answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
steposvetlana
14 days 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:
Leona [4.1K]14 days ago
8 0

Detailed derivation:

dA/dt = 6 - 0.02A

dA/dt = -0.02 (A - 300)

Rearranging terms.

dA / (A - 300) = -0.02 dt

Integrate both sides.

ln(A - 300) = -0.02t + C

Isolate A.

A - 300 = Ce^(-0.02t)

A = 300 + Ce^(-0.02t)

Apply initial condition to determine 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)

You might be interested in
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?
babunello [3635]

Answer:

The transformation is a reflection over the x-axis followed by a translation 6 units left and 2 units down.

Step-by-step explanation:

To determine the order of transformations from ΔABC to ΔA"B"C", note that the figure first changes to ΔA'B'C', and then to ΔA''B''C''.

The transition from ΔABC to ΔA'B'C' involves a reflection over the x-axis, as ΔA'B'C' appears as a mirror image flipped vertically.

Next, moving from ΔA'B'C' to ΔA''B''C'' entails shifting the figure left by 6 units and downward by 2 units. This matches a translation by -6 in the x direction and -2 in the y direction.

Thus, the accurate description is:

Reflection across the x-axis followed by a translation of -6 units in x and -2 units in y.

4 0
15 days ago
Read 2 more answers
Write three numbers for which you would use the hundreds place to compare to 35,712​
Leona [4166]

Answer:

  • 35,694
  • 35,981
  • 35,102

Step-by-step explanation:

If you compare numbers based on the hundreds digit, the digits to the left (thousands and ten-thousands) remain the same, while the hundreds digit differs.

This applies for any five-digit numbers structured like:

(3)(5)(not 7)(any digit)(any digit).

Digits to the right of the decimal point, as well as those in the tens and ones places, don't impact this comparison.

5 0
15 days ago
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? m – negative StartFractio
zzz [4022]

Answer: To remove fractions prior to solving, each term in the equation must be multiplied by 4.

Step-by-step explanation:

Consider the given expression:

-\frac{3}{4}m-\frac{1}{2}=2+\frac{1}{4}m

It is essential to simplify this before attempting to solve it.

Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.

Break down the denominators into their prime components:

4=2*2=2^2\\2=2

Select 2^2, as it possesses the greatest exponent. Thus:

LCD=2^2=4

Ultimately, to remove the fractions before solving, multiply both sides by 4:

(4)(-\frac{3}{4}m)-(4)(\frac{1}{2})=(4)(2)+(4)(\frac{1}{4}m)\\\\-3m-2=8+m

7 0
1 day ago
Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?
Zina [3914]
Without specific options available, I can provide guidance on where to focus your attention.

The end behavior of a function refers to how the graph behaves (upwards or downwards) as it nears positive or negative infinity within its domain. Essentially, we’re investigating the direction the graph tends towards on both sides.

In this scenario, as the value of x grows, the graph descends, while it ascends when x diminishes. Seek out a comparable occurrence.
4 0
10 days ago
Read 2 more answers
C) Your parents have been advised to save 5% of their income for your college education
Svet_ta [4321]

48,948 * 5% = 2447.4

7 0
8 days ago
Read 2 more answers
Other questions:
  • If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (StartFraction r Over s EndFraction) (6)?
    10·1 answer
  • The function g(x) is graphed. On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- a
    6·2 answers
  • Ben has 400 counters in a bag. He gives 35 of the counters to Sonia 130 of the counters to Phil 75 of the counters to Lance What
    14·2 answers
  • Three judges measure the lap times of a runner and each measurement is different from the others by a few hundredths of a second
    13·1 answer
  • A sailboat travels a distance of 2 1/2 miles in 1/6 of an hour.Which complex fraction represents the unit rate in miles per hour
    9·1 answer
  • The final score of a figure skating competition is determined by finding the average of six judges' scores. Write a formula for
    5·2 answers
  • Given the points below find XY. Round to the nearest hundred. X(-9,2) Y(5,-4)
    12·2 answers
  • What is the equation of the translated function, g(x), if f(x) = x2?
    7·1 answer
  • What is the range of the function represented by the graph?
    9·2 answers
  • Mike has coffee worth $4 per pound that he wishes to mix with 20 pounds of coffee worth $7 per pound to get a mixture that can b
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!