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dybincka [34]
3 years ago
13

Radium-226 has a half-life of 1620 years. for a 150 gram sample, how many grams will remain after 200 years?

Mathematics
1 answer:
VashaNatasha [74]3 years ago
3 0
Ah, yes

if you start with P amount of something and the half life is h units (in years) and the time elapsed is t (in years) then the amount left is A

the equation is
A=P(\frac{1}{2})^\frac{t}{h}


so
given
h=1620
P=150
t=200
so
A=150(\frac{1}{2})^\frac{200}{1620}
A=150(\frac{1}{2})^\frac{10}{81}
use your calculator
A≈137.69781917515g
about 138grams left
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Graph the equation y = x2 + 8x + 12 on the accompanying set of axes. You must
UkoKoshka [18]

Answer:

Step-by-step explanation:

Roots:  set y = x^2 + 8x + 12 = 0 and solve for x:  x + 6 = 0, so x = -6 is one root.  The other is x = -2.  The corresponding points are (-6, 0) and (-2, 0).

y-intercept:  Let x = 0.  Then y = 12.  The y-intercept is (0, 12).

Axis of symmetry:  x = -b / (2a) => x = -8/(2*1) = -4:  x = -4

Vertex y-value:  evaluate y at x = - 4:  (-4)^2 + 8(-4) + 12 = -4:    (-4, -4)

Arbitrarily chosen x value:  x = 1 => 1^2 + 8(1) + 12 = 21:     (1, 21)

The five points are:  (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21).  The vertex is (-4, -4).  The parabolic graph opens UP.

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3 years ago
Find the values of x, y, and z. The diagram is not to scale.
rosijanka [135]

Answer:

x= 81°, z= 99°, y°=68°

Step-by-step explanation:

considering the part of the triangle where 36° , 63° and x° is located as ΔABC.

to find the measure of x we use angle sum property.

We know that the sum of the angles of a triangle is always 180°. Therefore, if we know the two angles of a triangle, and we need to find its third angle, we use the angle sum property. We add the two known angles and subtract their sum from 180° to get the measure of the third angle.

so,

∠A + ∠B +∠C = 180°

36° + 63° + x° = 180°

99° + x° = 180°

x° = 180 - 99

x° = 81°

When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.

x° + z° = 180°

81° + z = 180°

z= 180 - 81

z= 99°

considering the next part of the triangle where 13° , z° and y° is located as ΔACD

to find the measure of y we use angle sum property.

∠A + ∠C + ∠D = 180°

13° + z° + y° = 180°

13°+99°+y°= 180°

112°+ y° = 180°

y°= 180- 112

y° = 68°

5 0
2 years ago
The height of a square pyramid-shaped gift box is one half the length of
Schach [20]

Answer:

15 inches

Step-by-step explanation:

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V = a²(h/3)

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h =1/2 a

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4500 = a² * a/2 * 1/3

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(27000)⅓ = a

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h = 1/2a

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5 0
3 years ago
Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins
elixir [45]

Answer:

( l+w)

Step-by-step explanation:

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3 years ago
Read 2 more answers
Which angles are coterminal with an angle drawn in standard position measuring 282°?
vampirchik [111]

Answer:

−438°, -78°, 642°

Step-by-step explanation:

Given angle:

282°

To find the co-terminal angles of the given angle.

Solution:

Co-terminal angles are all those angles having same initial sides as well as terminal sides.

To find the positive co-terminal of an angle between 360°-720° we will add the angle to 360°

So, we have: 282\°+360\°=642\°

To find the negative co-terminal of an angle between 0° to -360° we add it to -360°

So, we have:  282\°-360\°=-78\°

To find the negative co-terminal of an angle between -360° to -720° we add it to -720°

So, we have:   282\°-720\°=-438\°

Thus, the co-terminal angles for  282° are:

−438°, -78°, 642°

7 0
3 years ago
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