Answers
Compute the first few derivatives to reveal a pattern:
f(x) = x sin(x)
f '(x) = x cos(x) + sin(x)
f ''(x) = (-x sin(x) + cos(x)) + cos(x) = -x sin(x) + 2 cos(x)
f '''(x) = (-x cos(x) - sin(x)) - 2 sin(x) = -x cos(x) - 3 sin(x)
f ''''(x) = (x sin(x) - cos(x)) - 3 cos(x)) = x sin(x) - 4 cos(x)
f ⁽⁵⁾(x) = (x cos(x) + sin(x)) + 4 sin(x) = x cos(x) + 5 sin(x)
f ⁽⁶⁾(x) = (-x sin(x) + cos(x)) + 5 cos(x) = -x sin(x) + 6 cos(x)
f ⁽⁷⁾(x) = (-x cos(x) - sin(x)) - 6 sin(x) = -x cos(x) - 7 sin(x)
f ⁽⁸⁾(x) = (x sin(x) - cos(x)) - 7 cos(x) = x sin(x) - 8 cos(x)
and so on.
The pattern should be clear: for some integer k,
• if n = 4k, then f ⁽ⁿ ⁾(x) = x sin(x) - n cos(x)
• if n = 4k + 1, then f ⁽ⁿ ⁾(x) = x cos(x) + n sin(x)
• if n = 4k + 2, then f ⁽ⁿ ⁾(x) = -x sin(x) + n cos(x)
• if n = 4k + 3, then f ⁽ⁿ ⁾(x) = -x cos(x) - n cos(x)
80 is a multiple of 4, so the 80th derivative falls in the first category. Then
f ⁽⁸⁰⁾(x) = x sin(x) - 80 cos(x)
Related Questions
How does the graph of g(x)=(x-1)^3+5 compare to the parent function f(x)=x^3
Answers
Answer:
it is one to the right and 5 up compared to its parent function.
Step-by-step explanation:
the (x-1)3 means that the graph is shifted one to the right and the + 5 means that you have to shift the garph 5 up also.
If y varies directly as x, and y = 7 when x = 3, find y when x = 7
Answers
Answer:
AStep-by-step explanation:Direct variation, by definition, has the form shown below:
y=kx
Where k is the constant of proportionality.
Given the information in the problem, you can find k:
7=3k
k=7/3
Now you can find y when x=7 as following:
y=(7/3)x
Substitute values.
y=(7*7)/3
y=49/3
Explain answer !!
( WILL GIVE BRAINLEST)
Answers
Larissa: y = 250 - 25x
Chucho: y = 30 +30x
4 weeks
Step-by-step explanation: It says it in the problem, and you can see they cross at 4 weeks
Answer:
Larissa: y = 250 - 25x
Chucho: y = 30 +30x
4 weeks
Step-by-step explanation:
A highway inspector needs an estimate of the mean weight of trucks crossing a bridge on the interstate highway system. she selects a random sample of 49 trucks and finds a mean of 15.8 tons with a sample standard deviation of 3.85 tons. the 90 percent confidence interval for the population mean is:
Answers
Answer:
14.90 to 16.70 tons
Step-by-step explanation:
We are given;
Sample size; n = 49
Mean; x¯ = 15.8
Sample standard deviation; s = 3.85
At 90% Confidence interval, z = 1.645
Formula for confidence interval is;
CI = x¯ ± z(s/√n)
Thus;
CI = 15.8 ± 1.645(3.85/√49)
CI = 15.8 ± 0.90
CI = 14.90 to 16.70 tons
9x -1 = 80
A -10
B 9
C 10
D -9
Answers
Answer:
The answer is B!
Step-by-step explanation:
Add 1 to both sides, then divide 80 by 9!
216. Determine the volume of a 75-inch cube.
a. 22.5 cu in
b. 166 cu in
c. 216 cu in
d. 421.88 cu in
Answers
Answer:
c
Step-by-step explanation:
because you have to know how many 8nches is a cube
f(x) = 7x² + 21x - 70
factor
Answers
Answer:
Step-by-step explanation:
f(x)=7(x^2+3x-10)=7(x+2)(x-5)
If a number is reduced by 40% and it becomes 192, what was the original price?
