Answer:
P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
Step-by-step explanation:
Given:
f(x) = ln(x)
n = 4
c = 3
To find:
nth Taylor polynomial for the function, centered at c
Solution:
The Taylor series for f(x) = ln x centered at 3 is:
[tex]P_{n}(x) = f(c) + \frac{f'(c)}{1!}(x-c)+\frac{f''(c)}{2!}(x-c)^{2} +\frac{f'''(c)}{3!}(x-c)^{3}+...+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since c = 3 So,
[tex]P_{4}(x) = f(3) + \frac{f'(3)}{1!}(x-3)+\frac{f''(3)}{2!}(x-3)^{2} +\frac{f'''(3)}{3!}(x-3)^{3}+...+\frac{f^{n} (3)}{n!}(x-3)^{n}[/tex]
Now
f(3) = ln 3
f'(x) = 1/x ⇒ f'(3) = 1/3
f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9
f'''(x) = 2/x³ ⇒ f'''(3) = 2/3³ = 2/27
f[tex]^{(4)}[/tex] (x) = -6/x⁴ ⇒ f[tex]^{(4)}[/tex] (3) = -6/3⁴ = -6/81 = - 2/27
So Taylor polynomial for n=4 is:
P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
Been working for 30 minutes can’t wrap my head around this, need help fast!
Answer:
It's D.
Step-by-step explanation:
If you want me to explain it, I will. But it seems like you need the answer fast. So if you still don't understand it later, then I will try to explain it...but it'll take some time. :)
All you have to do is move all the points to the right 6 numbers because it says x+6. For example, A is (-5,-1). Move to the right 6 times, so (-5+6,-1) which is (1, -1). So the new point of A is (1, -1). Do the same with the others. Now that we got the new rectangle in the fourth quadrant, you want to move it counterclockwise around the origin, which is 0. Clockwise is like a clock, it goes around the middle going to the right. Counterclowise is the same, except it goes to the left around the middle of the clock. You can sort of apply that to this. Go counterclockwise around the middle, in this case being the origin, 0. Move the rectangle up to the first quadrant because counterclockwise is going around to the left. So, if the rectangle goes around to the left, then that means that it is now vertical...because it turns to the left making it straight if you go counterclockwise. Now the point A is on the bottom left because the rectangle got turned. If you turned it properly, then A should be at (1,1). Apply the same thing to the other points. D is the only one with point A being at the point (1,1), so that is correct. Check the other points anyway.
[tex]2(4z - 2) = 44[/tex]
can you help me
2(4z−2) = 44
Simplify both sides of the equation.
Distribute:
(2)(4z)+(2)(−2) = 44
8z + −4 = 44
8z − 4 = 44
Add 4 to both sides.
8z − 4 + 4 = 44 + 4
8z = 48
Divide both sides by 8
8z/8 48/8
z = 6
Answer:
z=6
Step-by-step explanation:
Categorical(qualitative) or quantitative. Indicate whether quantitative data are continuous or discrete.
1. Gender
2. Age
3. Grade Point Average
4. Number of Courses Currently Enrolled
5. Enrollment Status (Part-Time or Full-Time)
Answer:
1. Gender - qualitative
2. Age - Quantitative (Discrete)
3. Grade point Average - quantitative (Continuous )
4. Number of courses currently enrolled - quantitative (discreet)
5. Enrollment Status - qualitative
Step-by-step explanation:
Qualitative variables are those which are non-numeric, usually made up of strings or words. The quantitative variables are numeric, usually composed of digits and numbers.
Discreet variables have a finite or limited number of values which are countable as opposed to continuous variables with a non-finite range and hence, uncountable.
Gender is a qualitative variable as it is composed of non-nemeric labels which could be either Male or Female.
Age - is numeric and hence quantitative, since age is usually expressed in years, hence it is discreet.
Grade point Average is a quantitative and continuous variable due to its numeric nature and the fact that it can take up an infinite number of possible values including decimal values.
Number of courses enrolled is numeric can take a finite number of values, hence, it is discreet.
Enrollment status is qualitative as it is split into :
Part time or full time.
What is negative 500 minus 150 I think it’s -650 I’m helping my son
The question is on the picture.
Jess borrows 250 from the bank. The band chargEs 11% simple interest over 2 years.
How much will Jess owe the bank at the end of 2 years?
Answer:
$305
Step-by-step explanation:
You have to use the following formula to calculate the accrued amount:
A=P(1 + rt), where:
A= accrued amount
P= principal amount= $250
r= rate of interest= 11%
t= time period= 2 years
Now, you have to replace the values in the formula:
A=250*(1+0.11*2)
A=250*(1+0.22)
A=250*1.22
A=305
According to this, at the end of 2 years, Jess owes the bank $305.
what’s the probability of drawing a jack on the first draw and a 3 on the second draw
Answer:
jgvi hhvh ihvyv
Step-by-step explanation:
Equation:
8-9 = 3(4-5a)
Solution:
16-a =6(4-5a) (step 1)
16-a=24-5a (step 2)
16+ 40 = 24 (step 3)
4a=8 (step 4)
a=2
(step 5)
which statement describes the error in the solution?
Answer:
the answer is 988 .........
An Olympic swimming pool is 50 m long, 25 m wide, and 1.5 m deep. How many Olympic pools would be filled by the dollar bills spent by the U.S. federal government in 2011
Answer:
Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.
Step-by-step explanation:
The dimensions of a dollar bill are 15.5956 cm by 6.6294 cm by 0.010922 cm. The U.S. federal government spent $3.8 trillion in fiscal year 2011.
An Olympic swimming pool is 50 m long, 25 m wide, and 1.5 m deep. How many Olympic pools would be filled by the dollar bills spent by the U.S. federal government in 2011
From above,
The volume for the dimension of the dollar bill = 15.5956 cm × 6.6294 cm × 0.010922 cm
The volume for the dimension of the dollar bill = 1.12922 cm³
The volume for the dimension of the dollar bill = 1.12922 × 10⁻⁶ m³
The volume of the pool = 50 m × 25 m × 1.5 m
The volume of the pool = 1875 m³
Number of dollars bills that can be fitted in pool = volume of the pool/volume of the dimension of dollar bills
Number of dollars bills that can be fitted in Olympic pool =1875 m³ / 1.12922 × 10⁻⁶ m³
Number of dollars bills that can be fitted in Olympic pool = 1,660,438,180
Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.
Please help asap thanks so much
Complementary and adjacent.
The two angles are complementary because they add up to 90°. It's given that line JL is perpendicular to line MN, and perpendicular means they form a 90° angle where they intersect.
The two angles are adjacent because they are next to each other.
Find the distance between the pair of points.(-6, -20) and (-17, -22)
Answer:
Use the distance formula to determine the distance between two points.
5 √ 5
2. Sheldon was doing a science experiment about temperature. He first measured the
temperature of some water and found it was 17°C. Then he put the water in the freezer and
recorded the temperature two hours later. It had fallen to -11°C. What was the change in
temperature in two hours?
Answer:
Temperature dropped by 28°C in two hours
Step-by-step explanation:
Initial measurement:
t = 17°CMeasurement 2 hours later:
t = - 11°CThe difference:
-11°C - 17°C = -28°CTemperature dropped by 28°C in two hours
The graph below shows the number of pages that Victor has left to read in his book at the end of the day over seven days. Pages Left to Read in Victor’s Book On a coordinate plane, the x-axis is labeled Day and the y-axis is labeled Pages left. On day 0 there were 220 pages; Day 1, 180; Day 2, 170; Day 3, 140; Day 4, 140; Day 5, 100; Day 6, 60; Day 7, 40. Which statement is supported by the graph? Victor read 0 pages on day 4. Victor read 170 pages on day 2. Victor read the same number of pages on day 1 and on day 2. Victor read the same number of pages on day 3 and on day 4.
Answer:
C
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I had the same question and got it right
What’s the measure for angle C?
Answer:
152°
Step-by-step explanation:
Angles B and A of the isosceles triangle have the same measures, so we have ...
∠B = ∠A
(x -14)° = (x/2)°
2x -28 = x . . . . . . divide by °, multiply by 2
x = 28 . . . . . . . . . .add 28-x to both sides
Then the base angles, A and B, both have measure (x/2)° = 14°.
The third angle, C, will bring the total to 180°.
∠A + ∠B + ∠C = 180°
∠C = 180° - 2(14°)
∠C = 152°
Which of the numbers below is less than zero? Select all that apply.
A) 1.2
B) 7/2
C)-3.5
D)-0.75
E)-1/3
C D E
Step-by-step explanation:
All the numbers above (C D E) are negative, making them less than 0.
Answer:
C, D, and E. They are all negative, which means they are less than zero.
1.2 and 7/2 are more than one. 7/2 simplifies to 3 1/2.
12b + 9 = 12b + 11 what’s the answer
Answer: b∈∅
Step-by-step explanation:
Answer:
no solutions
Step-by-step explanation:
12b + 9 = 12b + 11
Subtract 12b from each side
12b-12b + 9 = 12b-12b + 11
9 = 11
This is never true, so there are no solutions
Write the following sentence using mathematical symbols. Twice the difference of x and 7 is greater than the reciprocal of 10.
