Find the general solution of the following equation: y'(t) = 3y -5
Answer:
The general solution of the equation is y = [tex]\frac{A}{3}e^{3t}[/tex] + 5
Step-by-step explanation:
Since the differential equation is given as y'(t) = 3y -5
The differential equation is re-written as
dy/dt = 3y - 5
separating the variables, we have
dy/(3y - 5) = dt
dy/(3y - 5) = dt
integrating both sides, we have
∫dy/(3y - 5) = ∫dt
∫3dy/[3(3y - 5)] = ∫dt
(1/3)∫3dy/(3y - 5) = ∫dt
(1/3)㏑(3y - 5) = t + C
㏑(3y - 5) = 3t + 3C
taking exponents of both sides, we have
exp[㏑(3y - 5)] = exp(3t + 3C)
3y - 5 = [tex]e^{3t}e^{3C}[/tex]
3y - 5 = [tex]Ae^{3t}[/tex] [tex]A = e^{3C}[/tex]
3y = [tex]Ae^{3t}[/tex] + 5
dividing through by 3, we have
y = [tex]\frac{A}{3}e^{3t}[/tex] + 5
So, the general solution of the equation is y = [tex]\frac{A}{3}e^{3t}[/tex] + 5
which algebraic experssion is a difference with two term
Answer:
ok
Step-by-step explanation:
" a difference " means subtract
5y - 7......u have 2 terms (5y and 7)...and it is the difference of 2 terms.
so ur answer is : 5y - 7
pls mark me as brilliant
PLEASE HELP!! ASAP NOWWWW Two races that a student runs every year are the 1492-mile race in his hometown and the -meter race in his college town. Complete parts (a) through (d) below.
Answer:
College town race is 31% of the home town race.
Step-by-step explanation:
Length of hometown race = 3 miles
Length of college town race = 1492 meters
Since 1 meter = 0.0006214 miles
Therefore, 1492 = 0.93 miles
Percentage of college town race to the hometown race,
= [tex]\frac{\text{College town race}}{\text{Home town race}}\times 100[/tex]
= [tex]\frac{0.93}{3}\times 100[/tex]
= 31%
Therefore, the college town race is 31% of the home town race.
Please Help Me!!!!!!!
20. What is the least amount of principal you can invest at an 8% interest rate to earn at least $1000 in interest in 3 years?(Round your answer to the nearest dollar.)
A. $240
B. $5167
C. $20000
D. $4167
E. $6367
F. cannot be determined
Answer:
F. cannot be determined
Step-by-step explanation:
not enough information
What is the product of (-6)(-7)(-1)
142
0 14
0 42
Answer:
-42
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
(-6)(-7)(-1)
Step 2: Multiply -6 and -7 together
(-6)(-7) = 42
Step 3: Multiply 42 and -1 together
42(-1) = -42
What is the absolute value of 9?
Answer:
the absolute value of 9 is 9
Write an equation in slope-intercept form for the line described. Slope 9/2, passes through (0,-13/2)
Use slope-intercept equation form: [tex]y=mx+b[/tex]
We know that the slope is 9/2
[tex]y=\frac{9}{2}[/tex]
[tex]y=\frac{9}{2}x+b[/tex]
To solve for b, we can plug in the point given, since it's on the line.
[tex]-\frac{13}{2}=\frac{9}{2}(0)+b[/tex]
[tex]b=-\frac{13}{2}[/tex]
So the equation is: [tex]y=\frac{9}{2}-\frac{13}{2}[/tex]
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Hannah has 3 places to hang pictures on her wall.she has 6 possible pictures all together. How many possible arrangements of pictures can she hang?
The number of possible arrangements of pictures she can hang on her wall is 120.
How many possible arrangements of pictures can she hang?
The number of possible arrangements can be determined by dividing the factorial of 6 by the factorial of 3.
Number of possible arrangements = 6! / 3!
( 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 6 x 5 x 4 = 120
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Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64
Answer:
A) reflection over the x-axis, plus a vertical translation
Answer:
A
Step-by-step explanation:
EDGE 2020
Plzzz help !!!!!! Plzzzz
write the roster from of
{ x:x is a factor of 42 }
Answer:
the correct answer is
{2,3,6,7,14,21,}
-2(4n-8) helphelphelp
Answer:
-8n+16. You can also put 16-8n
2[( 62 -52) + 4]
Need help
Answer:
28
Step-by-step explanation: USE PEDMAS
2[(62-52)+4] = 2[(10)+4]= 2[14]=28
The point (2,6) lies on the graph of the equation y = kx^2 - 3x. Find the value of K.
Answer:
k=3
Step-by-step explanation:
just did it
Find the slope of the line passing through the points P (2,5) and Q (8,2)
Observations that deal with descriptions that cannot be expressed with numbers are called?
Answer:
rrrrrrrrrrrtuuuuuuuuuuuuuuuuu
Step-by-step explanation:
What is the additive inverse of 3x+4
Answer: y = (x - 7)/3
Step-by-step explanation:
4 cm
1
1
1
1
1
4 cm
/
5 cm
What is the volume of the solid?
Answer:
I don't know what you are asking.
Evaluate 3^2 + (6-2)x4-6/3
Answer:
23
Step-by-step explanation:
9+4x4-2
9+16-2
9+16-2
23
Answer:
23
Step-by-step explanation:
3 ^ 2 = 9
6 - 2 = 4
4 * 4 = 16
16 + 9 = 25
6/3/ = 2
25 - 2 = 23
7. Solve: 33 +21 + 3 - 5
Answer:
52
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
Step 1:
33 + 21 + 3 - 5
Step 2:
54 + 3 - 5
Step 3:
57 - 5
Answer:
52
Hope This Helps :)
Help just one question can you show steps
this is the answer hope this will help u
964,103 rounded to the nearest ten thousand
The cost C (in dollars) of making n watches is represented by C=15n+85. How many watches are made when the cost is $385?
Answer:
20=n
Step-by-step explanation:
Take 385 and subtract 85. You get 300. Divide 300 by 15n. You get 20.
20=n
If you want to double check, replace n with 20 so the equation is
C=(15x20)+85
Hope I help!
Tyler needs to complete this table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup contains 16 tablespoons. What belongs in cell A?
Answer: 96 teaspoons
Step-by-step explanation:
If 1 cup contains 16 tablespoons the 2 cups will contain;
= 16 * 2
= 32 tablespoons
If 1 tablespoon contains 3 teaspoons then 32 tablespoons will contain;
= 32 * 3
= 96 teaspoons
Two cruise ships left the same port. After two hours, Ship A is 30 miles west and 18 miles north of the port and Ship B is 10 miles west and 27 miles south of the port. If there is a tug boat located one-fifth of the way from Ship A to Ship B, find the location of the tug boat relative to the port.
Answer:
1.10
Step-by-step explanation:
that's your answer
The location of the tug boat relative to the port will be 30.83 miles.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles.
The distance of ship A from the port is x
X²= 18²+30²
X²= 324+900
X²=1224
X=34.9857 miles
Bearing from port:-
Tanθ= 18/30
θ = tan^-1 3/5
θ= 31°
N 31° E
The distance of ship B from the port is y.
Y²= 27²+10²
Y²= 729+100
Y²= 829
Y=28.7924 miles
Bearing from port:-
Tanθ = 2.2
θ = 69.7°
90-69.7= 20.3
N 20.3°W
The distance between the two ships is z.
Z²=34.9857²+28.7924²-2(24.9857)(28.7924)cos(31+69.7°)
Z²= 2053+267.1
Z²= 2320.1
Z=48.18 miles
One-fifth of 48.18
=9.63 miles
The distance of the boat is D.
D/sin 60 = 34.9857/sin 100.7
D=30.83 miles
Therefore, the location of the tug boat relative to the port will be 30.83 miles.
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An emu that measures 22 inches in height is 14 inches less than 2 times the height of a stuffed toy canary. What is the height of the stuffed toy canary? Jesus thinks the height of the canary is 18 inches. Is this true or false?
Answer: The height of the stuffed toy canary is 18 inches so Jesus is right.
Step-by-step explanation:
We can represent the first statement by the equation 22= 2x - 14 where x is the height of the stuffed toy canary so solve for x
22 = 2x -14 Add 14 to both sides
+14 +14
36 = 2x Divide both sides by 2
x = 18
Jesus is right.
Write an equation that has a slope of 2 and goes through the point (2, 1).
Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
When given the slope and a point and we are asked to find the equation of the line, we can use the point-slope form.
The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Let's let m be 2 and let (2,1) be x₁ and y₁. Thus:
[tex]y-1=2(x-2)[/tex]
Distribute the right:
[tex]y-1=2x-4[/tex]
Add 1 to both sides:
[tex]y=2x-3[/tex]
And that's our equation.
And we're done!
Given the graph, find the distance of GH. Round to the nearest tenth.
Answer:
GH = 6.3 units
Step-by-step explanation:
Assuming that 1 box represents 1 unit, the coordinate pair of G = (-2, -3), while H = (0, 3).
Distance between G and H = [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] G(-2, -3) = (x_1, y_1) [/tex]
[tex] H(0, 3) = (x_2, y_2) [/tex]
[tex] GH = \sqrt{(0 - (-2))^2 + (3 - (-3))^2} [/tex]
[tex] GH = \sqrt{(2)^2 + (6)^2} [/tex]
[tex] GH = \sqrt{4 + 36} = \sqrt{40} [/tex]
[tex] GH = 6.3 units [/tex] (nearest tenth)
What are the chances that a coin toss will result in heads? (vs. tails)?
Answer:
50/50
Step-by-step explanation:
there are only two sides so they both get 50 percent
Answer: 1 in 2 chance
Step-by-step explanation: because there are only 2 sides and can only land on one side
The students plan to eat lunch at a park. Each table can only seat 6 stud
If there are 48 students, how many tables are needed?
Answer:
They would need 8 tables.
Step-by-step explanation:
if there is 6 students on one table
6. 6. 6. 6+6+6+6+6+6+6+6= 48
6. 6. 6×8= 48 students
6. 6. 6.