Answers
Answer:
320
Step-by-step explanation:
use square root property to solve for k
(k+5)= -24
Answers
Answer:
k= -29
Step-by-step explanation:
$0.25 per bottle water
$0.40 per bottle water
$0.50 per bottle water
6-pack
12-pack
24-pack
Answers
Answer:
24-pack
Step-by-step explanation:
you are paying less per bottle than the other 2 packs.
What is the value of
7/3 divided by 5/6
Answers
Answer:
multiply the dividend denominator by the divisor numerator to make a new denominator:
7 x 6
3 x 5
=
42
15
Thus, the answer to 7/3 divided by 5/6 in fraction form is:
42
15
To make the answer to 7/3 divided by 5/6 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
42/15 = 2.8
The answer is rounded to the nearest four decimal points if necessary.
42/15 can be simplified to 14/5.
14/5 is an improper fraction and should be written as 2 4/5.
Step-by-step explanation:
42/25 = 2 4/5 = 2.8 is the value of 7/3 divided by 5/6 .
Here, we have,
given that,
7/3 divided by 5/6
so, we get,
7/3 / 5/6
=7/3 x 6/5
multiply the dividend denominator by the divisor numerator to make a new denominator:
7 x 6/3 x 5
= 42/15
Thus, the answer to 7/3 divided by 5/6 in fraction form is:
42/15
To make the answer to 7/3 divided by 5/6 in decimal form, we simply divide the numerator by the denominator from the fraction answer above:
42/15 = 2.8
The answer is rounded to the nearest four decimal points if necessary.
42/15 can be simplified to 14/5.
14/5 is an improper fraction and should be written as 2 4/5.
Learn more about the Division here:
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5×70=5×(_×10)
5×70=(5×_)x10
5×70=_×10=_
Answers
Answer:
7
7
35 * 10 = 350
Step-by-step explanation:
We have 5 * 70 split up into multiple ways, and we need to provide an answer at the end of it.
5 * 70 = 5 * (__ * 10)
We have to equal the value of 5 * 70 by inputting the missing number.
What times 10 equals 70?
7.
5 * 70 = (5 * __) * 10
This goes for the same as the one before, what times 5 equals 5 * 70 to the same amount?
7.
5 * 70 = __ * 10 = __
Now for the final part, we take the information from before and implement to here, what is 5 * 7?
35.
Now do 35 * 10 :
35 * 10
350
Can you guys help me on question eight?!
Answers
Answer: Car Rental Company A and B
Step-by-step explanation: Everyone else charges higher prices! Good luck! :D
what is the sum of one and the product of one and a number
Answers
Answer:
the answer for this problem is 1 +×
Step-by-step explanation:
you must frame the equation with a number x
after that you have to translate the x into the equation and it can be written as
1×(1× ×)=1+×
Helpppppp plssss
Consider the numbers z= 2 + 5i, w = -3- 2i, and u=-1+2i.
z+w is equal to -1+vi
w-u is equal to - 4i
u + w is equal to -4 -
Answers
Answer:
Step-by-step explanation: 4i = i4 so divide that into one half and you get 4r
Answer:
3, 2, 0
Step-by-step explanation:
just trust me
In what quadrant are the eyeglasses
Answers
Answer:
3rd Quadrant
Step-by-step explanation:
Hope the above solution will help you
An airplane is currently flying at an altitude of 37,000 feet. The airplane is scheduled to land at an airport 100 miles
away. Find the average angle at which the airplane must descend for landing. Round your answer to the nearest
degree.
Answers
Answer:
4degrees
Step-by-step explanation:
Given the following
Height of the airplane = 37000feet
distance covered on landing = 100miles = 100(5280)
distance covered on landing = 528,000feet
Using the SOH CAH TOA
sin theta = opposite/hyp
sin theta = 37000/528000
sin theta = 37/528
theta = arcsin (37/528)
theta = 4 degrees
Hence average angle at which the airplane must descend for landing is 4degrees
A number increased by 20% becomes 227. what is the number?
Answers
Answer: I think it's 272.4
Step-by-step explanation: hope it helps thx for the free points :)
5 x (h + 3) for h = 7
Evaluate the expression
Answers
Answer:
ummm im so sorry but i forgot while answering
Step-by-step explanation:
opps
Your welcome
Which set of ordered pairs satisfies the equation
f(x)=7x+20
Answers
Answer:
The 2nd one
Step-by-step explanation:
Solve the inequality for x and identify the graph of its solution.
