ] / 2a

x = [-1 +- sqr root (1 - 4 * 1 -30) ] / 2*1

x = [-1 +- sqr root (1 + 120) ] / 2

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Step-by-step explanation:

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3 years ago

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Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.

Shtirlitz [24]

Answer:

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

Step-by-step explanation:

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

$V=\pi r^2h=256$

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

$S=2\pi rh+2\pi r^2$

To solve this, we can express h in function of r:

$V=\pi r^2h=256\\\\h=\frac{256}{\pi r^2}$

And replace it in the surface equation

$S=2\pi rh+2\pi r^2=2\pi r(\frac{256}{\pi r^2})+2\pi r^2=\frac{512}{r} +2\pi r^2$

To optimize the function, we derive and equal to zero

$\frac{dS}{dr}=512*(-1)*r^{-2}+4\pi r=0\\\\\frac{-512}{r^2}+4\pi r=0\\\\r^3=\frac{512}{4\pi} \\\\r=\sqrt[3]{\frac{512}{4\pi} } =\sqrt[3]{40.74 }=3.44$

The radius that minimizes the surface is r=3.44 cm.

The height is then

$h=\frac{256}{\pi r^2}=\frac{256}{\pi (3.44)^2}=6.88$

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

$S=2\pi rh+2*(2\pi r^2)=2\pi rh+4\pi r^2$

We derive and equal to zero

$\frac{dS}{dr}=512*(-1)*r^{-2}+8\pi r=0\\\\\frac{-512}{r^2}+8\pi r=0\\\\r^3=\frac{512}{8\pi} \\\\r=\sqrt[3]{\frac{512}{8\pi}}=\sqrt[3]{20.37}=2.73$

The radius that minimizes the real surface is r=2.73 cm.

The height is then

$h=\frac{256}{\pi r^2}=\frac{256}{\pi (2.73)^2}=10.92$

The height that minimizes the real surface is h=10.92 cm.

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4 years ago