Please Help:

Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.

Korolek [52]

Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t

7 0

3 years ago

In the diagram shown, line m is parallel to line n . Justine says that ∠3 ∠ 3 and ∠7 ∠ 7 are supplementary angles. Is she correc

agasfer [191]

The correct answer is C.

Because by looking at the diagram you can see that angles 7 and 8 are intersected

6 0

3 years ago

Write the fact family for 5,8,and 40

Juli2301 [7.4K]

A fact family is basically just different equations with the same numbers getting the same/different numbers as answers you might say...
this will make more sense:
5x8=40
8x5=40
40/8=5
40/5=8

4 0

3 years ago

The sum of two numbers is 51. The larger number is 17 more than the smaller number. What are the numbers ?

Serggg [28]

Answer:

The numbers are 17 and 34.

Step-by-step explanation:

I just subtracted 17 from 51, it equals 34, and 34 is 17 more than 17. Add 34 and 17 and you get 51.

4 0

3 years ago

Find the distance between P1(4,16degrees) and P2(-2,177degrees) on the polar plane.

bazaltina [42]

Polar coordinates give the distance from the origin and the angle from the positive x axis. Cartesian coordinates give the distance from the x and y axes.

You can draw a right triangle with these values. (see attached)
If you know the r value and theta of that triangle below, you can use trig to find x and y.

Let's convert (4, 16°) to Cartesian coordinates.

Note that since our angle is acute, (in Quadrant I) our sine and cosine will both be positive, as you should be able to derive from the unit circle, where cosine is represented as an x value and sine is represented as a y value.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(16°) = x/4
4cos(16°) = x ≈ 3.84504678375

sine = oppsite / hypotenuse
sinθ = y/r
sin(16°) = y/4
4sin(16°) = y ≈ 1.10254942327<span>

So (4, 16°) </span>⇒ (3.84504678375, 1.10254942327).

Let's convert (-2, 177°) to Cartesian coordinates.
Whenever you have a negative radius, that means to put the point opposite where it would have been if it had a positive radius. (see attached)

In that case, we can essentially add 180° to our current 177° to the same effect. That means that (-2, 177°) = (2, 357°).

Note that since our angle is in Quadrant IV, our cosine will be positive, but our sine will be negative. (as derived from the unit circle) We don't have to worry about this since our calculator figures this for us, but you should pay attention to it if you are converting from Cartesian to polar.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(357°) = x/2
2cos(357°) = x ≈ 1.99725906951

sine = opposite / hypotenuse
sinθ = y/r
sin(357°) = y/2
2sin(357°) = y ≈ -0.10467191248

So (-2, 177°) ⇒ (1.99725906951, -0.10467191248).

Now we must use the distance formula with our two points.
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d\approx\sqrt{(1.99725906951-3.84504678375)^2+(-0.10467191248-1.10254942327)^2}$
$d\approx\sqrt{-1.84778771^2+-1.20722134^2}$
$d\approx\sqrt{3.41431942+1.45738336}$
$d\approx\sqrt{4.87170278}$
$\boxed{d\approx2.20719342}$

7 0

3 years ago