These questions are about calculus, I would greatly appreciate your help on both questions! .
asap , please !
Answers
The 107th derivative of f(x) =cos(x) is sin(x).
What is derivative of a function?The derivative of y = f(x) function is the rate of change of y with respect to the independent variable x.
Derivative is represented by [tex]\frac{d}{dx}[/tex] and
First derivative to y is given by [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]
Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.
[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]
Given f(x) = cos(x)
Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]
The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]
Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]
[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]
Eighth derivative if cos(x) is cos(x)
and so on
Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x) is -sin(x)
The second, sixth, tenth.... derivative of f(x) =cos(x) is -cos(x)
The fourth , eighth , 12th,... derivative of f(x) =cos(x) is cos(x)
We can say that very multiple of fourth derivative of f(x) =cos(x) is cos(x)
We can write 107 as 104 + 3
As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)
[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]
Therefore, the 107th derivative of f(x) =cos(x) is sin(x).
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Related Questions
Draw AABC with vertices at A(1,6), B(1, 1) and C(5, 1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E = 90°, and
EF = BC.
Paste a picture of your drawing in the answer box.
Answers
The picture of the triangle ΔDEF is attached below.
A triangle can be defined as a basic polygon which has 3 sides.
The sum of all the interior angles of a triangle is given by 180°.The area of any triangle is calculated by [tex]\frac{1}{2}[/tex] × base × height.In a right-angled triangle the side opposite the largest angle which is 90° is called the hypotenuse.Pythagoras' theorem states that the sum of the squares of the legs of aright-angles triangle is equal to the square of the hypotenuse of the triangle.In the given ΔABC we see that AC is the hypotenuse and the two sides AB and AC are the legs of the triangle.
m∠B=90°
The ΔDEF is drawn such that m∠E=90° and AB=DE and EF=BC .
Therefore we can say that the two triangles are congruent by SAS axiom of congruency.
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PLEASE HELP!!!What is the effect on the graph of
f(x)=∣x∣when the function is changed to g(x)=∣3x∣+1?
A.
The graph is compressed vertically and shifted to the right 1 unit.
B.
The graph is stretched vertically and shifted to the left 1 unit.
C.
The graph is stretched horizontally and shifted up 1 unit.
D.
The graph is compressed horizontally and shifted up 1 unit.
Answers
Answer:
24
23fc
23
45jh4
66
35g
35
56
34
Your cell phone plan costs $24.99 per month plus $0.19 for each text message you send or receive. You have at most $34 to spend on your cell phone bill. What is the maximum number of text
messages that you can send or receive next month?
The maximum number of text messages is
Answers
Answer:
33
messages
Step-by-step explanation:
84x7 complete the equation
Answers
Answer:
The answer to your question is 588
Answer:
588
Hope this helps
A theater charges $8 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $5200. At one show, 25% of the main-floor seats and 50% of the balcony seats were
income was $1800 How many seats are on the main floor and how many are in the balcony?
Answers
By solving a system of equations we can see that there are 400 main-floor seats and 500 balcony seats.
How many seats are on the main floor and how many are in the balcony?Let's define the two variables:
x = number of seats on the main-floor.y = number of balcony seats.We know that if all the seats are sold, then the total income is $5,200, we can write the equation:
x*$8 + y*$4 = $5,200
And if 25% of the main-floor and 50% of the balcony seats are sold, then we get an income of $1800, then we can write:
0.25*x*$8 + 0.5*y*$4 = $1,800
x*$2 + y*$2 = $1,800
So we have a system of equations:
x*$8 + y*$4 = $5,200
x*$2 + y*$2 = $1,800
If we subtract twice the second equation for the first one we get:
(x*$8 + y*$4) - (x*$2 + y*$2) = $5,200 - 2*$1,800
x*$4 = $1,600
x = $1,600/$4 = 400
So there are 400 seats on the main-floor.
