Final answer:
The 55th derivative of y = cos(3x) is recognized by repeating the derivative patterns of cosine functions and is found to be -27cos(3x).
Explanation:
The 55th derivative of y = cos(3x) can be found by recognizing that the derivatives of sine and cosine functions repeat every four steps. Considering the pattern cos(x) -> -sin(x) -> -cos(x) -> sin(x) -> cos(x), and that the derivative of cos(3x) is -3sin(3x), we can determine that the pattern repeats every four derivatives with a factor of 3n, where n is the number of times the derivative is taken.
The 55th derivative will be the same as the third derivative in the cycle, but with an iteration count of 55/4, which leaves a remainder of 3, so the 55th derivative will be -27cos(3x).
Unknown angle measures?
A line goes through the point (6,–2) and has a slope of –3.
What is the value of a if the point (a,7) lies on the line?
The value of a in the point (a, 7) is 3
The slope intercept equation is as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
Let's find b using (6, -2)
m = -3
y = -3x + b
-2 = -3(6) + b
-2 = -18 + b
b = -2 + 18
b = 16
Therefore,
y = -3x + 16
let's find the value of a in (a, 7)
7 = -3x + 16
7 - 16 = -3x
-9 = -3x
x = -9 / -3
x = 3
Therefore,
a = 3
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Whats the value of x?
4x=5x-12
x=
Which number below best represents a temperature of 59.18 degrees above zero? A. -69.18 B. 69.18 C. 59.18 D. -59.18
please help i will give a brainlist if you get it right
find the median of the data set: -66, -48, -52, -42
write a word phrase for each algebraic expression
1. 100 - 5n
2. 25r + 6
what number would you add to both sides of x^2-20x=5 to complete the square
Find the solution of the initial value problem. dp/dt=5e^t, p(0)=25
The equation is [tex]p = 5e^{t} +20[/tex].
IntegrationIt is a method of summing up parts to find the whole. It is a reverse process of differentiation.
Given
dp/dt=5e^t
To findThe value of p.
How to get the value of p?dp/dt=5e^t is given
[tex]\begin{aligned} \dfrac{dp}{dt} &= e^{t} \\\int dp &= \int {5e^{t} } \, dt \\\int dp &= 5 \int {e^{t} } \, dt \\p &= 5e^{t} +c\\\end{aligned}[/tex]
It is given that at t=0, p will be 25, then
[tex]p = 5e^{t} + c\\c = p - 5e^{t}\\c= 25 - 5e^{0}\\c= 25 - 5 * 1\\c= 20[/tex]
Hence the equation will be [tex]p = 5e^{t} +20[/tex].
Thus, the equation is [tex]p = 5e^{t} +20[/tex].
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If Jessie is 24 years younger than her mother and if the sum of their ages is 84, how old is Jessie?
What is 781,407 rounded to the nearest ten thousand What is 781,407 rounded to the nearest ten thousand?
Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.
How much time passes until the second bus catches up with the first bus?
Final answer:
The second bus catches up with the first bus in 2 hours.
Explanation:
To calculate how much time passes until the second bus catches up with the first bus, we need to find the distance between them when the second bus starts and the relative speed between the two buses.
When the second bus starts, the first bus has already traveled for 1 hour (from 4:00 p.m. to 5:00 p.m.) at a speed of 40 mph. Therefore, the first bus has covered a distance of 40 miles.
The relative speed between the two buses is the difference in their speeds, which is 60 mph - 40 mph = 20 mph.
Using the formula: t = d / v, where t is the time, d is the distance, and v is the speed, we can calculate the time it takes for the second bus to catch up with the first bus:
t = 40 miles / 20 mph = 2 hours.
Therefore, it takes 2 hours for the second bus to catch up with the first bus.
Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let h represent the number of hats.
What is the minimum number of hats Jason will need to sell to make a profit?
A. 15h>750+3.5h
B. 3.5h≥750+15h
C. 3.5h>750+15h
D. 15h<750+3.5h
Question 9
If x is a small negative integer and y is a large positive integer, which of the following expressions must be positive?
A x * y
B y − x
C y ÷ x
D x ÷ y
What does it mean if the determinant of a matrix is 0?
Final answer:
The determinant of a matrix is 0 means the matrix is singular, indicating no unique solution for the corresponding system of equations, or in geometry, that space is compressed to a lower dimension.
Explanation:
When the determinant of a matrix is 0, it signals that the matrix does not have an inverse and is considered singular. In practical terms, this means that the system of equations that corresponds to the matrix does not have a unique solution. For instance, in a square matrix, if the determinant is zero, it may indicate that the rows or columns are linearly dependent, meaning that at least one row or column is a scalar multiple of another, resulting in redundant information. In geometry, if we're dealing with transformation matrices, a determinant of zero implies that the transformation compresses the space into a lower dimension, effectively 'flattening' it, and thus, the original geometrical figure loses its volume.
vector is flying his helicopter at 200 miles per hour. how long has he been flying if he has traveled 1,200 miles? A. 2 hours B. 60 hours C. 6 hours D. 10 hours??? please help
How do you find the median of these numbers $17.49, $11.29, $16.89, $11.79?
What is the scale factor use to create this dilation?
What is the y-coordinate of the vertex of the parabola that is given by the equation below?x = -2.5(y - 3)2 + 5?
Translate this sentence into an equation.
The sum of 14 and holly's age is 55.
Use the variable h to represent holly's age.
Final answer:
The sentence 'The sum of 14 and Holly's age is 55' can be translated into the equation 14 + h = 55, where h represents Holly's age.
Explanation:
To translate the sentence into an equation, we identify the mathematical operations described by the sentence. The sentence 'The sum of 14 and Holly's age is 55' indicates an addition operation involving Holly's age and the number 14. Using the variable h for Holly's age, we form the equation 14 + h = 55. This is a simple linear equation where h represents an unknown value that can be solved for.
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers? Which three expressions could be used to represent the numbers? n; n - 4; 4n n; 4 - n; n + 4 n; n/4; n + 4
Answer:
Numbers: 11, 7 and 44
Expressions: n, n - 4, 4n
Step-by-step explanation:
We have that A + B + C = 62, where A, B and C represent numbers.
We know that the 2nd number (B) is equal to the first number (A), diminished by 4. This means B = A - 4
We also know that the 3rd number (C) is four times the first (A), that is to say 4*A. This means C = 4*A
If we replace this information in the first expression, we have
A + B + C = A + (A - 4) + (4*A) = 62
We change an equation of 3 variables to an equation of just one. Now we solve it putting together the terms that have the variable A:
A + A - 4 + 4*A = 62
2A + 4A - 4 + 4 = 62 + 4
6A = 66
A = 11
Our first number is 11, now we find B and C:
B = A - 4 = 11 - 4 = 7
C = 4A = 4*11 = 44
So, the numbers are 11, 7 and 44
If we change the A for a "n", the expressions that represent the numbers are n, n - 4 and 4n
The three angles of a triangle are in the ratio 3:3:4. What information can you give about the triangle?
Which of the following is NOT equivalent to the ratio: 12/4 A.6/2 B. 36/12 C.24/16 D.240/80
A sample of 36 is drawn from your population and a sample mean of 86 is computed. is this sample mean in the extreme 5% or the middle 95 %
BRAINLIESTTTTTTTTTTT!!
1. For the following system, if you isolated x in the second equation to use the Substitution Method, what expression would you substitute into the first equation?
2x + y = 8
−x − 3y = −12
3y + 12
−3y + 12
3y − 12
−3y − 12
2. please check my answer for the picture question
solve for y: 7/9y = 42
On Saturday,miguel biked 36 kilometers in 2 hours. What was his average rate of speed in kilometers per hour?
The average rate of speed of Miguel when he biked on Saturday given the distance and time is 18 kilometers per hour.
What is the average speed?
Average speed is the rate at which an object moves with respect to time. Average speed is determined by dividing total distance travelled by time.
Average speed = total distance / time
36 / 2 = 18 kilometers per hour.
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Please help! 20 points!
12/3 = 4
it was dilated with a scale factor of 4
n2-14n+49 what’s the answer
I want to know the answer of this question