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Yuliya22 [10]
3 years ago
10

Show that A(t)=300−250e0.2−0.02t satisfies the differential equation ⅆAⅆt=6−0.02A with initial condition A(10)=50 .

Mathematics
1 answer:
Elina [12.6K]3 years ago
8 0

Step-by-step explanation:

dA/dt = 6 − 0.02A

dA/dt = -0.02 (A − 300)

Separate the variables.

dA / (A − 300) = -0.02 dt

Integrate.

ln(A − 300) = -0.02t + C

Solve for A.

A − 300 = Ce^(-0.02t)

A = 300 + Ce^(-0.02t)

Use initial condition to find C.

50 = 300 + Ce^(-0.02 × 10)

50 = 300 + Ce^(-0.2)

-250 = Ce^(-0.2)

C = -250e^(0.2)

A = 300 − 250e^(0.2) e^(-0.02t)

A = 300 − 250e^(0.2 − 0.02t)

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Rewrite this number in appropriate scientific notation of 4,770,000
Cerrena [4.2K]
The number 4,770,000 in appropriate scientific notation would be 4.770000x10^16

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3 years ago
The points(0,2) and (4,-10) lie on the same line and the points (-5,-3) and (2,11) lie on another line. Determine by graphing wh
joja [24]
You are asked to do this problem by graphing, which would be hard to do over the Internet unless you can do your drawing on paper and share the resulting image by uploading it to Brainly.

If this were homework or a test, you'd get full credit only if you follow the directions given.

If <span>The points(0,2) and (4,-10) lie on the same line, their slope is m = (2+10)/(-4), or   m =-3.  Thus, the equation of this line is y-2 = -3x, or y = -3x + 2.

If </span><span>points (-5,-3) and (2,11) lie on another line, the slope of this line is:

m = 14/7 = 2.  Thus, the equation of the line is y-11 = 2(x-2), or y = 11+2x -4, or y = 2x + 7.

Where do the 2 lines intersect?  Set the 2 equations equal to one another and solve for x:

</span>y = -3x + 2 = y = 2x + 7.  Then 5x = 5, and x=1.

Subst. 1 for x in y = 2x + 7, we get y = 2(1) + 7 = 9.

That results in the point of intersection (2,9).

Doing this problem by graphing, on a calculator, produces a different result:  (-1,5), which matches D.

I'd suggest you find and graph both lines yourself to verify this.  If you want, see whether you can find the mistake in my calculations.

3 0
3 years ago
Help will give Brainly points
Nesterboy [21]
No they are not… not the same size
3 0
2 years ago
PLEASE HELP, I’LL GIVE BREAINLIST!
zzz [600]

Answer:

1/72

Step-by-step explanation:

Not entirely sure but i do hope it helps

5 0
3 years ago
Read 2 more answers
N n N n N n N n N n n N N Suppose that you were to draw a random sample of one letter from the set of letters above. Two possibl
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Answer:

10/13 = 76.92%

Step-by-step explanation:

The question is missing some information because the underline is missing.

If we make table based on if the letter upper case (A) or lower case(a), and if the letter underlined(B) vs not underlined(b) the data will be:

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B           4           3         7

b           3           3         6

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4 0
3 years ago
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