Using the first equation we can find:
x*$8 + y*$4 = $5,200
400*$8 + y*$4 = $5,200
$3,200 + y*$4 = $5,200
y*$4 = $5,200 - $3,200 = $2,000
y = $2,000/$4 = 500
So there are 500 balcony seats.
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express 7.065 as a mixed number
Answers
Answer: [tex]7 \frac{13}{200}[/tex]
Step-by-step explanation:
7.065=
[tex]7 \frac{65}{1000}[/tex]= ==> GCF of 65 and 1000 is 5
[tex]7 \frac{65/5}{1000/5}[/tex]=[tex]7 \frac{13}{200}[/tex]
Write a function g whose graph represents the indicated transformation of the graph of f.
f(x) = 3x ; translation 5 units up
the translated function is g(x) =
Answers
Answer:
g(x) = 3x +5
Step-by-step explanation:
You want the function that results from translating f(x) = 3x upward by 5 units.
TranslationThe y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.
The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:
(x, f(x) +5) . . . . . graph translated 5 units up
Using the given definition of f(x), this becomes ...
(x, 3x +5)
The translated function is defined as g(x), so we have ...
(x, g(x)) = (x, 3x +5)
or ...
g(x) = 3x +5
A survey of 541 adults aged 18-24 year olds was conducted in which they
were asked what they did last Friday night. It found:
181 watched TV
• 180 hung out with friends
• 150 ate pizza
• 46 watched TV and ate pizza, but did not hang out with friends
• 36 watched TV and hung out with friends, but did not eat pizza
• 29 hung out with friends and ate pizza, but did not watch TV
• 25 watched TV, hung out with friends, and ate pizza
How may 18-24 year olds did not do any of these three activities last Friday
Answers
Answer: 30
Step-by-step explanation:
181+180+150=
361+150=511
541-511=30 18-24 year olds
**46 of 181 students that watched TV ate pizza and the same 46 students of the 150 students that ate pizza watched TV.
Hey y’all, 10 pm now :( got one more question and then I’ll be gone so pls help
Answers
Answer:
x=27 or x= -8
Step-by-step explanation:
rearrange the terms
convert the expression
simplify the expression
rewrite the equation
solve the equation
formulate new equations
I can't show the full steps since there's no image
Answer:
this is answers
scan and see
solve 3cosx = 2+cosx
Answers
x= 0.
Step-by-step explanation:1. Write the expression.[tex]3cosx = 2+cosx[/tex]
2. Divide both sides by 3.[tex]\frac{3cosx}{3} = \frac{2+cosx}{3} \\\\\frac{3cosx}{3} = \frac{2}{3} +\frac{cosx}{3} \\ \\cosx=\frac{2}{3} +\frac{cosx}{3}[/tex]
3. Subtract [tex]\frac{cosx}{3}[/tex] from both sides.[tex]\frac{3cosx}{3} = \frac{2+cosx}{3} \\\\\frac{3cosx}{3} = \frac{2}{3} +\frac{cosx}{3} \\ \\cosx-\frac{cosx}{3}=\frac{2}{3} +\frac{cosx}{3}-\frac{cosx}{3}\\ \\\\cosx-\frac{cosx}{3}=\frac{2}{3}[/tex]
4. Simplify the fraction subtraction.[tex]\frac{3cosx}{3} -\frac{cosx}{3}=\frac{2}{3}\\ \\\frac{3cosx-cosx}{3}=\frac{2}{3}[/tex]
5. Multiply both sides by 3.[tex]3*\frac{3cosx-cosx}{3}=\frac{2}{3}*3\\ \\3cosx-cosx=\frac{6}{3}\\ \\3cosx-cosx=2[/tex]
6. Solve the subtraction.[tex]2cosx=2[/tex]
7. Divide both sides by 2.[tex]\frac{2cosx}{2} =\frac{2}{2} \\ \\cosx=1[/tex]
8. Take [tex]cos^{-1}[/tex] from both sides.[tex]cos^{-1}(cosx) =cos^{-1}(1)\\ \\x=cos^{-1}(1)\\ \\x=0.[/tex]
Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
E (-8,9)
F(-4,9)
G(-4,2)
D(2,-8)
Answers
The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).
A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.
Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:
E'( - 9, - 8 )
When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:
F'( - 9, - 4 )
When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:
G'( - 2, - 4 )
When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:
D'( 8, 2 )
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What is the slope of a line that passes through the ordered pairs (0,1) and (3,5)?
Answers
The slope of a line that passes through the ordered pairs (0,1) and (3,5) would be m = 4/3.
What is the slope of a line which passes through points ( p,q) and (x,y)?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal. Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
WE have been given line that passes through the ordered pairs (0,1) and (3,5).
Slope = m
Therefore,
[tex]m = \dfrac{y-q}{x-p}\\\\m = \dfrac{5 -1}{3-0}\\\\m = \dfrac{4}{3}[/tex]
Hence, the slope of a line that passes through the ordered pairs (0,1) and (3,5) would be [tex]m = \dfrac{4}{3}[/tex].
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V = 4 + at, solve for a.
Answers
Answer: a=(V-4)/t
Step-by-step explanation:
V = 4 + at
V-4=at
a=(V-4)/t
If x varies directly as y and when x = 5, y = 20. Find the relationship between x and y.
Answers
the relationship between x and y when x varies directly is 4 x = y.
We know that when x varies directly with y, then:
x = k y
Now, we have x = 5 and y = 20
Substituting the values in the expression, we get that:
5 = 20 k
k = 5 / 20
k = 1 / 4
So, we get the relation as:
x = 1 / 4 y
4 x = y
Therefore, the relationship between x and y when x varies directly is 4 x = y.
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After a person gets a 2% raise in salary, the new salary is $11874. What was the original salary?
Answers
Answer:
Original salary was $11641.17Step-by-step explanation:
Let the initial salary be x.
Set equation and solve for x:
x + 2% of x = 11874x + x*2/100 = 11874x + 0.02x = 118741.02x = 11874x = 11874/1.02x = 11641.17 (rounded to the nearest cent)
Answer:
The original salary is $11641.18.
Step-by-step explanation:
The equation will be,
→ x + (x × 2)/100 = 11874
Now the original salary will be,
→ x + (x × 2)/100 = 11874
→ x + 0.02x = 11874
→ 1.02x = 11874
→ x = 11874/1.02
→ x = 11641.1764706
→ [ x = 11641.18 ]
Hence, original salary is $11641.18.
Lucy paid $120 for an item at the store that was 20 percent off the original price. what was the original price?
Answers
Answer:
$150
Step-by-step explanation:
Given the following question:
Lucy paid 120 dollars for an item
The item was 20% off
What was the original price? To find the original price we will need to use the formula to calculate percentages.
20% of 150
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times150}{100}[/tex]
[tex]20\times150=3000[/tex]
[tex]3000\div100=30[/tex]
[tex]150-30=120[/tex]
[tex]=120[/tex]
Which means our original price is "$150."
Hope this helps.
mayas penny bank is 1/2 full. after she adds 120 pennies,it is 2/3 full. How,many pennis can mayas bank hold?
Answers
Answer:
720
Step-by-step explanation:
We are looking for the difference between 2/3 and 1/2, which we know to be 120. To subtract fractions of different denominators, we need to find the common denominator (this can be found by finding the LCM of both denominators)
120 = 2/3 - 1/2 = 4/6 - 3/6
1/6 = 120
We can multiply 120 by 6 to find the value of the full bank.
1/1 = 720
7. An aircraft flies 400 km from a point O on a bearing of 025°
and then 700 km on a bearing of 080° to arrive at B.
a) How far north of O is B?
b) How far east of O is B?
Answers
Answer:
484 km north858 km eastStep-by-step explanation:
You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.
Coordinate transformationFor some distance r and bearing angle θ, the (north, east) coordinates will be ...
(north, east) = (r·cos(θ), r·sin(θ))
ApplicationFor the trip at hand, the final coordinates of the plane are ...
a)Distance north = (400 km)cos(25°) +(700 km)cos(80°)
= 362.52 km +121.55 km = 484.07 km
B is about 484 km north of O.
b)Distance east = (400 km)sin(25°) +(700 km)sin(80°)
= 169.05 km +689.37 km = 858.41 km
B is about 858 km east of O.
__
Additional comment
Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...
(x, y) = (r·cos(θ), r·sin(θ))
You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.
Does 7*10 to fifth power equal 7*100,000?
Answers
Step by step
7x 10^5 = 700,000
7 x 100,000 = 700,000
This is a positive power of 10 so you move the decimal point 5 places to the right
7.
Becomes
700,000
And 7 x 100,000
Becomes
700,000
Find the a) down payment, and b) amount of the mortgage loan. 2. Alvira and Barry Gomez purchased a home priced at $280,000. They put down 40%.
Answers
The down payment is $112,000.
And, Amount of the mortgage loan is $168,000.
Here,
Alvira and Barry Gomez purchased a home priced at $280,000.
They put down 40%.
We have to find down payment.
And, Amount of the mortgage loan.
What is Down payment?
A sum of money that a buyer pays in the early stages of purchasing an expensive good or service is called down payment.
Now,
Alvira and Barry Gomez purchased a home priced at $280,000.
They put down 40%.
Hence, The down payment = $280,000 x 40%
= $280,000 x 40 / 100
= $112,000
And, Amount of the mortgage loan = Total amount - Down payment
= $280,000 - $112,000
= $168,000
Therefore, The down payment is $112,000.
And, Amount of the mortgage loan is $168,000.
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Question 5
A swimming pool has a length of 30 ft, a width of 12 ft, and a uniform depth of 8 ft. How many gallons of water does it hold?
(Hint: Find the volume in cubic ft and then use dimensional analysis to convert to gallons. 7.5 gal - 1 cubic ft.)
Round your answer to the nearest whole gallon, but do not include a unit of measure with your response.
Answers
1,718 gallons
Because 12-Feet by 30-Inches and able to hold up to 1,718 gallons of water!
How much cardboard will Jayden need to make the box?
OA 60 ft²
OB. 96 ft²
OC. 128 ft²
OD. 144 ft²
Answers
Jayden needs (C) 128 ft² cardboard to make a box.
What are parallelograms?A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. The congruence of opposite sides and angles is a direct result of the Euclidean parallel postulate, and neither condition can be proven without resorting to the Euclidean parallel postulate or one of its equivalent formulations.The net is made up of six parallelograms, each representing one of the box's faces.
Four rectangular faces with dimensions of 6 ft × 4 ftThe other two faces are square in shape, with side lengths of 4 feet.The area represented by the net can be used to estimate how much cardboard Jayden will need to make the box.
The calculations are as follows:
Rectangular faces: length × height = 6 ft × 4 ft = 24 ft²Square faces: side length² = (4 ft)² = 16 ft²So, our rectangles and two squares:
4 × 24 ft² + 2 × 16 ft² = 96 ft² + 32 ft² = 128 ft².Therefore, Jayden needs (C) 128 ft² cardboard to make a box.
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At a certain company, the average starting salary s for a new worker is $25,000. The actual salary has an absolute deviation of at most $1800. Write and solve an inequality to find the range of the starting salaries.
Answers
The range of the salary will be the closed interval [23,200, 26,800].
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
A new hire at one organization may expect to get an average beginning pay of $25,000 per year. The absolute divergence from the real compensation is no more than $1800.
Let 'x' represent the actual salary. Then the inequality is given as,
|x - 25,000| ≤ 1800
- 1,800 ≤ x - 25,000 ≤ 1,800
25,000 - 1,800 ≤ x ≤ 25,000 + 1,800
23,200 ≤ x ≤ 26,800
The range of the salary will be the closed interval [23,200, 26,800].
