Answer:
a. k = 24 b. y = [tex]Ae^{4t} + Be^{6t}[/tex]
Step-by-step explanation:
a. Find the value of the constant k
Since [tex]y = e^{4t}[/tex] is a solution of d²y/dt² -10dy/dt + ky = 0, then [tex]y = e^{4t}[/tex] must satisfy the equation.
So, d²y/dt² = [tex]16e^{4t}[/tex] and dy/dt = [tex]4e^{4t}[/tex]
So, d²y/dt² -10dy/dt + ky = 0
[tex]16e^{4t}[/tex] - 10([tex]4e^{4t}[/tex]) + k([tex]e^{4t}[/tex]) = 0
[tex]16e^{4t}[/tex] - [tex]40e^{4t}[/tex] + [tex]ke^{4t}[/tex] = 0
- [tex]24e^{4t}[/tex] + [tex]ke^{4t}[/tex] = 0
- [tex]24e^{4t}[/tex] = -[tex]ke^{4t}[/tex]
So, k = 24
b. Find the general solution to this equation.
Since k = 24, our equation is
d²y/dt² -10dy/dt + 24y = 0
The characteristic equation is thus
m² - 10m + 24 = 0
Factorizing this we have
m² - 6m - 4m + 24 = 0
m(m - 6) - 4(m - 6) = 0
(m - 6)(m - 4) = 0
m - 6 = 0 or m - 4 = 0
m = 6 or m = 4
Since we have real roots for the characteristic equation, then, the general solution is
y = [tex]Ae^{4t} + Be^{6t}[/tex]
1. Write an equivalent expression for 3(y - 6) + 4
Answer:
3y - 6
Step-by-step explanation:
You basically want to first distribute then combine like terms
3 ( y - 6 + 4 )
Do PEMDAS
3*y + 3 * -6 + 3* 4
( This is the distributed part)
3y - 18 + 12
3y - 6
( This is the combing like terms)
Hope this helped!
Please help I am bad at math and need to be somewhere soon so please help me asap
The band booster and the athletic booster clubs sell tickets for a fund-raiser. The band booster sells eight more than twice the number of tickets the athletic booster sells. The band booster club sells 280 tickets. Find the number of tickets the athletic booster club sells.
A. 144 tickets
B. 132 tickets
C. 136 tickets
D. 148 tickets
Answer:
C
Step-by-step explanation:
(280 - 8)/2 = Athletic booster tickets
(280-8)/2 = (272)/2 = 136
a, b, and c represent three different digits. If you add up all of the six two - digit numbers that can be written with these digits, where you don't use the same digit twice in each number, then the sum will be 528. Find these digits.
Answer:
The answer is 7, 8 and 9. The Two-digit numbers are: ab, ac, ba, bc, ca, cb
The Sum of them is: 10a + b + 10a + c + 10b + a + 10b + c + 10c + a + 10c + b = 528
22a + 22b + 22c = 528
a + b + c = 528/22
a + b + c = 24 The only option of three different digits with the sum of 24 is 7, 8 and 9.
Hope this helps, stay safe, and merry christmas!
What is the best interpretation of c(20) = 65 in terms of the problerm?
Answer:
I think C would be 3.25
Step-by-step explanation:
Because if you divide 65/20+3.25 sorry if i'm wrong.
Nine children join hands to form a circle how many hands
8 ft
15 ft
What is the length of the hypotenuse?
C =
feet
Answer:
C = 17
Explanation:
C is the square root of a^2 + b^2
8^2 + 15^2
64 + 225
289
the square root of 289 is 17
which statement about 2(×+4) is true ?
Answer:
The answer is 2x + 8
Step-by-step explanation:
Use 3.14 for pi
A bicycle tire has a radius of 12 inches. If the tire rotates 20 {times, about how many inches did
it travel? Round to the nearest inch.
Answer:9342
Step-by-step explanation:
I am smart UwU
There are 33 times as many boys as girls in a room. If 4 boys and 4 girls leave the room, then there will be 5 times as many boys as girls in the room. In total, how many boys and girls were in the room originally
Answer:
here are 3 times as many boys as girls in a room. If 4 boys and four girls leave the room, then there will be 5 times as many boys as girls in the room. In total, how many boys and girls were in the room originally?
8 girls
24 boys
There were 24 boys and 8 girls in the room originally.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Given that there are 3 times as many boys as girls in a room.
If 4 boys and 4 girls leave the room, then there will be 5 times as many boys as girls in the room.
Let's assume the number of boys would be b
And the number of girls would be g
According to the given condition, the required solution would be as:
b = 3g ....(i)
b - 4 = 5 (g - 4) ....(ii)
Substitute the value of b = 3g in equation (ii), and solve for g
3g - 4 = 5 (g - 4)
3g - 4 = 5g - 20
5g - 3g = 20 - 4
2g = 16
g = 8
Substitute the value of g = 8 in equation (i), and solve for b
b = 3 × 8
b = 24
Hence, there are 24 boys and 8 girls in the room.
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Find the volume of a hemisphere of radius 5 cm.
Answer:
the volume of a hemisphere with a radius of 5 feet is 261.67 cubic feet.
Step-by-step explanation:
determine whether the following two lines are parallel perpendicular coincident or intersecting y=-4x+2 and 16y=4x+8
Answer:
i dont know
Step-by-step explanation:
but i wish you luck
What is the correct answer?
Answer:
pretty sure its B the degree is the biggest number of exonent and the leading coefficient is the number in front of the x that is the biggest. u can look up the graph for end behavior.
Step-by-step explanation:
During the 1920s, buying stock on credit was called buying on speculation. buying on a gamble. buying on margin. buying on margin call.
During the 1920s, buying stock on credit was called buying on margin or margin trading. Hence, option C is correct.
What is a margin trading?An act of buying shares or securities of a company without the actual need of having funds in the account, is known as margin trading. A credit facility is granted by the broker to the trader to do margin trading.
In case the trader generates a profit while buying on margin, he or she would get only an amount of the profit made by him or her over such trade. In case of losses, the balance amount became the liability of the trader.
Hence, option C states about margin trading.
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Please help me with the work! Thanks
Answer:
i cant see te pic that good
Step-by-step explanation:
Is it legal to keep monkeys in a refrigerator in the United States?
Answer:
I don't really know but I think it is.
Step-by-step explanation:
A bag has 5 yellow marbles, 3 red marbles, and 2 blue marbles. Quinn randomly picks a marble from the bag and returns it before another is picked. How many times would Quinn expect to a blue marble if he picks a marble 200 times
Answer:
He would expect to see the blue marble 40 times. Hope this helps!
Step-by-step explanation:
Answer:
40 blue marbles
Step-by-step explanation:
You would find the probability of a blue marble
2 blue/ ( 5+3+2) total
2 divided by 10 is 1/5
Then, you multiply 200 and 1/5 together, which would equal 40.
Quinn should expect to pick 40 blue marbles.
What is the next fraction in this sequence
Answer:
the next fraction is 12/15.
Step-by-step explanation:
if you convert each fraction to have a denominator of 15, the numerators will be 4, 6, 8, and 10. the only number that could be next in the sequence is 12
I'll give brainly if right
Answer: 3.6
Step-by-step explanation:
18/5 simplified equals 3 3/5.
3/5 = 0.6
3 + 0.6 = 3.6
In conclusion, the answer is 3.6.
Hope this helps!
Evaluate: 4x + 8 + x -2 -3x when x= 5
Step-by-step explanation:
4x + 8 + x - 2 - 3x
= 2x + 6
= 2(5) + 6
= 16.
Answer:
4*5 + 8 + 5 - 2 - 3*5 = 20 + 8 + 5 - 2 - 15 = 28 + 5 - 2 - 15 = 33 - 2 - 15 = 31 - 15 = 16
In 60 seconds, a car in a parade travels 0.2 mile. The car traveled the last 0.05 mile in 12 seconds. How long did it take for the car to travel 0.1 mile?
Answer:
First 0.1 miles: 32 seconds
Last 0.1 miles: 28 seconds
Step-by-step explanation:
The car traveled 0.2 mile in 60 seconds.
The last 0.05 miles were done in 12 seconds.
Then the first 0.2 - 0.05 = 0.15 miles were done in 60 - 12 = 48 seconds. The speed of the car was: 0.15/48 = 0.003125 mi/s
At this speed it takes 0.1/0.003125 = 32 s to travel the first 0.1 mile.
In the second 0.1 mile, 0.05 miles are done at the same speed than before. It takes 0.05/0.003125 = 16 s, the next 0.05 miles were traveled in 12 seconds, making a total of 16+12 = 28 seconds
True or false: If two triangles have two pairs of corresponding angles congruent, along with a pair of non-included sides congruent, then the triangles are always congruent
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Therefore, it is true.
Check the Show sine and cosine of ∠A and Show sine and cosine of ∠B boxes. Move point B to various locations so that m∠A is approximately 15°, 30°, 45°, 60°, and 75°. In each case, record m∠A and m∠B and record the sine and cosine of ∠A and ∠B. What relationship do you observe between the sine and cosine of ∠A and the sine and cosine of ∠B?
Answer:
the pic has the answer
Explanation:
The relationship between the sine and cosine of ∠A and the sine and cosine of ∠B for given angles, sin(A) = cos(B) and
sin(B) = cos(A)
What are complementary angles?"Two or more angles are complementary if their sum is 90° "
For given question,
∠A and ∠B are complementary angles.
⇒ ∠A + ∠B = 180°
For ∠A = 15° the measure of ∠B is 75°
For ∠A = 30° the measure of ∠B is 60°
For ∠A = 45° the measure of ∠B is 45°
For ∠A = 60° the measure of ∠B is 30°
For ∠A = 75° the measure of ∠B is 15°
So, the sine and cosine of ∠A and ∠B would be,
∠A ∠B sin(A) cos(A) sin(B) cos(B)
15° 75° 0.25 0.97 0.97 0.26
30° 60° 0.5 0.87 0.87 0.5
45° 45° 0.71 0.71 0.71 0.71
60° 30° 0.87 0.5 0.5 0.87
75° 15° 0.97 0.26 0.26 0.97
From above records, we can observe that sin(A) = cos(B) and
sin(B) = cos(A)
Therefore, the relationship between the sine and cosine of ∠A and the sine and cosine of ∠B for given angles, sin(A) = cos(B) and
sin(B) = cos(A)
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What is the value of k^16 - 16^k, if x = 13^2 * 15^4 * 17^6 * 19^8 and is a multiple of 16^k, where k is a whole number?
Note: ^ means to the power of
Answer:
I tried but I kept getting weird numbers
Step-by-step explanation:
in ACE, G is the centroid and BE = 9. find BG and GE
Answer:
b-g is 3
g-e is 6
Step-by-step explanation:
good luck, have a good day, can i get brainliest
GE = 6 and BG = 3
What is centroid?The point in which the three medians of the triangle intersect is known as the centroid of a triangle.
Given that, G is the centroid and BE = 9
The centroid point G divides the segment BE in the ratio 2:1, such that GE is twice the length of BE,
BG = 1/3*BE
BG = 1/3*9 = 3
And,
GE = 2/3*9 = 6
Hence, GE = 6 and BG = 3
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What are the zeros of the function
A small cube with side length 6y is placed inside a larger cube with side length 4/2. What is the difference in the
volume of the cubes?
• (4x2 -by) (16** +24x2y+38y?)
• (63-4x2) 36y2 +24x+y+ 16x
• (4x2-by)(4x4 +24x+y+by?)
• (4x2 + 8y)(18** – 24x+y+38y?)
Answer:
Step-by-step explanation:
Side length of a small cube = 6y
Side length of a larger cube = 4x²
This small cube is placed inside a larger cube. We need to find the difference in the volume of the cubes.
Volume of small cube, [tex]V_1=(6y)^3=216y^3[/tex]
Volume of lager cube,
[tex]V_2=(4x^2)^3\\\\=64x^6[/tex]
Difference in the volume of the cubes,
[tex]\Delta V=V_2-V_1\\\\=64x^6-216y^3[/tex]
We can simplify the above expression :
[tex]\because \ (a^3-b^3)=(a-b)(a^2+ab+b^2)\\\\(4x^2)^3-(6y)^3=(4x^2-6y)((4x^2)^2+4x^2\times 6y +(6y)^2)\\\\=(4x^2-6y)(16x^4+24x^2y+36y^2)[/tex]
So, the difference in the volumes of the cubes is [tex](4x^2-6y)(16x^4+24x^2y+36y^2)[/tex].
Answer:
see image below
Step-by-step explanation:
Which rectangular equation is formed by eliminating the parameter?
y = t^3
x = t + 5
Given :
Two equations :
y = t³
x = t + 5
To Find :
Rectangular equation formed by eliminating the parameter.
Solution :
Putting value of t from second equation to first equation.
We get :
[tex]y = ( x-5)^3[/tex]
Also, t from equation first :
[tex]t = \sqrt[3]{y}[/tex]
Putting the value of t and equation two, we get :
[tex]x = \sqrt[3]{y}+5[/tex]
Therefore, rectangular equation is formed by eliminating the parameter is :
y = ( x - 5)³ and x = ∛y + 5 .
The rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
The options are:
y = (x + 5)³x = (y + 5)³y = (x - 5)³y = (x - 5)²It is given that:The parametric equations are:
y = t³
x = t + 5
From the second equation that is x = t + 5
Take the value of t and plug in the equation y = t³:
t = x - 5
y = (x - 5)³
The above equation represents a cubic equation.
Thus, the rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
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SOMEONE PLEASE HELP IF U GET IT RIGHT ILL GIVE U 15 POINTS PLEASE
Answer:
There is no solution, y-int of one line is positive
Step-by-step explanation:
There is no solution because there are no shared points between both lines, and the y intercept of the blue line is positive, because it is above the x-axis.
please help :{
Jannie has a budget of less than $240 to spend on jeans and shirts. She spends $95 on jeans. If the cost of each shirt is $22.50, how many can she buy without going over the budget? *
Answer: She can buy 6 shirts
Step-by-step explanation: You subtract 95 from 240, which gives you 145 so you do 145/22.5 which will give you 6.4444 but you can't buy .44 of a shirt so you round down and you get 6.
Which inequality is true?
+
-3
-2
-1
0
1
2.
3
011
A
ن نے
024-2 1/2
1 1 1 1
Plssss help!!
Answer:
2 awnser is the right on