Can i get some help please. Which expressions are equivalent to

For the differential equation dy/dt=ky, k is a constant, y(0)=24, and y(1)=18. What is the value of k?

Gre4nikov [31]

The equation is separable, so solving it is trivial:

$\dfrac{\mathrm dy}{\mathrm dt}=ky\implies\dfrac{\mathrm dy}y=k\,\mathrm dt$

Integrating both sides gives

$\ln|y|=kt+C\implies y=e^{kt+C}=Ce^{kt}$

Given $y(0)=24$ and $y(1)=18$ , we find

$24=C$

$18=Ce^k=24e^k\implies e^k=\dfrac34\implies k=ln\dfrac34$

so the answer is E.

8 0

3 years ago

Read 2 more answers

Whats the distance between the points (2, 7) and (2, 15)

sveta [45]

Answer:

The distance between the points (2, 7) and (2, 15) is 8.

Step-by-step explanation:

<u>What is the Distance between Two Points?</u>

For any two points there is exactly one line segment connecting them. The distance between two points is the length of the line segment connecting them. Note that the distance between two points is always positive. Segments that have equal length are called congruent segments.

How to Solve:

Formula:

$\sqrt{(x2-x1)^2+(y2-y1)^2}$

Putting Values:

$=\sqrt{(2-2)^2+(15-7)^2}$

$=\sqrt{(0)^2+(8)^2}$

$=\sqrt{0+64}$

$=\sqrt{64}$

$=8$

7 0

2 years ago

analyze the diagram below and complete the instructions that follow . find the value of z. A.11 B.32 C.50 D.68

masha68 [24]

Answer:

50

Step-by-step explanation:

x = √30² - 18² = √576 = 24

tan A = 18/24 = 3/4

∠A = ∠B

tan B = tan A = 24 / y = 3 / 4

y = (24 x 4) / 3 = 32

Z = y + 18 = 32 + 18 = 50

3 0

3 years ago

How can you represent all of the solutions to systems of inequalities?

Dimas [21]

Answer:A closed, or shaded, circle is used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . The point is part of the solution. An open circle is used for greater than (>) or less than (<). The point is not part of the solution. Solving" systems of linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions". So I graph each inequality, and then find the overlapping portions of the solution regions.Step 1: Line up the equations so that the variables are lined up vertically. Step 2: Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same. Step 3: Subtract the two equations. Step 4: Solve the one variable system.

Step-by-step explanation:

hope this helps have a great night ❤️❤️❤️

6 0

3 years ago

Area of a 12 ft circle

Mnenie [13.5K]

113.10 feet, 16,286 square inches, 12.566 square yards, 10.507 square meters, 105,071 square centimeters

4 0

2 years ago