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5- b = 2t Solve for t or f I give extra points
Answers
Answer:
[tex]t = - \frac{1}{2} b + \frac{5}{2} [/tex]
what is the perimeter of a regular, triangular yield sign with aside length of 15 in
Answers
45 inches s the perimeter of a regular, triangular yield sign with aside length of 15 in
What is perimeter?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, so its perimeter is equal to the sum of those three lengths.
The perimeter of a square can be easily calculated if one side and all other sides are given as being the same length; for example, a square with sides measuring 5 inches long has a perimeter of 20 inches because 5 x 4 = 20. By multiplying the sum of the length and width by two, one can determine a rectangle's perimeter.
We will use the simple perimeter formula as yield sign is equilateral triangle
So, 15 × 3 = 45 inches
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PLEASE HELP!
The data show what an apartment resident paid per month for her electric bill during a calendar year.
$56, $72, $120, $120, $122, $124, $128, $135, $152, $168, $183, $200
Use the data to answer the questions.
What is 1.5 ∙ IQR?
A: 40
B: 60
C: 80
What is the lower boundary?
A: 60
B: 66
C: 120
What is the upper boundary?
A: 160
B: 220
C: 251.5
Which sentence describes the outliers?
A: There are no outliers.
B: The outlier is less than the lower boundary.
C: The outlier is greater than the upper boundary.
Answers
Using the median concept and the quartiles, we have that:
1.5 IQR is: B. 60.The lower boundary is: A. 60.The upper boundary is: B. 220.The sentence that describes the outliers is: B: The outlier is less than the lower boundary.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.Values that are more than 1.5 IQR from either quartile are considered outliers.In this problem, there are 12 elements, hence:
Q1 is the 0.25 x 12 = 3rd element.Q3 is the 0.75 x 12 = 9th element.Thus, Q1 = 120, Q3 = 160 and the IQR is:
IQR = 160 - 120 = 40.
1.5 IQR is: 1.5 x 40 = 60.
The boundaries are:
120 - 60 = 60. (lower).160 + 60 = 220(upper).There is a value less than 60 in the data set, hence the sentence that describes the outliers is: B: The outlier is less than the lower boundary.
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Answer:
Use the data to answer the questions.
What is 1.5 ∙ IQR? ✔ 60
What is the lower boundary? ✔ 60
What is the upper boundary? ✔ 220
Which sentence describes the outliers? ✔ The outlier is less than the lower boundary.
Step-by-step explanation:
edge 2023
4(xy)² – 2x + 5y for x = 6 and y
=2
Answers
Answer:
574
Step-by-step explanation:
4[12]²-12+10
4(144)-2
576-2
574
Hope this helps!
Can you please help with this
Answers
The fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
How to simplify the given fraction?Here we want to simplify the fraction 24/56. To do so, we need to find the greatest common factor between 24 and 56, to find that, we need to write both of these numbers as a product of their prime factors.
We will get:
24 = 2*2*2*3
56 = 2*2*2*7
We can identify the greatest common factor between parenthesis:
24 = (2*2*2)*3
56 = (2*2*2)*7
So the greatest common factor is 2*2*2 = 8, then we can divide both numerator and denominator by 8, we will get:
24/8 = 3
56/8 = 7
Then the fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
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3. Write the number: three hundred
seven thousand, fifty-nine and six
tenths
S
Answers
if angle 2=6x+8 and angle 4=4x+11 what is the value of angle 2?
Answers
Answer:
17
Step-by-step explanation:
Angle 2 and angle 4 are alternate exterior angles so they congruent angles which means they have same angle measurement.
To find the measure of angle 2 we first need to find the value of x.
And to do that we can write the following equation based on the information we have in hand:
6x + 8 = 4x + 11 transfer like terms to the same side of the equation
6x - 4x = 11 - 8 add/subtract like terms
2x = 3 divide both sides by 2
x = 1.5 now to find the measure of angle 2 replace x with 1.5
6×(1.5)+8 = 17