Answer:
2(x-7) > 1/10
Step-by-step explanation:
The statement says, twice the difference of x and 7. This implies that it wants the difference of x and 7, x - 7, and it wants twice that difference so:
2 ( x - 7 )
The statement continues that this twice the difference of x and 7 is greater than the reciprocal of 10. The reciprocal of 10 is 0.1 or 1/10.
Hence, the statement should be written as such:
2 ( x - 7 ) > 1/10 OR 2 ( x - 7 ) > 0.1
Cheers.
Jada is evaluating 8 × 3 × 4. She doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first. Which property is Jada using? PLEASE HELP!!
Answer: Associative property
Step-by-step explanation:
From the question, we are informed that Jada is evaluating 8 × 3 × 4 and that she doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first.
The property that Jada is using is the Associative property. This has to do with regrouping of the numbers and then multiplying the numbers in different groups.
n/12 = 300 n = pls help again
Answer: 3600
Step-by-step explanation: N= 3,600
3,600/12= 300
Answer:
n=0, or n=3600
Step-by-step explanation:
If your question is n/12 = 300n, n=0
Otherwise n/12=300, n=3600
Multiply both sides by 12 to isolate variable
what is the median of 3 3 4 5 5 5 6 6 6 7 8
Answer:
5
Step-by-step explanation:
The median is the middle number of the list when put in order from smallest to largest
3 3 4 5 5 5 6 6 6 7 8
There are 11 numbers so the middle number is the 6th ( 5 on the left and 5 on the right
3 3 4 5 5 5 6 6 6 7 8
Which set is closed under subtraction?
the set of whole numbers
the set of natural numbers
the set of rational numbers
the set of irrational numbers
Answer:
Set of rational numbers
Step-by-step explanation:
Answer:
the set of rational numbers
Step-by-step explanation:
Edge 2021
In the U.S., 79,816,000 people age 25 and over have completed at least a bachelor’s degree. This is 36% of the population. How many people are age 25 and over in the U.S.?
Answer:
79,816,000 people
Step-by-step explanation:
Given:
People Age 25 above = 79,816,000 people
Required
Determine the population of people over 25
The first statement of the question reads:
"In the U.S., [tex]79,816,000[/tex] people age 25 and over......"
This statement answers your question;
Hence;
Required Population = 79,816,000 people
what is 57/5as a decimal
Answer:
11.4
Step-by-step explanation:
57/5 as a mixed number is 11 2/5.
2/5 of a number is also known as 4/10 or 0.4, so add that to 11 to get 11.4.
Answer:
11.4
Step-by-step explanation:
57/5 = 11.4
Graphing form equation for y=x^3
Answer:
Step-by-step explanation:
Solve for x using
cross multiplication.
Answer:
Step-by-step explanation:
5X * 4-->20X
8(2X+3)--> 16X+24
20X=16X+24
4X=24
x=6
Answer:
x = 6
Step-by-step explanation:
(5x) ×4=8× (2x+3)
20x = 16x + 24
20x- 16x = 24
4x = 24
divide both sides by 4 to get the value of x
4x/4 = 24/ 4
x = 6
g find the 2 components of vector b = 2i + j - 3k, one parallel to a = 3i - j and another one perpendicular to a
Answer:
The components of [tex]\vec{b}[/tex] parallel and perpendicular to [tex]\vec {a}[/tex] are [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex] and [tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex], respectively.
Step-by-step explanation:
Let be [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec a = 3\,i-j[/tex], the component of [tex]\vec b[/tex] parallel to [tex]\vec a[/tex] is calculated by the following expression:
[tex]\vec b_{\parallel} = (\vec b \bullet \hat{a}) \cdot \hat{a}[/tex]
Where [tex]\hat{a}[/tex] is the unit vector of [tex]\vec a[/tex], dimensionless and [tex]\bullet[/tex] is the operator of scalar product.
The unit vector of [tex]\vec a[/tex] is:
[tex]\hat{a} = \frac{\vec {a}}{\|\vec a\|}[/tex]
Where [tex]\|\vec {a}\|[/tex] is the norm of [tex]\vec a[/tex], whose value is determined by Pythagorean Theorem.
The component of [tex]\vec{b}[/tex] parallel to [tex]\vec {a}[/tex] is:
[tex]\|\vec {a}\| = \sqrt{3^{2}+(-1)^{2}+0^{2}}[/tex]
[tex]\|\vec {a}\| = \sqrt{10}[/tex]
[tex]\hat{a} = \frac{1}{\sqrt{10}} \cdot (3\,i-j)[/tex]
[tex]\hat{a} = \frac{3}{\sqrt{10}}\,i -\frac{1}{\sqrt{10}} \,j[/tex]
[tex]\vec{b}\bullet \hat{a} = (2)\cdot \left(\frac{3}{\sqrt{10}} \right)+(1)\cdot \left(-\frac{1}{\sqrt{10}} \right)+(-3)\cdot \left(0\right)[/tex]
[tex]\vec b \bullet \hat{a} = \frac{5}{\sqrt{10}}[/tex]
[tex]\vec b_{\parallel} = \frac{5}{\sqrt{10}}\cdot \left(\frac{3}{\sqrt{10}}\,i-\frac{1}{\sqrt{10}}\,j \right)[/tex]
[tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex]
Now, the component of [tex]\vec {b}[/tex] perpendicular to [tex]\vec{a}[/tex] is found by vector subtraction:
[tex]\vec{b}_{\perp} = \vec {b}-\vec {b}_{\parallel}[/tex]
If [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex], then:
[tex]\vec{b}_{\perp} = (2\,i+j-3\,k)-\left(\frac{3}{2}\,i-\frac{1}{2}\,j \right)[/tex]
[tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex]
Select the correct answer. A bottlenose dolphin is 10 feet below sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation, y, after x seconds? A. y = 9x − 10 B. y = -9x − 10 C. y = 9x + 10 D. y = -9x + 10
Answer: y = -9x − 10
Step-by-step explanation: y represents the elevation of the bottlenose dolphin. The dolphin begins at 10 feet below sea level or -10. It then becomes to dive, go deeper under the water at a rate of 9 feet per second, or -9.
The equation y = -9x - 10 will equal the amount of feet below sea level that the dolphin is at. Below sea level will always be indicated with a negative number.
If you wish to have $60,000 in 8 years, how much do you need to deposit in the bank today if the account pays 9% using present value and future value.
Answer:
Amount to deposit= $26799.0
Step-by-step explanation:
Amount A = $60,000
Years t = 8 years,
Rate R = 9% .
A= p(1+r/n)^(nt)
60000= p(1+0.09/9)^(9*9)
60000= p(1+0.01)^(81)
60000= p(1.01)^81
60000= p(2.23888)
60000/2.23888= p
26799.1138= p
P= $26799.0
Amount to deposit= $26799.0
To be able to have $60,000 after 8 years at a rate of 9% per annum, the amount to deposit today is $30,111.98
You can solve this using the Future Value formula which is:
Future value = Present value x ( 1 + rate)^ number of years
You have everything except the present value so solve for it:
60,000 = PV x ( 1 + 9%)⁸
60,000 = PV x 1.9925626416901921
PV = 60,000 / 1.9925626416901921
PV = $30,111.98
In conclusion, you should deposit $30,111.98 today.
Find out more about this at https://brainly.com/question/14715827.
Simplify the equation 9z-3z=48
Answer: z=8
Step-by-step explanation:
9z-3z=48
6z=48 ⇔ combine like terms
z=8
Hope this helps
Answer:
z = 8
Step-by-step explanation:
9z - 3z = 48
6z = 46
z = 8
Nidhi is thinking of a number n, and she wants her sister to guess the number. Her first clue is that eight less than three times her number is between one and nineteen. Write a compound inequality that shows the range of numbers that Nidhi might be thinking of
Answer:
The range of numbers that Nidhi might be thinking of is between 3 and 9.
Step-by-step explanation:
We are given that Nidhi is thinking of a number n, and she wants her sister to guess the number.
Her first clue is that eight less than three times her number is between one and nineteen.
Let the number Nidhi is thinking be 'n'.
So, eight less than three times her number means that;
[tex](3\times \text{n}) - 8 = 3\text{n}-8[/tex]
Now, according to the question; the above equation is between one and nineteen, so;
[tex]1< 3\text{n}-8 < 19[/tex]
Adding 8 to the whole expression;
[tex]1+8< 3\text{n}-8 +8< 19+8[/tex]
[tex]9< 3\text{n}< 27[/tex]
Dividing the whole expression by 3;
[tex]\frac{9}{3} < \frac{3\text{n}}{3} < \frac{27}{3}[/tex]
[tex]3< \text{n}< 9[/tex]
Hence, the range of numbers that Nidhi might be thinking of is between 3 and 9.