[1x + 1]< 2
Choose the answer that gives both the correct solution and the correct graph.
Answers
Answer:
x<1
Step-by-step explanation:
[1x + 1]< 2
Simplify both sides of the inequality.
x+1<2
Subtract 1 from both sides.
x+1−1<2−1
x<1
Answer:
x<1
On the graph line, the circle is open on number 1 and is going left
Someone please help!! 50 points! I have no idea how to do these so If someone could please give the steps and answer it would be greatly appreciated!
Answers
Answer:
3. 97*
4. 43*
5. 4*
6. E = 15*
Step-by-step explanation:
14 divided by 2 = 7 + 90 = 97
5 divided by 2 = 2.5 rounded to nearest tenth makes 3 + 40 = 43
8 divided by 2 = 4 -AB = 4B
DE3* x EF5* = 15
Answer:
MK = 7, DE = 4.2, m∠B = 48°, sin (E) = 4/5Step-by-step explanation:
Question 3
This is a 30° right triangleMK is opposite to 30° angle ⇒ LK = 2MK ⇒ MK = 14/2 = 7Question 4
FE = 5m∠F = 40°DE/FE = tan (F)DE = 5 tan (40°) = 4.2 (rounded)Question 5
AB = 8AC = 12cos (B) = 8/12 = 2/3m∠B = arccos (2/3) = 48° (rounded)Question 6
sin (E) = DF/EF = 4/58 1/5-2 7/8 fractions
Answers
i removed my answer because it was wrong look at the other peoples answers
Answer: 213/40 or 5.325
Step-by-step explanation:
We can find common denominators for 8 1/5 and 2 7/8.
The Lowest Common Denominator for 8 1/5 and 2 7/8 is 40.
8 1/5 = 41/5 = 328/40.
2 7/8 = 23/8 = 115/40.
Now we can subtract.
328/40 - 115/40 = 213/40.
Therefore, the answer is 213/40 or 5 13/40.
The attendance at a new weekly exercise class doubled each week until week 4, when it reached its maximum capacity of 24 people
Answers
Answer:
Half Maximum capacity a week 3. And the class started off with 3 people.
Step-by-step explanation:
Which of the following is something a lender will not consider when reviewing your loan application?
a collateral
b. family size
c. credit score
d. debt-to-Income (DTI) ratio
Answers
Answer:
B family size
Step-by-step explanation:
The lender will not consider family size when reviewing your loan application.
What is Loan application?Loan applications could be declined for so many reasons. However, in a situation where an application is not granted, it is good to find out the reasons behind the decision so as to avoid repeating such in subsequent applications.
Another step to be taken after the denial of the application is to look for an alternative lender and make another application.
One may also need to improve on the application to avoid another denial this time around.
Since Lenders have different risk appetites and preferences. What one lender tells about your creditworthiness is not necessarily what another will. They may view your finances as well enough to apply.
Learn more about the Loan application;
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Zoey's dog has a water bowl with a diameter of 6 inches. Sam's
dog has a water bowl with a diameter of 10 inches. What is the
approximate difference in the circumference (distance around)
ut of the two water bowls?
Answers
Answer:
12.56 inches
Step-by-step explanation:
Circumference: C = 2*pi*r
I will be using 3.14 in place of pi
Divide the diameters by 2, so 3 for Zoey and 5 for Sam
Multiply (2*3.14*3) and (2*3.14*5)
For Zoey you get 18.84 and for Sam you get 31.4
31.4-18.84= 12.56 in difference
graph the line with the slope 3 passing through the point (2,-1)
Answers
Answer:
I can't draw at the moment but I'll try to teach how as best as I could.
Draw the Cartesian plane (x and y-axis)Locate the point (2, -1). To do this, go to x=2 then go down by 1 unit. Plot it or mark this point by a dot.Then from this dot, go 3 units to the right. After that, go up by 1 unit and mark that with a dot. By this time, you now have 2 dots.Connect them and that's it.calculate the scale factor will mark branylis
Answers
Answer:
I think it is D. K= 11/2
What is Y= -3/10x-8 written in standard form?
Answers
Hope this helps!
2+2-3+70-32+454-10-40=
Answers
Answer:
443
Step-by-step explanation:
Answer:
449
Step-by-step explanation: